Home Physical Sciences Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
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Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method

  • Showkat Ahmad Lone , F. M. Allehiany , Sadia Anwar , Sana Shahab , Anwar Saeed EMAIL logo and Sayed M. Eldin EMAIL logo
Published/Copyright: October 18, 2023
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 12 Issue 1

Abstract

This work investigates the ternary hybrid nanofluid flow over an extending curved surface. The surface is impermeable and convective with hot working fluid water. Additionally, TiO 2 , CoFe 2 O 4 , and MgO nanoparticles are suspended with water to form a tri-hybrid nanofluid. The modeled equations are presented in the partial differential equation form and are then converted to ordinary differential equations with appropriate similarity variables. The semi-analytical solution is determined by homotopy analysis method. The impacts of magnetic field, Joule heating, chemical reaction, Brownian motion, and thermophoresis on flow profiles, Nusselt number, and Sherwood number are determined using tables and figures. The findings of this study demonstrated that as the magnetic parameter upsurges, the velocity distribution shrinkages, while the temperature distribution escalates. The greater curvature factor boots the velocity, thermal, and volumetric fraction distribution. The thermal and volumetric fraction distributions are the increasing functions of thermophoresis factor. The higher magnetic factor, Eckert number, and thermal Biot number increase the Nusselt number, while they reduce the higher Brownian and thermophoretic factors. The higher thermophoresis and Brownian motion factors heighten the Sherwood number. Furthermore, it has been noted that using nanofluid (TiO2-water) and hybrid nanoliquid (TiO2-CoFe2O4/water), the transfer of energy rate increases by up to 17.31 and 31.72% as the nanoparticle parameter increases from 0.01 to 0.04, respectively. However, the energy transference rate in case of ternary hybrid nanoliquid (TiO2-MgO-CoFe2O4/water) is 47.972%.

Keywords: nanofluid; hybrid nanofluid; ternary hybrid nanofluid; convective heat transfer; Joule heating; chemical reaction; curved surface

Nomenclature

( r , s )

curvilinear coordinates ( m )

TiO2

titanium dioxide

b

positive fixed number

T f

surface temperature ( K )

C p

specific heat capacity ( J K − 1 kg − 1 )

σ

electrical conductivity ( S m − 1 )

Rc

curvature factor

Ec

Eckert number

γ

chemical reaction factor

Nb

Brownian motion factor

f ′ ( η )

velocity field

MgO

magnesium oxide

u w = b s

stretching velocity ( m s − 1 )

CoFe2O4

cobalt ferrite

ρ

density ( kg m − 3 )

C w

surface volumetric fraction distribution ( mol m − 3 )

k

thermal diffusivity ( W K − 1 m − 1 )

M

magnetic factor

Bi

thermal Biot number

Q

heat source parameter

Sc

Schmidt number

Nt

thermophoresis factor

1 Introduction

Titanium dioxide (TiO2) is an inorganic substance that is used extensively as a white pigment. Compared with many other inorganic pigments, TiO2 has the advantages such as high stability, being non-toxic, and low cost. TiO2 has three polymorphs: anatase, rutile, and brookite, but only anatase and rutile crystal forms are used as pigments. Both anatase and rutile crystals have very high refractive indices, and their particles can scatter visible light almost completely. In the early application of TiO2 as pigment, it was found that paint faded more rapidly than others when painted films were exposed to the Sun and ultraviolet light. Coating with inorganic compounds such as alumina or silica suppressed the catalytic activity on the surface and improved the weather resistance. Hence, titanium dioxide is used in a wide range of applications such as white pigment.

Modifications of metal oxide nanoparticles with metallic element are the ideal choice for heterogeneous photocatalysis to eliminate different kinds of contamination from wastewater. Among the metal and metal oxide nanoparticles, MgO nanoparticles played a significant role in antimicrobial activity, dye degradation, and phenol degradation activity. Ag nanoparticles are, without a doubt, the most widely used inorganic nanoparticles with huge applications. MgO nanoparticles acquired additional consideration due to their vast applications in medical, catalysis, as absorbents, etc.

The reason for cobalt spinel ferrites (CoFe2O4) gaining so much attention is because of their excellent chemical and good mechanical stabilities at room temperature, their moderate saturation magnetization, high coercivity, and their strong anisotropy. The chemical and mechanical stabilities of cobalt spinel ferrites are very different from their bulk counterparts. Due to all of these properties, cobalt ferrites have been broadly used in biotechnology, catalysis, biomedical, magnetic drug delivery, solar cells, magnetic cards, recording devices, and sensors. CoFe2O4 nanoparticles should have high magnetization values and narrow-size distribution for catalysis applications.

Nanofluid flow refers to the movement of a fluid that contains suspended tiny particles with diameters typically fluctuating from 1 to 100 nm. The flow behavior of nanofluids is different from that of pure fluids, as the nanoparticles can affect the viscosity, thermal flow, and flow characteristics of the fluid. Nanofluids have been extensively used recently due to their potential applications in areas such as energy storage, electronic cooling, and biomedical engineering. The idea of such fluids was floated first by Choi and Eastman [1] to augment the thermal behavior of normal fluids. The flow behavior of nanofluids is influenced by numerous factors, comprising the size and shape of nanoparticles, the volumetric fraction distribution and type of the nanoparticles, the flow rate and temperature of the fluid, and the geometry of the system. Mourad et al. [2] executed a numerical analysis of the entropy production and magnetohydrodynamics (MHD) natural convection of a Cu-water nanofluid that was enclosed within a wavy cylinder and heated Koch snowflake. Acharya et al. [3] deliberated on nanofluid flow on a gyratory disk using the influences of nanolayer and diameter of nanoparticles and determined that temperature has increased for progression in nanolayer ratio as well as thermal radiation but has declined with upsurge in diameter of nanoparticles. Shahid et al. [4] conducted numerical experiment for bioconvective nanofluid flow on a porous sheet. Bhatti et al. [5] scrutinized MHD Williamson nanofluid flow through a spinning circular sheet with influence of microorganisms and proved that the liquid velocity has weakened with progression in nanoparticles’ volumetric fraction distribution and magnetic factor, while, on the other side, the thermal distribution has augmented. Wijayanta [6,7] reported on the thermal evaluation of natural convection in an opening using the numerical approach to estimate the laminar natural convective flow along with heat exchange in triangle-shaped cavities. Makarim et al. [8] investigated numerically the Marangoni convection that occurs when steam is absorbed into a water-soluble lithium bromide solution. Kumar et al. [9] investigated theoretically the mathematical model of nanoliquid flow past a sheet with the impact of magnetic factor and chemically reactive effects.

Hybrid nanofluid flow is fluid flow that contains a mixture of two or more dissimilar nature of nanoparticles, such as metal oxide and carbon-based nanoparticles. The combination of nanoparticles can lead to synergistic effects, where the resulting nanofluid has enhanced thermal and/or mechanical properties compared to a single-component nanofluid. The flow behavior of hybrid nanofluids can be more complex than that of single-component nanofluids, as the different types of nanoparticles can interact with each other and with the base fluid in various ways. The properties of hybrid nanofluids can be influenced by factors such as the nature of the particles, particle–fluid interactions, and the flow conditions. The aim of investigating hybrid nanofluid is to gain a better idea about the flow behavior and properties of hybrid nanofluids, as well as to develop methods for optimizing their performance in various applications such as thermal management in electronic devices and energy storage systems. Zhang et al. [10] discussed hybrid nanofluid flow on a surface using nickel and tantalum nanoparticles using the effects of magnetic field and have concluded that flow has propagated faster in case of tantalum nanoparticles and Darcy number, while it has declined with progression in magnetic effects. Khan et al. [11] inspected bioconvective nanofluid flow with impact of binary chemical reactions, viscous dissipation, and activated energy on a heated needle. Chu et al. [12] examined MHD hybrid nanofluid flow through a channel using the impact of nanoparticles’ shape. Ojjela [13] discussed numerically the thermal transportation for silica–alumina hybrid nanofluid flow using modeling simulation. Gumber et al. [14] discussed the thermal flow for hybrid nanofluid flow on a surface using impacts of suction as well as injection and thermal radiations. Slimani et al. [15] discussed the MHD hybrid nanofluid’s flow with heat distribution in a trimmed cone with open domains that were stimulated by a magnetic flux. The study reveals that the rate of Nusselt number enhances with an upshot of magnetic flux.

Ternary hybrid nanofluid flow states the movement of a fluid that contains three different types of nanoparticles suspended in it. As discussed earlier, nanofluids are made by dispersing tiny particles, typically less than 100 nm in size, into a pure fluid. These particles are often metallic, ceramic, or carbon-based, and they can considerably alter the thermal and rheological properties of the fluid. A ternary hybrid nanofluid flow would contain three different types of nanoparticles, which could potentially lead to unique properties such as improved thermal conductivity or enhanced heat transfer characteristics. Arif et al. [16] analyzed the heat transmission of fractal model for ternary hybrid nanofluid flow in a conduit using different shapes of nanoparticles. Shahzad et al. [17] inspected the influences of pressure variation on ternary hybrid nanofluid flow through a circular conduit. When three unlike forms of nanoparticles are dispersed into a base fluid, they can considerably alter the heat and rheological characteristics of liquid, leading to unique behavior. Sudharani et al. [18] assessed computationally the ternary hybrid nanofluid flow affected by linearly radiated effects and slip flow and have deduced that the thermal flow performance has amplified more in case of ternary hybrid nanoparticles in comparison with other two fluids. The study of ternary hybrid nanofluid flow involves both computational modeling and experimental studies to better understand the behavior and potential applications of these complex fluids. Guedri et al. [19] inspected the thermally radiative flow of ternary hybrid nanofluid on a nonlinearly elongating surface using the Darcy–Forchheimer model.

Convective heat transfer refers to the transfer of heat through fluid and solid surface, typically a gas or a liquid that is in motion. The heat is transferred due to the movement of the fluid, which carries thermal energy away from the surface and transports it to another location. Convective heat transfer is an important mechanism in different phenomena, like cooling of electronic devices, the transfer of heat in a car’s radiator, and the circulation of air in a room. The analysis and prediction of convective heat transfer is an important area of study in many fields, including engineering, physics, and materials science. Shevchuk [20] inspected convective heat transportation for geometry of disk and cone by using the advanced asymptotic expansion method and turning effects of the cone on flow model. Olayemi et al. [21] inspected the parametric convective thermal transportation for fluid flow on a cylinder placed in a square conduit and deduced that the rate of heat transmission has been observed to rise with increasing aspect ratio and Rayleigh number. Manna et al. [22] discussed MHD fluid flow and production of entropy on a circular surface subject to the impact of convective thermal transportation. Wang and Wang [23] simulated computationally the convective heat transportation through a packed bed and have proved that the fluid flow and thermal transportation are affected by the porosity factor. Shi et al. [24] discussed the convective thermal transportation properties for fluid flow on a cylinder through a confined space.

