Home Dynamics of convective slippery constraints on hybrid radiative Sutterby nanofluid flow by Galerkin finite element simulation
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Dynamics of convective slippery constraints on hybrid radiative Sutterby nanofluid flow by Galerkin finite element simulation

  • Jamel Bouslimi EMAIL logo , Ali A. Alkathiri , Abdulaziz N. Alharbi , Wasim Jamshed , Mohamed R. Eid EMAIL logo and Mohamed Lamjed Bouazizi
Published/Copyright: March 11, 2022
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 11 Issue 1

Abstract

The heat transport and entropy formation of an unsteady Sutterby hybrid nanofluid (SBHNF) are investigated in this work. SBHNF’s flowing and thermal transport properties are investigated by exposing the nanofluid to a slippery hot surface. This analysis includes the influences of solid-shaped nanoparticles, porous materials, radiative flux, and viscous dissipative flow. The Galerkin finite element technique (G-FEM) is used to find self-similar solutions to equations that are then transformed into ODEs using appropriate transformations. This research considers two diverse kinds of nanosolid-particles, copper (Cu) and graphene oxide (GO), using non-Newtonian engine-oil (EO) as the working fluid. In the flowing, energy, skin friction, Nusselt number, and entropy production, important findings for the various variables are visually depicted. The most notable finding of the analysis is that when SBHNF (GO–Cu/EO) is compared to a typical nanofluid (Cu–EO), the thermal transmission rate of SBHNF (GO–Cu/EO) gradually increases. Furthermore, heat transfer is greatest for spherical-shaped nanoparticles and lowest for lamina-shaped nanoparticles. The entropy in the model is increased when the size of the nanoparticles ϕ is increased. The comparable impact is noticed once the radiation flowing N r and Deborah number λ increase.

Keywords: Sutterby hybrid nanofluid; entropy generation; viscous dissipation; finite element; shaped-factor

Abbreviations

A

unsteadiness parameter

b

initial stretching rate

B i

Biot number

B r

Brinkman number

C f

frictional force factor

C p

specific heat ( J kg − 1 K − 1 )

E G

dimensional entropy ( J / K )

E

column vectors of order

E c

Eckert number

h

heat transport factor

κ

thermal conductivity ( W m − 1 K − 1 )

k 0

thermal conductivity of the surface

k ⁎

absorbent factor

n

power-law index

N r

radiation parameter

N G

dimensionless entropy generation

Nu x

local Nusselt number

P r

Prandtl number ( ν / α )

q r

radiative heat flux

q w

wall heat flux

Q

heat source

R e

Reynolds number

S

suction/injection parameter

v 1 , v 2

velocity component ( m s − 1 )

U w

velocity of the stretching sheet

V w

vertical velocity

x , y

dimensional space coordinates ( m )

Greek symbols

¥

fluid temperature

ξ

effective extending rate

¥ w

temperature at wall

¥ ∞

ambient temperature

ϕ

size of nanomolecules

ρ

density ( kg m − 3 )

Ω

dimensionless temperature gradient

λ

Deborah number

σ ⁎

Stefan–Boltzmann constant

ψ

stream function

χ

similarity variable

θ

dimensionless temperature

Λ

velocity slip parameter

μ

dynamic viscosity ( kg m − 1 s − 1 )

ν

kinematic viscosity ( m 2 s − 1 )

α

thermal diffusivity ( m 2 s − 1 )