Joule heating is a phenomenon in which electrical energy is changed to thermal energy. This heat is generated as a consequence of the collisions among the electrons and the atoms or molecules in the material. Abbas et al. [25] inspected the Darcy–Forchheimer phenomenon for fluid flow on a porous sheet subject to the impacts of Joule heating. Naseem et al. [26] deliberated the effects of Joule heating on MHD fluid flow using variable temperature and deduced that thermal transportation has amplified with progression in the Eckert number and weakened with upsurge in the Prandtl number. Rahseed et al. [27] treated analytically the MHD fluid flow with impact of Joule heating, viscous variable forces, and chemically reactive effects and have deduced that velocity distribution weakened, while thermal panels have expanded with growth in magnetic factor. Mahdy et al. [28] inspected numerically the effects of convective thermal conditions and Joule heating on a stretched sheet and have solved their modeled equations effectively using HPM. Waqas et al. [29] discussed bioconvective MHD fluid flow on a radiating stretchable sheet using viscously dissipative and Joule heating effects. Mahanthesh et al. [30] examined the production of entropy radiative thermal transportation for fluid flow in a channel subject to Joule heating and nonlinear mixed convection effects. Gangadhar et al. [31] deliberated on MHD bioconvective fluid flow with influences of microorganisms and Joule heating.

Curved surfaces are used in many fields, including engineering, architecture, art, and design. They can provide strength and stability to structures, as well as aesthetic applications. In addition, curved surfaces can be used to optimize airflow, improve acoustics, and reduce drag in vehicles and aircrafts. There are many different types of curved surfaces, each with their own properties and applications. Examples include spheres, cylinders, cones, tori (donut-shaped surfaces), and more complex shapes such as hyperboloids and ellipsoids. Curved surfaces are common in everyday life and can be found in a variety of objects, including the human body, cars, airplanes, and buildings. They can be used for both aesthetic and functional purposes. For example, the curved surface of a car’s body can improve its aerodynamics and reduce drag, while the curved surface of a building can improve its structural stability and provide an interesting architectural design. Mishra and Upreti [32] conducted a comparative analysis for two different types of hybrid nanoparticles on a curved sheet using the Buongiorno model and have proved that mass transportation has augmented with progression in thermophoretic and chemically reactive factors. Maity and Kundu [33] examined chemically reactive and magnetically driven flow nanofluid on a curved surface with effects of radiation and have noted that growth in mass and temperature and Biot numbers have supported, respectively, the transportation of volumetric fraction distribution and temperature. Khan et al. [34] investigated the gold nanoparticle carrier for blood flow on a curved sheet using thermal radiation, suction, and MHD effects. Sun et al. [35] investigated experimentally the control flow on a curved surface of jet at Mach 5 hypersonic flow of fluid. Fuzhang et al. [36] discussed the time-based nanofluid flow on an exponentially elongating curved surface using chemically reactive effects.

Keeping in mind the aforementioned literature, the authors decided to present the homotopic solution of the ternary hybrid nanofluid flow on an extending curved surface. The curved surface is considered to be impermeable and convectively heat with a hot working fluid. Three different types of nanoparticles ( TiO 2 , CoFe 2 O 4 , and MgO ) are mixed with water (base fluid) to form ternary nanofluid. The purpose of this investigation is to answer the following research questions:

  • What are the impacts of the embedded factors on velocity, temperature, and volumetric fraction distribution profiles of the ternary hybrid nanofluid flow?

  • How were the flow profiles (i.e., velocity, temperature, and volumetric fraction distribution profiles) if we increase the radius of curvature parameter of the curved surface?

  • How do the skin friction, local Nusselt number, and Sherwood number behave for the increasing embedded factors?

Thus to answer these questions, we have presented this study in the following sections. Section 2 depicts the leading equations. Similarity variables are used for the transformation of partial differential equations into ordinary differential equations (ODEs). The application of the homotopy analysis method (HAM) technique for solving transformed ODEs is discussed in Section 3. The convergence of the HAM method is presented in Section 4. The results obtained using HAM, along with figures and a table, are showcased in Section 5. Finally, the conclusive outcomes are summarized in Section 6.

2 Problem statement

We have assumed the ternary hybrid nanofluid flow encompassing TiO 2 , CoFe 2 O 4 , and MgO nanoparticles over a curved sheet. The curved surface has curvilinear coordinates ( r , s ). The direction of the flow is denoted by s , while r represents the direction perpendicular to the flow. The stretching velocity of sheet is represented by u w = b s , where b is the positive fixed number. The magnetic field B 0 is used along r -direction. For the convectively heat surface with a hot fluid and temperature T f such that T f > T w , where T w is the surface temperature and T ∞ is its ambient value, the corresponding values for volumetric fraction distribution are C w and C ∞ . Figure 1 shows the geometrical explanation of problem. Additionally, the following suppositions have made as:

  1. The flow is affected by magnetic, Joule heating, and chemical reaction effects.

  2. The surface is assumed to be impermeable.

  3. The temperature and volumetric fraction distribution equations account for the effects of Brownian motion and thermophoresis.

Figure 1 Curved surface representation.
Figure 1

Curved surface representation.

Based on the aforementioned assumptions, the model equations can be expressed as follows [37,38,39]:

(1) ∂ ( ( r + R ) u r ) ∂ r + R ∂ u s ∂ s = 0 ,

(2) u s 2 r + R = 1 ρ T H ∂ p ∂ r ,

(3) u r ∂ u s ∂ r + R r + R u s ∂ u s ∂ s + u s u r r + R = − 1 ρ T H R r + R ∂ p ∂ s + μ T H ρ T H ∂ 2 u s ∂ r 2 + 1 r + R ∂ u s ∂ r − u s ( r + R ) 2 − σ T H B 0 2 ρ T H u s ,

(4) u r ∂ T ∂ r + R r + R u s ∂ T ∂ s = k T H ( ρ C p ) T H ∂ 2 T ∂ r 2 + 1 r + R ∂ T ∂ r + σ T H ( ρ C p ) T H B 0 2 u s 2 + Q 0 ( ρ C p ) T H ( T − T ∞ ) + ( ρ C p ) p ( ρ C p ) T H D B ∂ C ∂ r ∂ T ∂ r + D T T ∞ ∂ T ∂ r 2 ,

(5) u r ∂ C ∂ r + R r + R u s ∂ C ∂ s = D B ∂ 2 C ∂ r 2 + 1 r + R ∂ C ∂ r + D T T ∞ ∂ 2 T ∂ r 2 + 1 r + R ∂ T ∂ r − K r ( C − C ∞ ) .

The constraints at boundaries are as follows [40,41]:

(6) u s = u w = b s , u r = 0 , − k T H ∂ T ∂ r = h f ( T f − T ) , C = C w at r = 0 u s → 0 , ∂ u s ∂ r → 0 , T → T ∞ , C → C ∞ as r → ∞ .

The thermophysical properties of the ternary hybrid nanofluids are characterized as follows [19,42,43]:

(7) μ TH μ f = 1 ( 1 − χ 1 ) 2.5 ( 1 − χ 2 ) 2.5 ( 1 − χ 3 ) 2.5 , ρ TH ρ f = ( 1 − χ 1 ) ( 1 − χ 2 ) ( 1 − χ 3 ) + χ 3 ρ S 3 ρ f + χ 2 ρ S 2 ρ f + χ 1 ρ S 1 ρ f ρ f , ( ρ C p ) TH ( ρ C p ) f = ( 1 − χ 1 ) ( 1 − χ 2 ) ( 1 − χ 3 ) + χ 3 ( ρ C p ) S 3 ( ρ C p ) f + χ 2 ( ρ C p ) S 2 ( ρ C p ) f + χ 1 ( ρ C p ) S 1 ( ρ C p ) f ( ρ C p ) f , k NF k f = k S 1 + 2 k f − 2 χ 1 ( k f − k S 1 ) k S 1 + 2 k f + χ 1 ( k f − k S 1 ) , k HF k NF = k S 2 + 2 k f − 2 χ 2 ( k f − k S 2 ) k S 2 + 2 k f + χ 2 ( k f − k S 2 ) , k TH k HF = k S 3 + 2 k f − 2 χ 3 ( k f − k S 3 ) k S 3 + 2 k f + χ 3 ( k f − k S 3 ) σ NF σ f = σ S 1 + 2 σ f − 2 χ 1 ( σ f − σ S 1 ) σ S 1 + 2 σ f + χ 1 ( σ f − σ S 1 ) , σ HF σ NF = σ S 2 + 2 σ f − 2 χ 2 ( σ f − σ S 2 ) σ S 2 + 2 σ f + χ 2 ( σ f − σ S 2 ) , σ TH σ HF = σ S 3 + 2 σ f − 2 χ 3 ( σ f − σ S 3 ) σ S 3 + 2 σ f + χ 3 ( σ f − σ S 3 )

In the aforementioned properties, χ 1 , χ 2 , and χ 3 represent the TiO 2 , CoFe 2 O 4 , and MgO nanoparticle volume fractions, S 1 denotes the TiO 2 nanoparticle, S 2 represents the CoFe 2 O 4 nanoparticle, and S 3 denotes the MgO nanoparticle. The thermophysical characteristics of nanoparticles and water are presented in Table 1.

Table 1

Experimental values of H 2 O and nanoparticles [44,45]

Properties ρ C p k σ
H 2 O 997.1 4,179 0.613 0.05
TiO 2 4,250 686.2 8.9538 2.38 × 106
CoFe 2 O 4 4,907 700 3.7 5.51 × 109
MgO 45 955 45 1.42 × 10-3

To transform the aforementioned equations, the similarity variables are defined as follows [40,46,47,48]:

(8) η = r b ν f , u s = b s f ′ ( η ) , u r = − R r + R b ν f f ( η ) , p = ρ f ( b s ) 2 P ( η ) , θ ( η ) = T − T ∞ T f − T ∞ , φ ( η ) = C − C ∞ C f − C ∞ .

Using the aforementioned similarity variables, equation (1) becomes apparent, and equation (2) can be simplified as follows:

(9) ρ f ρ T H P ′ ( η ) = 1 η + R c f ′ 2 ( η ) .

Eq. (3) can be reduced as:

(10) ρ f ρ T H 2 Rc η + Rc P ( η ) = μ T H / μ f ρ T H / ρ f f ‴ ( η ) + 1 η + Rc f ″ ( η ) − 1 ( η + Rc ) 2 f ′ ( η ) − Rc η + Rc f ′ 2 ( η ) − σ T H / σ f ρ T H / ρ f M f ′ ( η ) + Rc η + Rc f ″ ( η ) f ( η ) + Rc ( η + Rc ) 2 f ′ ( η ) f ( η ) .

After differentiating equation (10) with respect to η and subsequently substituting it into equation (9), we obtain the following:

(11) μ T H / μ f ρ T H / ρ f f i v ( η ) + 2 ( η + Rc ) f ‴ ( η ) − 1 ( η + Rc ) 2 f ″ ( η ) + 1 ( η + Rc ) 3 f ′ ( η ) − σ T H / σ f ρ T H / ρ f M f ″ ( η ) + 1 ( η + Rc ) f ′ ( η ) + Rc ( η + Rc ) [ f ‴ ( η ) f ( η ) − f ″ ( η ) f ′ ( η ) ] + Rc ( η + Rc ) 2 [ f ″ ( η ) f ( η ) − f ′ 2 ( η ) ] − Rc ( η + Rc ) 3 f ′ ( η ) f ( η ) = 0 .

Likewise, the remaining equations are transformed as:

(12) 1 Pr k T H / k f ( ρ C p ) T H / ( ρ C p ) f θ ″ ( η ) + 1 ( η + Rc ) θ ′ ( ξ ) + Rc ( η + Rc ) θ ′ ( η ) f ( η ) + Nt θ ′ 2 ( η ) + Nb φ ′ ( η ) θ ′ ( η ) + σ T H / σ f ( ρ C p ) T H / ( ρ C p ) f M Ec f ′ 2 ( η ) + 1 ( ρ C p ) T H / ( ρ C p ) f Q θ ( η ) = 0 .

(13) ϕ ″ ( η ) + 1 ( η + Rc ) ϕ ′ ( η ) + Nt Nb ( η + Rc ) θ ′ ( η ) + η Sc ( η + Rc ) ϕ ′ ( η ) f ( η ) + Nt Nb θ ″ ( η ) − Sc γ ϕ ( η ) = 0 .

(14) f ′ ( 0 ) = 1 , f ( 0 ) = 0 , θ ′ ( 0 ) = Bi k T H / k f ( θ ( 0 ) − 1 ) , ϕ ( 0 ) = 1 , f ′ ( ∞ ) → 0 , f ″ ( ∞ ) → 0 , θ ( ∞ ) → 0 , ϕ ( ∞ ) → 0 .

Pressure can be reduced as:

(15) P ( η ) = η + Rc 2 Rc μ T H μ f f ‴ ( η ) + 1 η + Rc f ″ ( η ) − 1 ( η + Rc ) 2 f ′ ( η ) − σ T H σ f M f ′ ( η ) + ρ T H ρ f Rc η + Rc f ″ ( η ) f ( η ) + ρ T H ρ f Rc ( η + Rc ) 2 f ′ ( η ) f ( η ) − ρ T H ρ f Rc η + Rc f ′ 2 ( η ) ,

where R c = b ν f R is the curvature factor, M = σ f B 0 2 ρ f b is the magnetic parameter, Bi = h f k f ν f b is the thermal Biot number, E c = b 2 s 2 ( C p ) f ( T f − T ∞ ) is the Eckert number, Q = Q 0 b ( ρ C p ) f is the heat source parameter, γ = K r b is the chemical reaction factor, Nb = ( C f − C ∞ ) D B ( ρ C p ) n p ν f ( ρ C p ) f is the Brownian motion factor, Nt = D T ( T f − T ∞ ) ( ρ C p ) p ν f T ∞ ( ρ C p ) f is the thermophoresis factor, Sc = ν f D B is the Schmidt number, and Pr = ( ρ C p ) f ν f k f is the Prandtl number.

The quantities of interest are defined as follows:

(16) C f = τ r s ρ f s 2 b 2 , where τ r s = μ T H ∂ u ∂ r − u r + R r = 0 , Nu s = s q w k f ( T f − T ∞ ) , where q w = − k T H ∂ T ∂ r r = 0 , Sh s = − s q m D B ( C f − C ∞ ) , where q m = − D B ∂ C ∂ r r = 0 .

Using the similarity variables, the reduced form of equation (16) can be written as:

(17) Re s C f s = μ T H μ f f ″ ( 0 ) − 1 Rc f ′ ( 0 ) , Nu s Re s = − k T H k f θ ′ ( 0 ) , Sh = Sh s Re s = − ϕ ′ ( 0 ) ,

where Re s = b s 2 ν f is the local Reynolds number.

3 HAM solution

To apply HAM, we introduced the initial guesses and linear operators as follows:

(18) f 0 ( η ) = 1 − exp ( − η ) , θ 0 ( η ) = Bi ( k T H / k f ) + Bi exp ( − η ) , ϕ 0 ( η ) = exp ( − η ) ,

(19) L f ( η ) = f ‴ − f ′ , L θ ( η ) = θ ″ − θ , L ϕ ( η ) = ϕ ″ − ϕ ,

with properties:

(20) L f ( x 1 + x 2 η + x 3 exp ( − η ) + x 4 exp ( η ) ) = 0 , L θ ( x 5 exp ( − η ) + x 6 exp ( η ) ) = 0 , L ϕ ( x 7 exp ( − η ) + x 8 exp ( η ) ) = 0 ,

where x 1 − x 8 are the constants of general solution.

3.1 Advantages of HAM

HAM has several advantages over many traditional analytical methods. It is a series expansion method that does not directly depend on small or large physical parameters. Thus, it is applicable not only for weakly but also strongly nonlinear problems. HAM is a unified method for the Lyapunov artificial small parameter method, Delta expansion method, Adomian decomposition method, and homotopy perturbation method. It gives excellent flexibility to the expression of the solution and how the solution is explicitly obtained, and it provides great freedom in choosing the base functions of the desired solution and the corresponding auxiliary linear operator of homotopy. HAM provides a simple way to ensure the convergence of the solution series and is able to combine with other techniques used in nonlinear differential equations such as spectral methods and Padé approximants.

4 Validation

To confirm the validation of the coded problem in Mathematica 12.0 software, Tables 2 and 3 are shown. The validation is confirmed under some special conditions when K varies and χ 1 = χ 2 = χ 3 = M = 0.0 . Table 2 shows the skin friction ( − Re s C f s ) against different values of K . Upon comparing the present findings with the published results, it can be observed that the current results exhibit a high degree of similarity to the published results. Also, Table 3 displays the comparison of our results for − θ ( 0 ) with established results for variations in Pr , while other parameters are taken as Nb = Nt = Q = M = Ec = χ 1 = χ 2 = χ 3 = 0 , β → ∞ , and Rc → ∞ . In this table, the problem is converted to a flat sheet by taking the assumption when Rc → ∞ . In the flat surface problem, the current results and also close to the published results of the previously published works.

Table 2

Comparing the values of ‒ Re s C fs for variations in K and χ 1 = χ 2 = χ 3 = M = 0.0

R c 5 10 20 30 40 50 100 200 1000
Present outcomes 1.157565 1.072534 1.035464 1.023463 1.017346 1.013995 1.006963 1.003501 1.000798
Roşca and Pop [49] 1.15076 1.07172 1.03501 1.02315 1.01729 1.01380 1.00687 1.00342 1.00068
Afridi et al. [50] 1.1576312 1.0734886 1.0356098 1.0235310 1.0175866 1.0140492 1.0070384 1.0035641 1.0007993
Abbas et al. [51] 1.15763 1.07349 1.03561 1.02353 1.01759 1.01405 1.00704 1.00356 1.00079
Ahmad et al. [52] 1.157630 1.073490 — 1.023530 — 1.014050 — 1.003560
1.000790
Dey et al. [53] 1.157630 1.073490 — 1.0223 — — — — —
Table 3

Comparison of the values of ‒ θ ( 0 ) for different estimations of Pr , when Nb = Nt = Q = M = Ec = χ 1 = χ 2 = χ 3 = 0 and Rc → ∞

Pr 0.01 0.72 1.0 2.0 7.0 10
Present outcomes 0.015664 0.463144 0.581976 0.911361 1.895420 2.308034
Khan and Pop [54] — — — 0.9114 1.8954 —
Wang [55] — — — 0.9114 1.8954 —
Gorla and Sidawi [56] — — — 0.9114 1.8905 —
Devi and Devi [57] — — — 0.91135 1.89540 —
Grubka and Bobba [58] 0.0099 0.4631 0.5820 — — 2.3080
Gowda et al. [59] 0.00978 0.46273 0.58193 — — 2.30793

5 HAM convergence

The homotopic series solution contains the auxiliary factor ℏ . This parameter has the ability to control and adjust the series solution convergence. At 19th order of approximations, as given in Figure 2, the suitable range of velocity, temperature, and volumetric fraction distribution profiles have been obtained. From this figure, we can see that the velocity profile has the convergence area − 1.0 ≤ ℏ f ≤ 1.2 , temperature profile has the convergence area − 1.0 ≤ ℏ θ ≤ 0.9 , and the convergence area of the volumetric fraction distribution profile is − 1.0 ≤ ℏ ϕ ≤ 0.9 .

Figure 2 ℏ − \hslash - curves for f ‴ ( 0 ) f\prime\prime\prime (0) , θ ′ ( 0 ) \theta ^{\prime} (0) and ϕ ′ ( 0 ) \phi ^{\prime} (0) .
Figure 2

ℏ − curves for f ‴ ( 0 ) , θ ′ ( 0 ) and ϕ ′ ( 0 ) .