Subscripts

f , gf

base fluid

0

surface

p , p 1 , p 2

nanoparticles

nf

nanofluid

hnf

hybrid nanofluid

s

particles

Cu

copper nanoparticles

GO

graphene oxide particles

1 Introduction

Nanofluid which has unusual characteristics and is well-known as the suspending colloidal fluid with metallic or nonmetallic nanosolid-particles was studied and discussed by several investigators. Buongiorno [1] said the absolute swiftness of the nanoparticles can be regarded as the total velocities of basefluid and the relative velocity. Seven slip processes were then analyzed: inertia, Brownian, thermophoretic diffusivity, diffusio-phoresis, Magnus impact, drainage of fluids, and gravitational change. Then, he announced that the Brownian and thermophoretic diffusions can play an imperative role in the non-attendance of turbulent impacts. Increased thermal conduction of conventional thermal transmission fluids, for example, H2O, ethylene-glycol, and mineral oil, is achieved when nanoparticles are applied to a basic fluid. Nanofluids can thus be used for electrical cooling, cooling engines, solar water heating, nuclear reactor, oscillating heat tubing, and as transmission fluids for heat transmission [2]. Garoosi et al. [3] have studied numerically the nanofluids flowing in which using Buongiorno's model. Eiamsa-ard et al. [4] surveyed the improvement in heat transport of TiO2–H2O nanofluid into a heat exchanger tube fitted with superlative double-twisted strips. In different physical situations, recent additions are provided for the treatment of nanofluid with heat and mass transport [5,6,7].

Accurate simulation of nanofluid flowing with the macroscopic model is a prerequisite to building nanofluid-operating equipment [8]. Researchers have generally analyzed individual and two-phase macroscopic models. Provided that the relative speeds of nanoparticle and normal fluid are insignificant, the homogeneity monotonic model may be regarded as a single spectrum with its efficiencies. A homogeneous single-phase model has been used by Maiga et al. [9] for investigating forced convective flow of Al2O3–H2O and Al2O3–EG nanoliquids in a homogeneously heated tube at completely established laminar and turbulent flowing schemes. Temperature-dependent characteristics for the convection of nano-fluid models have been shown to predict that those heat transfer improvements are greater than that of nanofluid-dependent model used by Palm et al. [10]. Xuan and Roetzel [11] have suggested the dispersion approach for nanofluids. Heris et al. [12] used a dispersive model for the simulation of laminar nanofluid convection in a rotating duct. Mokmeli and Avval [13] utilized both homogeneity monotonic and dispersive schemes for the study of convection nanofluid heat transport. When comparing numerical findings with experimental values, the dispersive model has been seen to be more correct [8]. A recent survey on single phase nanofluid flows is presented in refs. [14,15,16].

The trend in the numerical investigations of heat transport of nanoliquid is to consider it to be a Newtonian fluid; however, it is well documented that numerous nanofluids display a non-Newtonian behavior so it is important to consider it. Consequently, in this analysis, we take account of the significance of non-Newtonian liquid as a Sutterby liquid. Fluid model in the type of Sutterby explains the flux of pseudoplastic behavior. Non-Newtonian Sutterby fluid has been many uses, including those used to spin the fluid in the full process of drilling operations. These liquids are too utilized in fabricated lubricant processing. Refs [17–29] provide more detailed information.

The Sutterby fluid model exhibits highly refined polymer solutions and is one of the non-Newton-based liquids used to analyze the rheological properties of various materials [30]. We are using the transition process to get the ODE system indirect. This program is solved numerically with a built-in shooting method. The leading values of the different parameters involved in speed, temperature, and concentration are defined. Speed, concentration, and temperature are calculated by numbers. The results obtained show that the speed is reduced by the parameter of the objects. Temperature and concentricity are augmented by the parameter [31]. The study of the behavior of non-Newtonian nanofluids is complex and difficult because of the indirect relationship between stress and stress level, and this is because many of the things that happen in the real world are not real and are not the same. It is very easy to solve a line problem but finding solutions to indirect problems is still very difficult. However, the results obtained by numerical methods give unstable points when sorted; otherwise, gaining a complete understanding of the indirect problem is also difficult. If an indirect problem involves unity or has many solutions this adds to the complexity of the numbers. Although numerical and mathematical methods for solving indirect problems are limited, they also have their advantages. Therefore, we cannot ignore any of these two methods, but it is usually fun to solve an indirect problem through analysis. In addition, perforated media is used to transport and conserve energy in many industrial systems, such as heat pipes, solid matrix heat exchangers, electric cooling, and chemical reactors [32]. Various solutions were reported by Hashim and Hamid [33] on Williamson nanofluid flow about suction variable in the current decade. There have been more recent debates [34–36] in regards to non-Newtonian nanofluids. Refs [37–48] provide recent information that considers nanofluids with flowing and heat transmission in a variety of physical descriptions.