6 Discussion of results

Next, the variations in different profiles (such as f ′ ( η ) , θ ( η ) , and ϕ ( η ) ) , heat transfer rate Nu s Re s , and mass transfer rate Sh s Re s via embedded factors are discussed. Therefore, we have displayed Figures 3–11 and Tables 4 and 5 in this regard. The default values for the embedded factors are selected as Rc = 5.0 , Ec = 0.5 , M = 1.0 , Bi = 0.5 , Pr = 6.0 , Q = 0.2 , γ = 0.1 , χ 1 = χ 2 = χ 3 = 0.04 , Nt = 0.1 , Nb = 0.1 , and Sc = 1.0 . Figure 3(a) and (b) shows the impression of χ 1 = χ 2 = χ 3 on velocity ( f ′ ( η ) ) and temperature ( θ ( η ) ) distributions, respectively. From both the figures, we see that the higher χ 1 = χ 2 = χ 3 reduces f ′ ( η ) while increasing θ ( η ) . The reason is that the higher values of χ 1 = χ 2 = χ 3 increase the density of the ternary hybrid nanofluid flow due to which the fluid becomes denser, and thus, the momentum boundary layer thickness and velocity profile reduce. On the other hand, the higher values of χ 1 = χ 2 = χ 3 increase the thermal conductivity of the ternary hybrid nanofluid flow, which, as a result, increases the thermal boundary layer thickness and temperature profile. The effects of magnetic factor ( M ) on velocity ( f ′ ( η ) ) and temperature ( θ ( η ) ) distributions are revealed in Figure 4(a) and (b). The velocity distribution reduces, while the thermal panels upsurge with growth in M . The greater M produces the Lorentz force that counteracts the flow of nanoparticles, and hence, the movement of nanoparticles reduces. Therefore, the greater M declines the velocity distribution. On the other hand, the opposite effect of M on temperature distribution is observed. This effect is for reducing the movement of nanoparticles because the greater Lorentz force opposes the flow motion, which results in a growth in θ ( η ) so upsurge in M boosts the temperature distribution. The effects of curvature factor ( R c ) on f ′ ( η ) , θ ( η ) , and ϕ ( η ) are displayed in Figure 5(a)–(c). The greater R c increases f ′ ( η ) , θ ( η ) , and ϕ ( η ) . In fact, “ R c ” represents the radius of the curved surface. As we increase R c , the curved surface transforms to become flat. So by this fact, as Rc → ∞ (say Rc = 1 , 000 ), the surface is not curved anymore. It is a fact that the velocity, temperature, and volumetric fraction distributions are higher on the flat surface compared to those on the curved surface. Thus, increasing R c increases the panels f ′ ( η ) , θ ( η ) , and ϕ ( η ) . The effect of heat source ( Q ) on θ ( η ) is portrayed in Figure 6 with a booting behavior in θ ( η ) . Actually, the increasing heat source means that we have provided extra heat to the nanofluid flow, which ultimately increases the internal heat of fluid flow. This internal temperature heightens the temperature at the boundary and so are the panels θ ( η ) . Therefore, the higher Q augments θ ( η ) . Figure 7(a) and (b) shows the effects of thermophoresis factor Nt on θ ( η ) and ϕ ( η ) . These graphs show that for larger values of Nt , both the thermal and volumetric fraction distributions increase in boundary layer area. This is attributed to the phenomenon that particles near a heated surface generate a thermophoretic force, aiding in the dispersion of particles away from the fluid region. Consequently, this leads to an increase in the thickness of the temperature and volumetric fraction distribution boundary layers. Thus, increasing Nt heightens both θ ( η ) and ϕ ( η ) . Figure 8(a) and (b) shows the impact of Nb on θ ( η ) and ϕ ( η ) . Upsurge in N b increases the thermal distribution and reduces the volumetric fraction distribution. The Brownian motion occurs when suspended nanoparticles move randomly in the base fluid caused by fast-moving molecules or atoms. It should be noted that the Brownian motion is related to nanoparticle size and usually occurs as aggregates or agglomerates. A large particle will have a very weak Brownian motion, and the factor ( Nb ) will have the smallest value. Boost in N b increases the boundary layer region, and boosting temperature distribution is depicted in Figure 8(a). Figure 8(b) shows, however, that a higher ( N b ) value results in a slower growth in nanoparticle volumetric fraction distribution. Figure 9 illustrates the effects of the Eckert number ( Ec ) on θ ( η ) with a growing behavior of θ ( η ) with variations in Ec . As E c grows, frictional heating produces heat in the fluid. The Eckert number is a physical parameter that signifies the ratio of kinetic energy to the specific enthalpy difference between a wall and a fluid. Consequently, as the Eckert number increases, there is a conversion of kinetic energy into internal energy through the work performed against viscous fluid forces. As a result, rising E c raises the values of θ ( η ) . Figure 10 shows the impact of Biot number ( Bi ) on θ ( η ) . Based on this figure, it can be observed that the temperature distribution increases with higher values of Bi . In fact, higher values of Bi enhance the heat transfer rate at the curved surface of the sheet. This increased rate of heat transfer results in the expansion of the temperature boundary layer thickness and subsequently raises the overall temperature. Consequently, higher values of Bi lead to an increased temperature distribution. Figure 11 displays the effect of the Schmidt number ( Sc ) on ϕ ( η ) , where an upsurge is noted in ϕ ( η ) for variations in S c . Actually, mass diffusivity and Schmidt number are inversely proportional to each other. So from here, as S c increases, the mass diffusivity increases that results in a reduction in ϕ ( η ) . Table 4 shows the variation in the Nusselt number via variations in M , Ec , Nb , Nt , Bi , and χ 1 = χ 2 = χ 3 . The increasing χ 1 = χ 2 = χ 3 shows the increasing variation in the Nusselt number. The reason is that the higher values χ 1 = χ 2 = χ 3 increase the thermal conductivity of the ternary hybrid nanofluid flow, which results in an augmenting variation in the Nusselt number. The higher magnetic factor increases the Nusselt number. The rationale behind this is that a higher magnetic factor diminishes the particle motion, thereby resulting in an increase in temperature and heat transfer rate at the curved surface. Consequently, the Nusselt number rises as the magnetic factor increases. Furthermore, higher values of the Eckert number and thermal Biot number also contribute to an increased Nusselt number. Conversely, the Nusselt number decreases with higher thermophoresis and Brownian motion factors. Similarly, the higher thermophoresis and Brownian motion factors heighten the Sherwood number, as shown in Table 5.

Figure 3 (a) Impression of χ 1 = χ 2 = χ 3 {\chi }_{1}={\chi }_{2}={\chi }_{3} on f ′ ( η ) f^{\prime} (\eta ) and (b) impression of χ 1 = χ 2 = χ 3 {\chi }_{1}={\chi }_{2}={\chi }_{3} on θ ( η ) \theta (\eta ) .
Figure 3

(a) Impression of χ 1 = χ 2 = χ 3 on f ′ ( η ) and (b) impression of χ 1 = χ 2 = χ 3 on θ ( η ) .

Figure 4 (a) impression of M M on f ′ ( η ) f^{\prime} (\eta ) and (b) impression of M M on θ ( η ) \theta (\eta ) .
Figure 4

(a) impression of M on f ′ ( η ) and (b) impression of M on θ ( η ) .

Figure 5 (a) Impression of Rc \text{Rc} on f ′ ( η ) f^{\prime} (\eta ) , (b) impression of Rc \text{Rc} on θ ( η ) \theta (\eta ) , and (c) impression of Rc \text{Rc} on ϕ ( η ) \phi (\eta ) .
Figure 5

(a) Impression of Rc on f ′ ( η ) , (b) impression of Rc on θ ( η ) , and (c) impression of Rc on ϕ ( η ) .

Figure 6 Impression of Q Q on θ ( η ) \theta (\eta ) .
Figure 6

Impression of Q on θ ( η ) .

Figure 7 (a) Impression of Nt \text{Nt} on θ ( η ) \theta (\eta ) and (b) impression of Nt \text{Nt} on ϕ ( η ) \phi (\eta ) .
Figure 7

(a) Impression of Nt on θ ( η ) and (b) impression of Nt on ϕ ( η ) .

Figure 8 (a) Impression of Nb \text{Nb} on θ ( η ) \theta (\eta ) and (b) impression of Nb \text{Nb} on ϕ ( η ) \phi (\eta ) .
Figure 8

(a) Impression of Nb on θ ( η ) and (b) impression of Nb on ϕ ( η ) .

Figure 9 Impression of Ec \text{Ec} on θ ( η ) \theta (\eta ) .
Figure 9

Impression of Ec on θ ( η ) .

Figure 10 Impression of Bi \text{Bi} on θ ( η ) \theta (\eta ) .
Figure 10

Impression of Bi on θ ( η ) .

Figure 11 Impression of Sc \text{Sc} on ϕ ( η ) \phi (\eta ) .
Figure 11

Impression of Sc on ϕ ( η ) .

Table 4

Nusselt number for different values of M , Ec , Nb , Nt , Bi , and χ 1 = χ 2 = χ 3

χ 1 = χ 2 = χ 3 M Ec Nb Nt Bi Nu s Re s
0.01 0.986684
0.02 1.243256
0.03 1.486474
0.04 1.625784
0.1 0.486546
1.2 0.497549
1.9 0.510753
0.3 0.609543
0.6 0.658074
0.9 0.697544
0.5 0.508538
0.7 0.497538
0.9 0.480746
0.1 0.696743
0.5 0.666436
0.9 0.620753
0.1 0.597438
0.3 0.637906
0.5 0.675274
Table 5

Sherwood number for different values of Nb and Nt

Nb Nt Sh s Re s
0.5 0.864753
0.7 0.896447
0.9 0.925789
0.1 0.596537
0.5 0.608637
0.9 0.612483

7 Conclusion

A ternary hybrid nanofluid flow with TiO 2 , CoFe 2 O 4 , and MgO nanoparticles over a curved sheet has been examined in this effort. The modeled equations are converted to ODEs using suitable similarity variables. The semi-analytical solution is determined by HAM. The impacts of magnetic field, Joule heating, chemical reaction, and other factors have been discussed on flow profiles and Nusselt, Sherwood numbers using figures and tables. By completing this theoretical analysis, the following concluding points are extracted:

  1. The velocity distribution exhibits a decreasing trend with respect to the magnetic parameter, while the temperature distribution demonstrates an increasing trend with respect to the magnetic parameter.

  2. The greater curvature parameter boots the flow, thermal, and volumetric fraction distributions.

  3. Higher heat source factor, the Eckert and thermal Biot numbers increase the thermal distribution.

  4. Thermal and volumetric fraction distributions are the growing functions of the thermophoresis factor.

  5. Thermal distribution has booted up with upsurge in the Brownian factor, while the volumetric fraction distribution panels have retarded with growth in the Brownian factor and the Schmidt number.

  6. The higher magnetic parameter, Eckert and thermal Biot numbers increase the Nusselt number while reduces with the higher Brownian and thermophoresis factors.

  7. Higher Brownian and thermophoresis factors heighten the Sherwood number.

Acknowledgments

This research was supported by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R259), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

  1. Funding information: This research was supported by the Princess Nourah Bint Abdulrahman University Researchers Supporting Project Number (PNURSP2023R259), Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

References

[1] Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. Int. Mech. Eng. Congr. Exhib. San Fr. CA (United States): 1995. p. 12–7. https://digital.library.unt.edu/ark:/67531/metadc671104/ (accessed October 2, 2021).Search in Google Scholar

[2] Mourad A, Abderrahmane A, Younis O, Marzouki R, Alazzam A. Numerical simulations of magnetohydrodynamics natural convection and entropy production in a porous annulus bounded by wavy cylinder and Koch snowflake loaded with Cu–Water nanofluid. Micromachines. 2022;13:182.10.3390/mi13020182Search in Google Scholar PubMed PubMed Central

[3] Acharya N, Mabood F, Shahzad SA, Badruddin IA. Hydrothermal variations of radiative nanofluid flow by the influence of nanoparticles diameter and nanolayer. Int Commun Heat Mass Transf. 2022;130:105781. 10.1016/J.ICHEATMASSTRANSFER.2021.105781.Search in Google Scholar

[4] Shahid A, Bhatti MM, Ellahi R, Mekheimer KS. Numerical experiment to examine activation energy and bi-convection Carreau nanofluid flow on an upper paraboloid porous surface: Application in solar energy. Sustain Energy Technol Assessments. 2022;52:102029.10.1016/j.seta.2022.102029Search in Google Scholar