Hybrid nanofluids were introduced by Suresh et al. [49] to extra improve the optimistic characteristics of nanoliquids. Hybrid nanofluids are built by the combination of two different kinds of nanosolid-particles. Recent research in the area of nanofluids has focused on hybrid nanofluid thermal systems. The effect of various kinds of nanoparticles, nanoparticle sizes, the volume of nanosolid-particles in the basis fluid, and thermophysical characteristics of nanofluids is nonetheless crucial. The three-dimensional flux of Cu–Al2O3/H2O hybrid nanofluid using the RK-Fehlberg integrated process is analyzed by Devi and Devi [50]. This is caused by Lorentz’s force by the unidirectional linear expansion of the plate. The findings showed that the Cu–Al2O3/H2O hybrid nanofluid heat exchange rate is higher than that of Cu–H2O nanofluid. Afrand et al. [51] examinated the influence on the rheology conduct of magnetite hybrid nanofluid-silver/ethylene glycol (Fe3O4–Ag/EG) of temperature distribution and nanoparticulate concentration. Hayat and Nadeem [52] took the hybrid Brinkman nanoliquid 3D flow, for an assessment of heat transfer characteristics on a linear extending and circular surface with radiative and homogeneity (heterogeneity) reactive flowing of CuO/H2O and Ag–CuO/H2O. Ghadikolaei et al. [53] scrutinized the thermo-physical characteristics of magnetohydrodynamics (MHD) mixture TiO2–Cu/H2O nanofluid with common geometrical shapes factor for nanoparticles. Hussain et al. [54] considered a hybrid nanofluid containing Al2O3–Cu/H2O flowing into an open cavity with an adiabatic quadrangular obstruction within the hollow. For numerical solution, the finite element method was utilized and the influences of various potential factors on hybrid nanofluid were addressed. Information on mixture nanoliquid flowing and heat transmission properties can be found in refs [55–59].

Recently, the thermodynamics second-law was employed [60] in order to minimize entropy production to find the optimum engineering scheme. The level of irresponsibilities accumulating during a process has been decided with entropy generation [61]. This can be used to test the efficiency of engineering devices with entropy analysis [62]. For example, Oztop and Salem [63] carried out an analysis of the entropy production for free and mixed convective heat transport models. A final volume approach was taken by Shahzad et al. [64] to examine wavy channel entropy and thermohydraulic efficiency with three-corrugation outlines, which are trapezoidal, sinusoidal, and triangular. Iron salt, tannin, and graphic oxide were assembled into GO–Fe3O4 hybrid nanofluid by Mehrali et al. [65] due to the stability and abundance. The overall thermal conductance of the system can be increased by 11% with the usage of hybrid solid nanoparticles. Under the effect of a magnetic field, the efficacy of heat transfer of GO–Fe3O4 mixed nanofluid enhances, while entropy is decreased with graphene usage instead of purified H2O by 41%. Using a hot stretched plate, Shahzad et al. [66] made an analysis on chemical reactions and entropy of the 2nd-grade nanofluid under the effect of nonlinear heat radioactivities and MHD. Increment in Reynolds, Brinkmann, and Hartmann numbers results in system entropy elevating, while reduction is observed for higher temperature. Similar analyses were conducted in refs [67–71] for entropy production of nanofluid with the expandable surfaces using diverse geometry.

The finite element technique is commonly used in mathematics and engineering models to numerically solve differential equations. Other applications include sophisticated geometry testing and different forms of material modeling. Khan et al. [72] developed a design-based model to investigate heat increase and thermal management in a separate lid-driven square cavity. They got numerical results using the Galerkin finite element approach (G-FEM). Mourad et al. [73] investigated uniform MHD free convection and heat transmission in a penetrable cavity using a hybrid Fe3O4-MWCNT/water nanofluid filled inner elliptic cylinder. To validate the governing equations, they employed the G-FEM. Rana et al. [74] presented an investigation on the electromagnetism aspect of nanofluid on an expandable cylinder under the suspension influence of gyrotactic algae using the Cattaneo–Christov mass and heat flux concept. They used the finite element approach to acquire the mathematical conclusions of the model’s governing equations. Shah et al. [75] investigated the magnetized non-Darcy flow of free convective hybrid nanofluid on a penetrable cylinder using a stable and ambient magnetic field as well as a constant heat source. To numerically resolve the governing set of equations, the control volume finite element approach was used. Nasrin et al. [76] probed the heat transmission behavior of mixture nanoliquids using sinusoidal and lid-driven cavities with trapezoidal shapes. They used the finite element approach to solve the controlling set of partial differential equations regulating fluid temperature and velocity.