[5] Bhatti MM, Arain MB, Zeeshan A, Ellahi R, Doranehgard MH. Swimming of Gyrotactic Microorganism in MHD Williamson nanofluid flow between rotating circular plates embedded in porous medium: Application of thermal energy storage. J Energy Storage. 2022;45:103511.10.1016/j.est.2021.103511Search in Google Scholar

[6] Wijayanta AT. Numerical solution strategy for natural convection problems in a triangular cavity using a direct meshless local Petrov-Galerkin method combined with an implicit artificial-compressibility model. Eng Anal Bound Elem. 2021;126:13–29.10.1016/j.enganabound.2021.02.006Search in Google Scholar

[7] Wijayanta AT. A localized meshless approach using radial basis functions for conjugate heat transfer problems in a heat exchanger. Int J Refrig. 2020;110:38–46.10.1016/j.ijrefrig.2019.10.025Search in Google Scholar

[8] Makarim DA, Suami A, Wijayanta AT, Kobayashi N, Itaya Y. Marangoni convection within thermosolute and absorptive aqueous LiBr solution. Int J Heat Mass Transf. 2022;188:122621.10.1016/j.ijheatmasstransfer.2022.122621Search in Google Scholar

[9] Kumar RSV, Dhananjaya PG, Kumar RN, Gowda RJP, Prasannakumara BC. Modeling and theoretical investigation on Casson nanofluid flow over a curved stretching surface with the influence of magnetic field and chemical reaction. Int J Comput Methods Eng Sci Mech. 2022;23:12–9.10.1080/15502287.2021.1900451Search in Google Scholar

[10] Zhang L, Bhatti MM, Michaelides MM, Marin M, Ellahi R. Hybrid nanofluid flow towards an elastic surface with tantalum and nickel nanoparticles, under the influence of an induced magnetic field. Eur Phys J Spec Top. 2022;231:521–33.10.1140/epjs/s11734-021-00409-1Search in Google Scholar

[11] Khan A, Saeed A, Tassaddiq A, Gul T, Mukhtar S, Kumam P, et al. Bio-convective micropolar nanofluid flow over thin moving needle subject to Arrhenius activation energy, viscous dissipation and binary chemical reaction. Case Stud. Therm Eng. 2021;25:100989.10.1016/j.csite.2021.100989Search in Google Scholar

[12] Chu Y, Bashir S, Ramzan M, Malik MY. Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects. Math Methods Appl Sci. 2023 Jul 15;46(10):11568–82.10.1002/mma.8234Search in Google Scholar

[13] Ojjela O. Numerical investigation of heat transport in Alumina–Silica hybrid nanofluid flow with modeling and simulation. Math Comput Simul. 2022;193:100–22.10.1016/j.matcom.2021.09.022Search in Google Scholar

[14] Gumber P, Yaseen M, Rawat SK, Kumar M. Heat transfer in micropolar hybrid nanofluid flow past a vertical plate in the presence of thermal radiation and suction/injection effects. Partial Differ Equations Appl Math. 2022;5:100240.10.1016/j.padiff.2021.100240Search in Google Scholar

[15] Slimani R, Aissa A, Oudina FM, Khan U, Sahnoun M, Chamkha AJ, et al. Natural convection analysis flow of Al2O3-Cu/water hybrid nanofluid in a porous conical enclosure subjected to the magnetic field. Eur Phys J Appl Phys. 2020;92:10904. 10.1051/EPJAP/2020200260.Search in Google Scholar

[16] Arif M, Persio LD, Kumam P, Watthayu W, Akgül A. Heat transfer analysis of fractional model of couple stress Casson tri-hybrid nanofluid using dissimilar shape nanoparticles in blood with biomedical applications. Sci Rep. 2023;13:4596.10.1038/s41598-022-25127-zSearch in Google Scholar PubMed PubMed Central

[17] Shahzad F, Jamshed W, Eid MR, Ibrahim RW, Aslam F, Isa SSPM, et al. The effect of pressure gradient on MHD flow of a tri-hybrid Newtonian nanofluid in a circular channel. J Magn Magn Mater. 2023;568:170320.10.1016/j.jmmm.2022.170320Search in Google Scholar

[18] Sudharani M, Prakasha DG, Kumar KG, Chamkha AJ. Computational assessment of hybrid and tri hybrid nanofluid influenced by slip flow and linear radiation. Eur Phys J Plus. 2023;138:257.10.1140/epjp/s13360-023-03852-2Search in Google Scholar

[19] Guedri K, Khan A, Sene N, Raizah Z, Saeed A, Galal AM. Thermal flow for radiative ternary hybrid nanofluid over nonlinear stretching sheet subject to Darcy–Forchheimer phenomenon. Math. Probl. Eng. 2022;2022:3429439.10.1155/2022/3429439Search in Google Scholar

[20] Shevchuk IV. An improved asymptotic expansion method for fluid flow and convective heat transfer in cone-and-disk geometries with rotating cone. Phys Fluids. 2023;35:43603.10.1063/5.0146556Search in Google Scholar

[21] Olayemi OA, Khaled AF, Temitope OJ, Victor OO, Odetunde CB, Adegun IK. Parametric study of natural convection heat transfer from an inclined rectangular cylinder embedded in a square enclosure. Aust J Mech Eng. 2023;21:668–81.10.1080/14484846.2021.1913853Search in Google Scholar

[22] Manna NK, Biswas N, Mandal DK, Sarkar UK, Öztop HF, Hamdeh NH. Impacts of heater-cooler position and Lorentz force on heat transfer and entropy generation of hybrid nanofluid convection in quarter-circular cavity. Int J Numer Methods Heat Fluid Flow. 2023;33:1249–86.10.1108/HFF-07-2022-0402Search in Google Scholar

[23] Wang SR, Wang CA. Numerical simulation of convective heat transfer in packed bed using open-source computational fluid dynamics. Powder Technol. 2023;422:118452.10.1016/j.powtec.2023.118452Search in Google Scholar

[24] Shi L, Zhu X, Du Z. Study on convective heat transfer characteristics of inclined jet impinging cylindrical target surface in the confined space. Appl Therm Eng. 2023;218:119316.10.1016/j.applthermaleng.2022.119316Search in Google Scholar

[25] Abbas A, Jeelani MB, Alharthi NH. Darcy–Forchheimer relation influence on MHD dissipative third-grade fluid flow and heat transfer in porous medium with joule heating effects: A numerical approach. Processes. 2022;10:906.10.3390/pr10050906Search in Google Scholar

[26] Naseem T, Fatima U, Munir M, Shahzad A, Kausar N, Nisar KS, et al. Joule heating and viscous dissipation effects in hydromagnetized boundary layer flow with variable temperature, Case Stud. Therm Eng. 2022;35:102083.10.1016/j.csite.2022.102083Search in Google Scholar

[27] Rasheed HU, Islam S, Zeeshan, Abbas T, Khan J. Analytical treatment of MHD flow and chemically reactive Casson fluid with Joule heating and variable viscosity effect. Waves Random Complex Media. 2022;1–17. 10.1080/17455030.2022.2042622.Search in Google Scholar

[28] Mahdy AMS, Babatin MM, Khader MM. Numerical treatment for processing the effect of convective thermal condition and Joule heating on Casson fluid flow past a stretching sheet. Int J Mod Phys C. 2022;33:2250108.10.1142/S012918312250108XSearch in Google Scholar

[29] Waqas H, Sadiq MA, Bahaidarah HMS. Gyrotactic bioconvection stratified flow of magnetized micropolar nanoliquid configured by stretchable radiating surface with Joule heating and viscous dissipation. Int Commun Heat Mass Transf. 2022;138:106229.10.1016/j.icheatmasstransfer.2022.106229Search in Google Scholar

[30] Mahanthesh B, Reddy CS, Srikantha S, Lorenzini G. Entropy generation analysis of radiative heat transfer in Williamson fluid flowing in a microchannel with nonlinear mixed convection and Joule heating. Proc Inst Mech Eng Part E J Process Mech Eng. 2022;09544089221074846. 10.1177/09544089221074846.Search in Google Scholar

[31] Gangadhar K, Lakshmi KB, Kannan T, Chamkha AJ. Bioconvective magnetized oldroyd-B nanofluid flow in the presence of Joule heating with gyrotactic microorganisms. Waves Random Complex Media. 2022;1–21. 10.1080/17455030.2022.2050441.Search in Google Scholar

[32] Mishra A, Upreti H. A comparative study of Ag–MgO/water and Fe3O4–CoFe2O4/EG–water hybrid nanofluid flow over a curved surface with chemical reaction using Buongiorno model. Partial Differ Equations Appl Math. 2022;5:100322.10.1016/j.padiff.2022.100322Search in Google Scholar

[33] Maity S, Kundu PK. Magnetically driven chemically reactive Casson nanofluid flow over curved surface with thermal radiation. Heat Transf. 2022;51:4882–905.10.1002/htj.22527Search in Google Scholar

[34] Khan U, Zaib A, Ishak A, Bakar AS, Animasaun IL, Yook SJ. Insights into the dynamics of blood conveying gold nanoparticles on a curved surface when suction, thermal radiation, and Lorentz force are significant: The case of Non-Newtonian Williamson fluid. Math Comput Simul. 2022;193:250–68.10.1016/j.matcom.2021.10.014Search in Google Scholar

[35] Sun Z, Shi Z, Li Z, Geng X, Sun Q, Chen S, et al. Experimental investigation of flow control of a curved-surface jet hypersonic flow. Phys Fluids. 2022;34:66107.10.1063/5.0094555Search in Google Scholar

[36] Fuzhang W, Anwar MI, Ali M, El-Shafay AS, Abbas N, Ali R. Inspections of unsteady micropolar nanofluid model over exponentially stretching curved surface with chemical reaction. Waves Random Complex Media. 2022;1–22. 10.1080/17455030.2021.2025280.Search in Google Scholar

[37] Nadeem S, Abbas N, Malik MY. Inspection of hybrid based nanofluid flow over a curved surface. Comput Methods Programs Biomed. 2020;189:105193. 10.1016/j.cmpb.2019.105193.Search in Google Scholar PubMed

[38] Sarada K, Gamaoun F, Abdulrahman A, Paramesh SO, Kumar R, Prasanna GD, et al. Impact of exponential form of internal heat generation on water-based ternary hybrid nanofluid flow by capitalizing non-Fourier heat flux model. Case Stud Therm Eng. 2022;38:102332.10.1016/j.csite.2022.102332Search in Google Scholar

[39] Dawar A, Islam S, Shah Z, Mahmuod SR. A passive control of Casson hybrid nanofluid flow over a curved surface with alumina and copper nanomaterials: A study on sodium alginate-based fluid. J Mol Liq. 2023;382:122018.10.1016/j.molliq.2023.122018Search in Google Scholar

[40] Sun X, Animasaun IL, Swain K, Shah NA, Wakif A, Olanrewaju PO. Significance of nanoparticle radius, inter‐particle spacing, inclined magnetic field, and space‐dependent internal heating: The case of chemically reactive water conveying copper nanoparticles. ZAMM‐J Appl Math Mech Für Angew Math Und Mech. 2022;102:e202100094.10.1002/zamm.202100094Search in Google Scholar