Studies on entropy production of SBHNF are infrequent, and none of the papers available addressed the impacts of a penetrable material, viscous dissipation, and radiation flux, shaped-factor via the extended sheet utilizing the nanoliquid Tiwari–Das scheme in detail [77]. The fluid, swiftness, and temperature in Tiwari-Das (monotonic model) are equivalent. The advantages of the single-phase approach are that the slip processes are ignored so that the model is simpler and numerically easy to solve. But the downside of the approach is that the numerical effects of certain situations vary from the results of experiments. Concentrations range from 3 to 20% in this model volume of nanoparticles. The effects of Cu–EO, GO–EO hybrid, and standard nanofluid were only approximated by numerical findings. Therefore, the present investigation focuses on the powerful liquid feature effects and entropy in a numbered system based on the Keller-box process (KBM) of SBHNF in a boundary-layer in order to bridge a gap.

The structure of the current article is as follows: governing mathematical equations are given in Section 2. Solution to the problem is established in Section 3. Galerkin finite element method employed during the numbering procedure is explained in Section 4. Section 5 tells about the validation of the code. In Section 6, we analyzed the development of entropy. Section 7 summarizes the findings as well as the debate. Outcomes along with future guidelines are provided in Section 8.

2 Flow model formulations

The mathematical flow equations show the moved horizontal plate with the irregular expanding velocity [78]:

(2.1) U w ( x , t ) = b x 1 − ξ t ,

where b is an original expanding rate. ¥ w ( x , t ) = ¥ ∞ + b ⁎ x 1 − ξ t is isolated surface temperature, for appropriateness, it is considered as constant at x = 0 . Here b ⁎ , ¥ w , and ¥ ∞ represent the rate of temperature variation, the temperature of the surface, and temperature of surroundings, respectively. According to the assumptions, the plate is slippery and temperature variation is subjected to the surface. The hybrid nanofluid is formulated at first with the addition of Cu solid nanoparticles in EO as basefluid at a fractional size ( ϕ R ) and it is constant at 0.09 throughout the investigation. Graphene oxide GO nanomolecules have been expanded in the mixture to achieve a hybrid nanofluid at the concentricity volume ( ϕ H ) .

2.1 Suppositions and terms of model

Following are the principles along with restrictions applicable to the flowing model:

  1. two-dimensional laminar unsteady flowing,

  2. boundary-layer estimates,

  3. Tiwari and Das (single-phase) technique,

  4. non-Newtonian SBHNF,

  5. porous medium,

  6. thermal radiation flux,

  7. viscous dissipation flow,

  8. shape-factor of nanomolecules,

  9. copper (Cu) and graphene oxide (GO) nanoparticles,

  10. engine-oil (EO) as the base fluid,

  11. porous elongated surface,

  12. slippery as well as convection boundary restrictions.

2.2 Sutterby fluid stress-tensor

In Sutterby model, the stress-tensor is defined as

(2.2) T = − p I + S .

where p and I denote pressure and identity-tensor, respectively, whereas S denotes an additional stress-tensor.

(2.3) S = μ 0 sinh − 1 ( E γ ̇ ) E γ ̇ ς A 1 ,

where μ 0 and E denote zero-shear rate viscosity and material time-constant, respectively. Underneath are the mathematical equations for the second invariant strain tensor γ ̇ and the first order Rivlin–Ericksen tensor A 1 .

(2.4) γ ̇ = tr ( A 1 ) 2 2 ,

and

(2.5) A 1 = ( grad V ) + ( grad V ) T .