[41] Dawar A, Wakif A, Saeed A, Shah Z, Muhammad T, Kumam P. Significance of Lorentz forces on Jeffrey nanofluid flows over a convectively heated flat surface featured by multiple velocity slips and dual stretching constraint: a homotopy analysis approach. J Comput Des Eng. 2022;9:564–82.10.1093/jcde/qwac019Search in Google Scholar

[42] Souayeh B, Ramesh K. Numerical scrutinization of ternary nanofluid flow over an exponentially stretching sheet with gyrotactic microorganisms. Mathematics. 2023;11(4):981.10.3390/math11040981Search in Google Scholar

[43] Priyadharshini P, Archana MV, Shah NA, Alshehri MH. Ternary hybrid nanofluid flow emerging on a symmetrically stretching sheet optimization with machine learning prediction scheme. Symmetry. 2023;15:1225.10.3390/sym15061225Search in Google Scholar

[44] Wang F, Nazir U, Sohail M, El-Zahar ER, Park C, Thounthong P. A Galerkin strategy for tri-hybridized mixture in ethylene glycol comprising variable diffusion and thermal conductivity using non-Fourier’s theory. Nanotechnol Rev. 2022;11:834–45.10.1515/ntrev-2022-0050Search in Google Scholar

[45] Acharya N, Maity S, Kundu PK. Framing the hydrothermal features of magnetized TiO2–CoFe2O4 water-based steady hybrid nanofluid flow over a radiative revolving disk. Multidiscip. Model Mater Struct. 2020;16:765–90. 10.1108/MMMS-08-2019-0151/FULL/XML.Search in Google Scholar

[46] Mishra A, Pandey AK, Kumar M. Thermal performance of Ag–water nanofluid flow over a curved surface due to chemical reaction using Buongiorno’s model. Heat Transf. 2021;50:257–78.10.1002/htj.21875Search in Google Scholar

[47] Abbas Z, Naveed M, Sajid M. Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. J Mol Liq. 2016;215:756–62.10.1016/j.molliq.2016.01.012Search in Google Scholar

[48] Algehyne EA, Wakif A, Rasool G, Saeed A, Ghouli Z. Significance of Darcy-Forchheimer and Lorentz forces on radiative alumina-water nanofluid flows over a slippery curved geometry under multiple convective constraints: a renovated Buongiorno’s model with validated thermophysical correlations. Waves Random Complex Media. 2022;1–30. 10.1080/17455030.2022.2074570.Search in Google Scholar

[49] Roşca NC, Pop I. Unsteady boundary layer flow over a permeable curved stretching/shrinking surface. Eur J Mech. 2015;51:61–7.10.1016/j.euromechflu.2015.01.001Search in Google Scholar

[50] Afridi MI, Qasim M, Wakif A, Hussanan A. Second law analysis of dissipative nanofluid flow over a curved surface in the presence of Lorentz Force: Utilization of the Chebyshev–Gauss–Lobatto spectral method. Nanomater. 2019;9:195. 10.3390/NANO9020195.Search in Google Scholar

[51] Abbas Z, Naveed M, Sajid M. Heat transfer analysis for stretching flow over a curved surface with magnetic field. J Eng Thermophys. 2013;22:337–45.10.1134/S1810232813040061Search in Google Scholar

[52] Ahmad S, Nadeem S, Muhammad N. Boundary layer flow over a curved surface imbedded in porous medium. Commun Theor Phys. 2019;71:344.10.1088/0253-6102/71/3/344Search in Google Scholar

[53] Dey D, Makinde OD, Chutia B. Hydromagnetic flow of dusty fluid with heat and mass transfer past a stretching curved surface in a porous medium. Lat Am Appl Res. 2022;52:201–6.10.52292/j.laar.2022.831Search in Google Scholar

[54] Khan WA, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf. 2010;53:2477–83.10.1016/j.ijheatmasstransfer.2010.01.032Search in Google Scholar

[55] Wang CY. Free convection on a vertical stretching surface. ZAMM‐J Appl Math Mech Für Angew Math Und Mech. 1989;69:418–20.10.1002/zamm.19890691115Search in Google Scholar

[56] Gorla RS, Sidawi I. Free convection on a vertical stretching surface with suction and blowing. Appl Sci Res. 1994;52:247–57.10.1007/BF00853952Search in Google Scholar

[57] Devi SU, Devi SPA. Heat transfer enhancement of cu− $ al_ {2} o_ {3} $/water hybrid nanofluid flow over a stretching sheet. J Niger Math Soc. 2017;36:419–33.Search in Google Scholar

[58] Grubka LG, Bobba KM. Heat transfer characteristics of a continuous stretching surface with variable temperature. J Heat Transfer. 1985;107:248–50.10.1115/1.3247387Search in Google Scholar

[59] Gowda RJP, Al-Mubaddel FS, Kumar RN, Prasannakumara BC, Issakhov A, Rahimi-Gorji A, et al. Computational modelling of nanofluid flow over a curved stretching sheet using Koo–Kleinstreuer and Li (KKL) correlation and modified Fourier heat flux model. Chaos Solit Fractals. 2021;145:110774.10.1016/j.chaos.2021.110774Search in Google Scholar
Received: 2023-05-16
Revised: 2023-08-11
Accepted: 2023-09-05
Published Online: 2023-10-18