In the case of ς = 0, the fluid is equivalent a Newtonian fluid, while at ς > 0 it is pseudoplastic (shear-thinning) fluid, and ς < 0 is dilatant (shear-thickening) fluid.

2.3 Geometric model

Figure 1 depicts the geometrical flow concept.

Figure 1 Scheme of the flow paradigm.
Figure 1

Scheme of the flow paradigm.

Figure 1 depicts the diagram of the flowing model. The flowing in this scheme is caused by the unidirectional extending of the surface. The flow slippery phenomenon occurs at the plate, and thermal jumping is used to transmit heat from the lamina to the liquid.

2.4 Model equations

The constituent flow formulas [79] of viscid SBHNF that have been adeptly modified with porous material, thermal radiative, and viscous dissipative flow under the accustomed boundary-layer approximation are

(2.6) ∂ v 1 ∂ x + ∂ v 2 ∂ y = 0 ,

(2.7) ∂ v 1 ∂ t + v 1 ∂ v 1 ∂ x + v 2 ∂ v 1 ∂ y = μ hnf ρ hnf 1 2 ∂ 2 v 1 ∂ y 2 1 − n b 2 2 ∂ v 1 ∂ y 2 − μ hnf ρ hnf k v 1 ,

(2.8) ∂ ¥ ∂ t + v 1 ∂ ¥ ∂ x + v 2 ∂ ¥ ∂ y = k hnf ( ρ C p ) hnf ∂ 2 ¥ ∂ y 2 − 1 ( ρ C p ) hnf ∂ q r ∂ y + 1 ( ρ C p ) hnf Q ( ¥ − ¥ ∞ ) + μ hnf ( ρ C p ) hnf ∂ v 1 ∂ y 2 .

Aziz et al. [58] gave the related boundary constraints:

(2.9) v 1 ( x , 0 ) = U w + N w ∂ v 1 ∂ y , v 2 ( x , 0 ) = V w , − k 0 ∂ ¥ ∂ y = h f ( ¥ w − ¥) ,

(2.10) v 1 → 0 , ¥ → ¥ ∞    as    y → ∞ .

Vector of flow velocity is defined as v ← = [ v 1 ( x , y , t ) , v 2 ( x , y , t ) , 0 ] . Time is represented by t , and ¥ presents the temperature of the fluid. Q is the heat source. N w is the slip length, V w is the porosity of the extending plate, while k symbolizes the porousness of the material.

2.5 Physical thermal characteristics of SBNF

Nanomolecules spread in EO induce modified thermo-physical properties. The equations of Table 1 synopsizes SBNF variables of the material [80,81].

Table 1

Thermo-physical features for nanoliquids

Features Nanoliquid
Dynamical viscidness ( μ ) μ nf = μ f ( 1 − ϕ ) − 2.5
Density ( ρ ) ρ nf = ( 1 − ϕ ) ρ f − ϕ ρ s
Heat capacity ( ρ C p ) ( ρ C p ) nf = ( 1 − ϕ ) ( ρ C p ) f − ϕ ( ρ C p ) s
Thermal conductivity ( κ ) κ nf κ f = ( κ s + ( m − 1 ) κ f ) − ( m − 1 ) ϕ ( κ f − κ s ) ( κ s + ( m − 1 ) κ f ) + ϕ ( κ f − κ s )

The nanoparticles volume factor ϕ is seen in Table 1. The standard fluid’s dynamical viscidity, density, working heat capacity, and thermal and electrical conductivities are represented by μ f , ρ f , ( C p ) f and κ f , respectively. The density, heat capacity, and thermal conductivity of the nanoparticle are represented by ρ s , ( C p ) s , and κ s , respectively.

2.6 Thermo-physical characteristics of SBHNF

The suspension of two unique kinds of nanomolecules inside the basic fluid is the main premise of hybrid nanofluids [82]. This boosts the heat transfer capability of conventional liquids and makes them a better heat interpreter than nanofluids. Table 2 demonstrates the content of SBHNF variables [57,59].