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  10. Influence of microalloying with B on the microstructure and properties of brazed joints with Ag–Cu–Zn–Sn filler metal
  11. Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids
  12. Study of mechanical properties of epoxy/graphene and epoxy/halloysite nanocomposites
  13. Effects of CaO addition on the CuW composite containing micro- and nano-sized tungsten particles synthesized via aluminothermic coupling with silicothermic reduction
  14. Cu and Al2O3-based hybrid nanofluid flow through a porous cavity
  15. Design of functional vancomycin-embedded bio-derived extracellular matrix hydrogels for repairing infectious bone defects
  16. Study on nanocrystalline coating prepared by electro-spraying 316L metal wire and its corrosion performance
  17. Axial compression performance of CFST columns reinforced by ultra-high-performance nano-concrete under long-term loading
  18. Tungsten trioxide nanocomposite for conventional soliton and noise-like pulse generation in anomalous dispersion laser cavity
  19. Microstructure and electrical contact behavior of the nano-yttria-modified Cu-Al2O3/30Mo/3SiC composite
  20. Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition
  21. Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets
  22. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface
  23. Chitosan-capped silver nanoparticles with potent and selective intrinsic activity against the breast cancer cells
  24. Multi-core/shell SiO2@Al2O3 nanostructures deposited on Ti3AlC2 to enhance high-temperature stability and microwave absorption properties
  25. Solution-processed Bi2S3/BiVO4/TiO2 ternary heterojunction photoanode with enhanced photoelectrochemical performance
  26. Electroporation effect of ZnO nanoarrays under low voltage for water disinfection
  27. NIR-II window absorbing graphene oxide-coated gold nanorods and graphene quantum dot-coupled gold nanorods for photothermal cancer therapy
  28. Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress
  29. Investigation of different nanoparticles properties on the thermal conductivity and viscosity of nanofluids by molecular dynamics simulation
  30. Optimized Cu2O-{100} facet for generation of different reactive oxidative species via peroxymonosulfate activation at specific pH values to efficient acetaminophen removal
  31. Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating
  32. Appraising the dielectric properties and the effectiveness of electromagnetic shielding of graphene reinforced silicone rubber nanocomposite
  33. Synthesis of Ag and Cu nanoparticles by plasma discharge in inorganic salt solutions
  34. Low-cost and large-scale preparation of ultrafine TiO2@C hybrids for high-performance degradation of methyl orange and formaldehyde under visible light
  35. Utilization of waste glass with natural pozzolan in the production of self-glazed glass-ceramic materials
  36. Mechanical performance of date palm fiber-reinforced concrete modified with nano-activated carbon
  37. Melting point of dried gold nanoparticles prepared with ultrasonic spray pyrolysis and lyophilisation
  38. Graphene nanofibers: A modern approach towards tailored gypsum composites
  39. Role of localized magnetic field in vortex generation in tri-hybrid nanofluid flow: A numerical approach
  40. Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials
  41. Bioconvection transport of upper convected Maxwell nanoliquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction
  42. 3D printing of porous Ti6Al4V bone tissue engineering scaffold and surface anodization preparation of nanotubes to enhance its biological property
  43. Bioinspired ferromagnetic CoFe2O4 nanoparticles: Potential pharmaceutical and medical applications
  44. Significance of gyrotactic microorganisms on the MHD tangent hyperbolic nanofluid flow across an elastic slender surface: Numerical analysis
  45. Performance of polycarboxylate superplasticisers in seawater-blended cement: Effect from chemical structure and nano modification
  46. Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface
  47. Oxygen plasma assisted room temperature bonding for manufacturing SU-8 polymer micro/nanoscale nozzle
  48. Performance and mechanism of CO2 reduction by DBD-coupled mesoporous SiO2
  49. Polyarylene ether nitrile dielectric films modified by HNTs@PDA hybrids for high-temperature resistant organic electronics field
  50. Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates
  51. Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory
  52. Design and optimization of a TiO2/RGO-supported epoxy multilayer microwave absorber by the modified local best particle swarm optimization algorithm
  53. Mechanical properties and frost resistance of recycled brick aggregate concrete modified by nano-SiO2
  54. Self-template synthesis of hollow flower-like NiCo2O4 nanoparticles as an efficient bifunctional catalyst for oxygen reduction and oxygen evolution in alkaline media
  55. High-performance wearable flexible strain sensors based on an AgNWs/rGO/TPU electrospun nanofiber film for monitoring human activities
  56. High-performance lithium–selenium batteries enabled by nitrogen-doped porous carbon from peanut meal
  57. Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
  58. Exploring the potential of biogenic magnesium oxide nanoparticles for cytotoxicity: In vitro and in silico studies on HCT116 and HT29 cells and DPPH radical scavenging
  59. Enhanced visible-light-driven photocatalytic degradation of azo dyes by heteroatom-doped nickel tungstate nanoparticles
  60. A facile method to synthesize nZVI-doped polypyrrole-based carbon nanotube for Ag(i) removal
  61. Improved osseointegration of dental titanium implants by TiO2 nanotube arrays with self-assembled recombinant IGF-1 in type 2 diabetes mellitus rat model
  62. Functionalized SWCNTs@Ag–TiO2 nanocomposites induce ROS-mediated apoptosis and autophagy in liver cancer cells
  63. Triboelectric nanogenerator based on a water droplet spring with a concave spherical surface for harvesting wave energy and detecting pressure
  64. A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model
  65. Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect
  66. Induction of apoptosis and autophagy via regulation of AKT and JNK mitogen-activated protein kinase pathways in breast cancer cell lines exposed to gold nanoparticles loaded with TNF-α and combined with doxorubicin
  67. Effect of PVA fibers on durability of nano-SiO2-reinforced cement-based composites subjected to wet-thermal and chloride salt-coupled environment
  68. Effect of polyvinyl alcohol fibers on mechanical properties of nano-SiO2-reinforced geopolymer composites under a complex environment
  69. In vitro studies of titanium dioxide nanoparticles modified with glutathione as a potential drug delivery system
  70. Comparative investigations of Ag/H2O nanofluid and Ag-CuO/H2O hybrid nanofluid with Darcy-Forchheimer flow over a curved surface
  71. Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method
  72. Properties of ultra-high-performance self-compacting fiber-reinforced concrete modified with nanomaterials
  73. Prediction of lap shear strength of GNP and TiO2/epoxy nanocomposite adhesives
  74. A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids
  75. Fabrication and physicochemical characterization of copper oxide–pyrrhotite nanocomposites for the cytotoxic effects on HepG2 cells and the mechanism
  76. Thermal radiative flow of cross nanofluid due to a stretched cylinder containing microorganisms
  77. In vitro study of the biphasic calcium phosphate/chitosan hybrid biomaterial scaffold fabricated via solvent casting and evaporation technique for bone regeneration
  78. Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating over a curved surface
  79. Effects of nano-SiO2 additives on carbon fiber-reinforced fly ash–slag geopolymer composites performance: Workability, mechanical properties, and microstructure
  80. Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application
  81. Green synthesis and characterization of ginger-extract-based oxali-palladium nanoparticles for colorectal cancer: Downregulation of REG4 and apoptosis induction
  82. Abnormal evolution of resistivity and microstructure of annealed Ag nanoparticles/Ag–Mo films
  83. Preparation of water-based dextran-coated Fe3O4 magnetic fluid for magnetic hyperthermia
  84. Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm
  85. Effect of CNT film interleaves on the flexural properties and strength after impact of CFRP composites
  86. Self-assembled nanoscale entities: Preparative process optimization, payload release, and enhanced bioavailability of thymoquinone natural product
  87. Structure–mechanical property relationships of 3D-printed porous polydimethylsiloxane films
  88. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism
  89. Residual mechanical properties of concrete incorporated with nano supplementary cementitious materials exposed to elevated temperature
  90. Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution
  91. Lightweight and high-strength polyarylene ether nitrile-based composites for efficient electromagnetic interference shielding
  92. Review Articles
  93. Recycling waste sources into nanocomposites of graphene materials: Overview from an energy-focused perspective
  94. Hybrid nanofiller reinforcement in thermoset and biothermoset applications: A review
  95. Current state-of-the-art review of nanotechnology-based therapeutics for viral pandemics: Special attention to COVID-19
  96. Solid lipid nanoparticles for targeted natural and synthetic drugs delivery in high-incidence cancers, and other diseases: Roles of preparation methods, lipid composition, transitional stability, and release profiles in nanocarriers’ development
  97. Critical review on experimental and theoretical studies of elastic properties of wurtzite-structured ZnO nanowires
  98. Polyurea micro-/nano-capsule applications in construction industry: A review
  99. A comprehensive review and clinical guide to molecular and serological diagnostic tests and future development: In vitro diagnostic testing for COVID-19
  100. Recent advances in electrocatalytic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid: Mechanism, catalyst, coupling system
  101. Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery
  102. Review of the pharmacokinetics of nanodrugs
  103. Engineered nanoflowers, nanotrees, nanostars, nanodendrites, and nanoleaves for biomedical applications
  104. Research progress of biopolymers combined with stem cells in the repair of intrauterine adhesions
  105. Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites
  106. Antifouling induced by surface wettability of poly(dimethyl siloxane) and its nanocomposites
  107. TiO2 aerogel composite high-efficiency photocatalysts for environmental treatment and hydrogen energy production
  108. Structural properties of alumina surfaces and their roles in the synthesis of environmentally persistent free radicals (EPFRs)
  109. Nanoparticles for the potential treatment of Alzheimer’s disease: A physiopathological approach
  110. Current status of synthesis and consolidation strategies for thermo-resistant nanoalloys and their general applications
  111. Recent research progress on the stimuli-responsive smart membrane: A review
  112. Dispersion of carbon nanotubes in aqueous cementitious materials: A review
  113. Applications of DNA tetrahedron nanostructure in cancer diagnosis and anticancer drugs delivery
  114. Magnetic nanoparticles in 3D-printed scaffolds for biomedical applications
  115. An overview of the synthesis of silicon carbide–boron carbide composite powders
  116. Organolead halide perovskites: Synthetic routes, structural features, and their potential in the development of photovoltaic
  117. Recent advancements in nanotechnology application on wood and bamboo materials: A review
  118. Application of aptamer-functionalized nanomaterials in molecular imaging of tumors
  119. Recent progress on corrosion mechanisms of graphene-reinforced metal matrix composites
  120. Research progress on preparation, modification, and application of phenolic aerogel
  121. Application of nanomaterials in early diagnosis of cancer
  122. Plant mediated-green synthesis of zinc oxide nanoparticles: An insight into biomedical applications
  123. Recent developments in terahertz quantum cascade lasers for practical applications
  124. Recent progress in dielectric/metal/dielectric electrodes for foldable light-emitting devices
  125. Nanocoatings for ballistic applications: A review
  126. A mini-review on MoS2 membrane for water desalination: Recent development and challenges
  127. Recent updates in nanotechnological advances for wound healing: A narrative review
  128. Recent advances in DNA nanomaterials for cancer diagnosis and treatment
  129. Electrochemical micro- and nanobiosensors for in vivo reactive oxygen/nitrogen species measurement in the brain
  130. Advances in organic–inorganic nanocomposites for cancer imaging and therapy
  131. Advancements in aluminum matrix composites reinforced with carbides and graphene: A comprehensive review
  132. Modification effects of nanosilica on asphalt binders: A review
  133. Decellularized extracellular matrix as a promising biomaterial for musculoskeletal tissue regeneration
  134. Review of the sol–gel method in preparing nano TiO2 for advanced oxidation process
  135. Micro/nano manufacturing aircraft surface with anti-icing and deicing performances: An overview
  136. Cell type-targeting nanoparticles in treating central nervous system diseases: Challenges and hopes
  137. An overview of hydrogen production from Al-based materials
  138. A review of application, modification, and prospect of melamine foam
  139. A review of the performance of fibre-reinforced composite laminates with carbon nanotubes
  140. Research on AFM tip-related nanofabrication of two-dimensional materials
  141. Advances in phase change building materials: An overview
  142. Development of graphene and graphene quantum dots toward biomedical engineering applications: A review
  143. Nanoremediation approaches for the mitigation of heavy metal contamination in vegetables: An overview
  144. Photodynamic therapy empowered by nanotechnology for oral and dental science: Progress and perspectives
  145. Biosynthesis of metal nanoparticles: Bioreduction and biomineralization
  146. Current diagnostic and therapeutic approaches for severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) and the role of nanomaterial-based theragnosis in combating the pandemic
  147. Application of two-dimensional black phosphorus material in wound healing
  148. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part I
  149. Helical fluorinated carbon nanotubes/iron(iii) fluoride hybrid with multilevel transportation channels and rich active sites for lithium/fluorinated carbon primary battery
  150. The progress of cathode materials in aqueous zinc-ion batteries
  151. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part I
  152. Effect of polypropylene fiber and nano-silica on the compressive strength and frost resistance of recycled brick aggregate concrete
  153. Mechanochemical design of nanomaterials for catalytic applications with a benign-by-design focus
https://doi.org/10.1515/ntrev-2023-0125
Keywords for this article
nanofluid; hybrid nanofluid; ternary hybrid nanofluid; convective heat transfer; Joule heating; chemical reaction; curved surface
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Preparation of CdS–Ag2S nanocomposites by ultrasound-assisted UV photolysis treatment and its visible light photocatalysis activity
  3. Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk
  4. Aptamer-based detection of serotonin based on the rapid in situ synthesis of colorimetric gold nanoparticles
  5. Investigation of the nucleation and growth behavior of Ti2AlC and Ti3AlC nano-precipitates in TiAl alloys
  6. Dynamic recrystallization behavior and nucleation mechanism of dual-scale SiCp/A356 composites processed by P/M method
  7. High mechanical performance of 3-aminopropyl triethoxy silane/epoxy cured in a sandwich construction of 3D carbon felts foam and woven basalt fibers
  8. Applying solution of spray polyurea elastomer in asphalt binder: Feasibility analysis and DSR study based on the MSCR and LAS tests
  9. Study on the chronic toxicity and carcinogenicity of iron-based bioabsorbable stents
  10. Influence of microalloying with B on the microstructure and properties of brazed joints with Ag–Cu–Zn–Sn filler metal
  11. Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids
  12. Study of mechanical properties of epoxy/graphene and epoxy/halloysite nanocomposites
  13. Effects of CaO addition on the CuW composite containing micro- and nano-sized tungsten particles synthesized via aluminothermic coupling with silicothermic reduction
  14. Cu and Al2O3-based hybrid nanofluid flow through a porous cavity
  15. Design of functional vancomycin-embedded bio-derived extracellular matrix hydrogels for repairing infectious bone defects
  16. Study on nanocrystalline coating prepared by electro-spraying 316L metal wire and its corrosion performance
  17. Axial compression performance of CFST columns reinforced by ultra-high-performance nano-concrete under long-term loading
  18. Tungsten trioxide nanocomposite for conventional soliton and noise-like pulse generation in anomalous dispersion laser cavity
  19. Microstructure and electrical contact behavior of the nano-yttria-modified Cu-Al2O3/30Mo/3SiC composite
  20. Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition
  21. Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets
  22. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface
  23. Chitosan-capped silver nanoparticles with potent and selective intrinsic activity against the breast cancer cells
  24. Multi-core/shell SiO2@Al2O3 nanostructures deposited on Ti3AlC2 to enhance high-temperature stability and microwave absorption properties
  25. Solution-processed Bi2S3/BiVO4/TiO2 ternary heterojunction photoanode with enhanced photoelectrochemical performance
  26. Electroporation effect of ZnO nanoarrays under low voltage for water disinfection
  27. NIR-II window absorbing graphene oxide-coated gold nanorods and graphene quantum dot-coupled gold nanorods for photothermal cancer therapy
  28. Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress
  29. Investigation of different nanoparticles properties on the thermal conductivity and viscosity of nanofluids by molecular dynamics simulation
  30. Optimized Cu2O-{100} facet for generation of different reactive oxidative species via peroxymonosulfate activation at specific pH values to efficient acetaminophen removal
  31. Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating
  32. Appraising the dielectric properties and the effectiveness of electromagnetic shielding of graphene reinforced silicone rubber nanocomposite
  33. Synthesis of Ag and Cu nanoparticles by plasma discharge in inorganic salt solutions
  34. Low-cost and large-scale preparation of ultrafine TiO2@C hybrids for high-performance degradation of methyl orange and formaldehyde under visible light
  35. Utilization of waste glass with natural pozzolan in the production of self-glazed glass-ceramic materials
  36. Mechanical performance of date palm fiber-reinforced concrete modified with nano-activated carbon
  37. Melting point of dried gold nanoparticles prepared with ultrasonic spray pyrolysis and lyophilisation
  38. Graphene nanofibers: A modern approach towards tailored gypsum composites
  39. Role of localized magnetic field in vortex generation in tri-hybrid nanofluid flow: A numerical approach
  40. Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials
  41. Bioconvection transport of upper convected Maxwell nanoliquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction
  42. 3D printing of porous Ti6Al4V bone tissue engineering scaffold and surface anodization preparation of nanotubes to enhance its biological property
  43. Bioinspired ferromagnetic CoFe2O4 nanoparticles: Potential pharmaceutical and medical applications
  44. Significance of gyrotactic microorganisms on the MHD tangent hyperbolic nanofluid flow across an elastic slender surface: Numerical analysis
  45. Performance of polycarboxylate superplasticisers in seawater-blended cement: Effect from chemical structure and nano modification
  46. Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface
  47. Oxygen plasma assisted room temperature bonding for manufacturing SU-8 polymer micro/nanoscale nozzle
  48. Performance and mechanism of CO2 reduction by DBD-coupled mesoporous SiO2
  49. Polyarylene ether nitrile dielectric films modified by HNTs@PDA hybrids for high-temperature resistant organic electronics field
  50. Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates
  51. Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory
  52. Design and optimization of a TiO2/RGO-supported epoxy multilayer microwave absorber by the modified local best particle swarm optimization algorithm
  53. Mechanical properties and frost resistance of recycled brick aggregate concrete modified by nano-SiO2
  54. Self-template synthesis of hollow flower-like NiCo2O4 nanoparticles as an efficient bifunctional catalyst for oxygen reduction and oxygen evolution in alkaline media
  55. High-performance wearable flexible strain sensors based on an AgNWs/rGO/TPU electrospun nanofiber film for monitoring human activities
  56. High-performance lithium–selenium batteries enabled by nitrogen-doped porous carbon from peanut meal
  57. Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
  58. Exploring the potential of biogenic magnesium oxide nanoparticles for cytotoxicity: In vitro and in silico studies on HCT116 and HT29 cells and DPPH radical scavenging
  59. Enhanced visible-light-driven photocatalytic degradation of azo dyes by heteroatom-doped nickel tungstate nanoparticles
  60. A facile method to synthesize nZVI-doped polypyrrole-based carbon nanotube for Ag(i) removal
  61. Improved osseointegration of dental titanium implants by TiO2 nanotube arrays with self-assembled recombinant IGF-1 in type 2 diabetes mellitus rat model
  62. Functionalized SWCNTs@Ag–TiO2 nanocomposites induce ROS-mediated apoptosis and autophagy in liver cancer cells
  63. Triboelectric nanogenerator based on a water droplet spring with a concave spherical surface for harvesting wave energy and detecting pressure
  64. A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model
  65. Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect
  66. Induction of apoptosis and autophagy via regulation of AKT and JNK mitogen-activated protein kinase pathways in breast cancer cell lines exposed to gold nanoparticles loaded with TNF-α and combined with doxorubicin
  67. Effect of PVA fibers on durability of nano-SiO2-reinforced cement-based composites subjected to wet-thermal and chloride salt-coupled environment
  68. Effect of polyvinyl alcohol fibers on mechanical properties of nano-SiO2-reinforced geopolymer composites under a complex environment
  69. In vitro studies of titanium dioxide nanoparticles modified with glutathione as a potential drug delivery system
  70. Comparative investigations of Ag/H2O nanofluid and Ag-CuO/H2O hybrid nanofluid with Darcy-Forchheimer flow over a curved surface
  71. Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method
  72. Properties of ultra-high-performance self-compacting fiber-reinforced concrete modified with nanomaterials
  73. Prediction of lap shear strength of GNP and TiO2/epoxy nanocomposite adhesives
  74. A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids
  75. Fabrication and physicochemical characterization of copper oxide–pyrrhotite nanocomposites for the cytotoxic effects on HepG2 cells and the mechanism
  76. Thermal radiative flow of cross nanofluid due to a stretched cylinder containing microorganisms
  77. In vitro study of the biphasic calcium phosphate/chitosan hybrid biomaterial scaffold fabricated via solvent casting and evaporation technique for bone regeneration
  78. Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating over a curved surface
  79. Effects of nano-SiO2 additives on carbon fiber-reinforced fly ash–slag geopolymer composites performance: Workability, mechanical properties, and microstructure
  80. Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application
  81. Green synthesis and characterization of ginger-extract-based oxali-palladium nanoparticles for colorectal cancer: Downregulation of REG4 and apoptosis induction
  82. Abnormal evolution of resistivity and microstructure of annealed Ag nanoparticles/Ag–Mo films
  83. Preparation of water-based dextran-coated Fe3O4 magnetic fluid for magnetic hyperthermia
  84. Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm
  85. Effect of CNT film interleaves on the flexural properties and strength after impact of CFRP composites
  86. Self-assembled nanoscale entities: Preparative process optimization, payload release, and enhanced bioavailability of thymoquinone natural product
  87. Structure–mechanical property relationships of 3D-printed porous polydimethylsiloxane films
  88. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism
  89. Residual mechanical properties of concrete incorporated with nano supplementary cementitious materials exposed to elevated temperature
  90. Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution
  91. Lightweight and high-strength polyarylene ether nitrile-based composites for efficient electromagnetic interference shielding
  92. Review Articles
  93. Recycling waste sources into nanocomposites of graphene materials: Overview from an energy-focused perspective
  94. Hybrid nanofiller reinforcement in thermoset and biothermoset applications: A review
  95. Current state-of-the-art review of nanotechnology-based therapeutics for viral pandemics: Special attention to COVID-19
  96. Solid lipid nanoparticles for targeted natural and synthetic drugs delivery in high-incidence cancers, and other diseases: Roles of preparation methods, lipid composition, transitional stability, and release profiles in nanocarriers’ development
  97. Critical review on experimental and theoretical studies of elastic properties of wurtzite-structured ZnO nanowires
  98. Polyurea micro-/nano-capsule applications in construction industry: A review
  99. A comprehensive review and clinical guide to molecular and serological diagnostic tests and future development: In vitro diagnostic testing for COVID-19
  100. Recent advances in electrocatalytic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid: Mechanism, catalyst, coupling system
  101. Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery
  102. Review of the pharmacokinetics of nanodrugs
  103. Engineered nanoflowers, nanotrees, nanostars, nanodendrites, and nanoleaves for biomedical applications
  104. Research progress of biopolymers combined with stem cells in the repair of intrauterine adhesions
  105. Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites
  106. Antifouling induced by surface wettability of poly(dimethyl siloxane) and its nanocomposites
  107. TiO2 aerogel composite high-efficiency photocatalysts for environmental treatment and hydrogen energy production
  108. Structural properties of alumina surfaces and their roles in the synthesis of environmentally persistent free radicals (EPFRs)
  109. Nanoparticles for the potential treatment of Alzheimer’s disease: A physiopathological approach
  110. Current status of synthesis and consolidation strategies for thermo-resistant nanoalloys and their general applications
  111. Recent research progress on the stimuli-responsive smart membrane: A review
  112. Dispersion of carbon nanotubes in aqueous cementitious materials: A review
  113. Applications of DNA tetrahedron nanostructure in cancer diagnosis and anticancer drugs delivery
  114. Magnetic nanoparticles in 3D-printed scaffolds for biomedical applications
  115. An overview of the synthesis of silicon carbide–boron carbide composite powders
  116. Organolead halide perovskites: Synthetic routes, structural features, and their potential in the development of photovoltaic
  117. Recent advancements in nanotechnology application on wood and bamboo materials: A review
  118. Application of aptamer-functionalized nanomaterials in molecular imaging of tumors
  119. Recent progress on corrosion mechanisms of graphene-reinforced metal matrix composites
  120. Research progress on preparation, modification, and application of phenolic aerogel
  121. Application of nanomaterials in early diagnosis of cancer
  122. Plant mediated-green synthesis of zinc oxide nanoparticles: An insight into biomedical applications
  123. Recent developments in terahertz quantum cascade lasers for practical applications
  124. Recent progress in dielectric/metal/dielectric electrodes for foldable light-emitting devices
  125. Nanocoatings for ballistic applications: A review
  126. A mini-review on MoS2 membrane for water desalination: Recent development and challenges
  127. Recent updates in nanotechnological advances for wound healing: A narrative review
  128. Recent advances in DNA nanomaterials for cancer diagnosis and treatment
  129. Electrochemical micro- and nanobiosensors for in vivo reactive oxygen/nitrogen species measurement in the brain
  130. Advances in organic–inorganic nanocomposites for cancer imaging and therapy
  131. Advancements in aluminum matrix composites reinforced with carbides and graphene: A comprehensive review
  132. Modification effects of nanosilica on asphalt binders: A review
  133. Decellularized extracellular matrix as a promising biomaterial for musculoskeletal tissue regeneration
  134. Review of the sol–gel method in preparing nano TiO2 for advanced oxidation process
  135. Micro/nano manufacturing aircraft surface with anti-icing and deicing performances: An overview
  136. Cell type-targeting nanoparticles in treating central nervous system diseases: Challenges and hopes
  137. An overview of hydrogen production from Al-based materials
  138. A review of application, modification, and prospect of melamine foam
  139. A review of the performance of fibre-reinforced composite laminates with carbon nanotubes
  140. Research on AFM tip-related nanofabrication of two-dimensional materials
  141. Advances in phase change building materials: An overview
  142. Development of graphene and graphene quantum dots toward biomedical engineering applications: A review
  143. Nanoremediation approaches for the mitigation of heavy metal contamination in vegetables: An overview
  144. Photodynamic therapy empowered by nanotechnology for oral and dental science: Progress and perspectives
  145. Biosynthesis of metal nanoparticles: Bioreduction and biomineralization
  146. Current diagnostic and therapeutic approaches for severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) and the role of nanomaterial-based theragnosis in combating the pandemic
  147. Application of two-dimensional black phosphorus material in wound healing
  148. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part I
  149. Helical fluorinated carbon nanotubes/iron(iii) fluoride hybrid with multilevel transportation channels and rich active sites for lithium/fluorinated carbon primary battery
  150. The progress of cathode materials in aqueous zinc-ion batteries
  151. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part I
  152. Effect of polypropylene fiber and nano-silica on the compressive strength and frost resistance of recycled brick aggregate concrete
  153. Mechanochemical design of nanomaterials for catalytic applications with a benign-by-design focus
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