Table 2 Thermo-

physical properties of hybrid nanofluids

Features Hybrid nanofluid
Viscosity ( μ ) μ hnf = μ f ( 1 − ϕ R ) − 2.5 ( 1 − ϕ H ) − 2.5
Density ( ρ ) ρ hnf = [ ( 1 − ϕ H ) { ( 1 − ϕ R ) ρ f + ϕ R ρ p 1 } ] + ϕ H ρ p 2
Heat capacity ( ρ C p ) ( ρ C p ) hnf = [ ( 1 − ϕ H ) { ( 1 − ϕ R ) ( ρ C p ) f + ϕ R ( ρ C p ) p 1 } ] + ϕ z ( ρ C p ) p 2
Thermal conductivity ( κ ) κ hnf κ gf = ( κ p 2 + ( m − 1 ) κ gf ) − ( m − 1 ) ϕ H ( κ gf − κ p 2 ) ( κ p 2 + ( m − 1 ) κ gf ) + ϕ H ( κ gf − κ p 2 ) κ gf κ f = ( κ p 1 + ( m − 1 ) κ f ) − ( m − 1 ) ϕ R ( κ f − κ p 1 ) ( κ p 1 + ( m − 1 ) κ f ) + ϕ R ( κ f − κ p 1 )

Dynamic viscidity of mixture nanofluid, density, specific heat capacity, and thermal conductivity are all listed in Table 2 as μ hnf , ρ hnf , ρ ( C p ) hnf , and κ hnf . ϕ represents the volumetric coefficient of solid nanomolecules in a mono nanofluid. For the mixed nanofluid, ϕ hnf = ϕ R + ϕ H is the coefficient of hybrid nanoparticles. The dynamical viscidity, density, specific heat capacity, and thermal conductivity of the basefluid are represented by μ f , ρ f , ( C p ) f , κ f , and σ f . The densities, specific heat capacitances, and thermal conductances of the nanomolecules are represented by ρ p 1 , ρ p 2 , ( C p ) p 1 , ( C p ) p 2 , κ p 1 , and κ p 2 , where the subscripts p 1 and p 2 represents Cu and GO nanomolecules, respectively.

The nanomolecules’ shaped-factor defines the size of numerous nanomolecules. The empirical particle form factors are sphere = 3, hexahedron = 3.7221, tetrahedron = 4.0613, column = 6.3698, and lamina = 16.1576 [83].

2.7 Nanosolid-particles and basefluid lineaments

In Table 3 [84–86] of analysis, substantial features of the primary fluid of the engine oil are described.

Table 3

Fabricated materials’ thermo-physical attributes

Thermo-physical ρ ( kg / m 3 ) c p ( J / kgK ) k ( W / mK )
Copper ( Cu ) 8,933 385.0 401.00
Engine oil ( EO ) 884 1,910 0.144
Graphene oxide ( GO ) 1,800 717 5,000

2.8 Rosseland approximation

Due to the thicker non-Newtonian SBHNF, only a shortened distance can be covered by the radiative flow. So, the equation for Rosseland radiative flux given by Brewster [87] is applied in formula (2.8).

(2.11) q r = − 4 σ ⁎ 3 k ⁎ ∂ T 4 ∂ y ,

where σ ⁎ signifies Stefan–Boltzmann constant and k ⁎ symbolizes the rate.

3 Nondimensional transformed system

According to similarity transformation converting the controlling partial differential equations into ordinary differential equations (ODEs), equations (2.7) and (2.8) are boundary-value problem. Stream function ψ is specified as:

(3.1) v 1 = ∂ ψ ∂ y , v 2 = − ∂ ψ ∂ x .

The next specified similarity quantities are applied

(3.2) χ ( x , y ) = b ν f ( 1 − ξ t ) y , ψ ( x , y ) = ν f b ( 1 − ξ t ) x f ( χ ) , θ ( χ ) = ¥ − ¥ ∞ ¥ w − ¥ ∞ ,

in equations (2.7) and (2.8). We get

(3.3) f ‴ + 2 ϕ a ϕ b f f ″ − f ′ 2 + A f ′ + χ 2 f ″ − n 2 λ R e f ″ 2 f ‴ − 2 K f ′ = 0 ,

(3.4) θ ″ 1 + 1 ϕ d P r N r + P r ϕ c ϕ d f θ ′ − f ′ θ + − A θ + χ 2 θ ′ θ Q ϕ c + E c ϕ a ϕ c f ″ 2 = 0 ,

with

(3.5) f ( 0 ) = S , f ′ ( 0 ) = 1 + Λ f ″ ( 0 ) ,       θ ′ ( 0 ) = − B i ( 1 − θ ( 0 ) ) f ′ ( χ ) → 0 , θ ( χ ) → 0 ,    as    χ → ∞ ,

where χ and θ signify the similarity variable and nondimensional temperature, respectively. In equations (3.3)–(3.4), the consecutive thermo-physical structures ϕ a, ϕ b, ϕ c, and ϕ d for SBHNF are specified as

(3.6) ϕ a = ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 , ϕ b = ( 1 − ϕ 2 ) ( 1 − ϕ 1 ) + ϕ 1 ρ p 1 ρ f + ϕ 2 ρ p 2 ρ f ,

(3.7) ϕ c = ( 1 − ϕ 2 ) ( 1 − ϕ 1 ) + ϕ 1 ( ρ C p ) p 1 ( ρ C p ) f + ϕ 2 ( ρ C p ) p 2 ( ρ C p ) f ,

(3.8) ϕ d = ( κ p 2 + ( m − 1 ) κ nf ) − ( m − 1 ) ϕ 2 ( κ nf − κ p 2 ) ( κ p 2 + ( m − 1 ) κ nf ) + ϕ 2 ( κ nf − κ p 2 ) × ( κ p 1 + ( m − 1 ) κ f ) + ϕ 1 ( κ f − κ p 1 ) ( κ p 1 + ( m − 1 ) κ f ) − ( m − 1 ) ϕ 1 ( κ f − κ p 1 ) .

It is noted that equation (2.8) is satisfied directly. In all formulas, ′ symbols differentiate w.r.t χ . A = ξ b , λ = B 2 b 2 , and K = ν f ( 1 − ξ t ) b k , respectively, represent unsteadiness parameter, Deborah number, and porousness of material. P r = ν f α f is the Prandtl amount. Thermal diffusivity parameter, thermal radiative flow, and mass transport are specified as α f = κ f ( ρ C p ) f , N r = 16 3 σ ⁎ ¥ ∞ 3 κ ⁎ ν f ( ρ C p ) f , and S = − V w 1 − ξ t ν f   b , respectively. Λ = b ν f ( 1 − ξ t ) N w is the slippery velocity parameter. E c = U w 2 ( C p ) f ( T w − T ∞ ) and B i = h f k 0 ν f ( 1 − ξ t ) b are the Eckert number and Biot number, respectively. Similarity parameter ( ξ ) and time ( t ) are the parameters on which other variables depend. Hence, a non-similar solution for the model is obtained by determining the final results for locally related parameters.

3.1 Drag force and Nusselt number

The combination of drag force ( C f ) and Nusselt number ( Nu x ) are interesting physical quantities that can control the fluid flow and are specified as [79]

(3.9) C f = τ w ρ f U w 2 , Nu x = x q w k f ( ¥ w − ¥ ∞ ) ,

where τ w and q w are determined as

(3.10) τ w = μ hnf ∂ v 1 ∂ y + n B 2 3 ∂ v 1 ∂ y 3 y = 0 , q w = − k hnf 1 + 16 3 σ ⁎ ¥ ∞ 3 κ ⁎ ν f ( ρ C p ) f ∂ ¥ ∂ y y = 0 .

The dimensionless transmutations (3.2) are implemented to obtain

(3.11) C f Re x 1 2 = 1 ϕ a f ″ ( 0 ) + n 3 λ R e f ″ ( 0 ) 3 , Nu x Re x − 1 2 = − k hnf k f ( 1 + N r ) χ ′ ( 0 ) ,

[ χ e , χ e + 1 ]

where C f represents the coefficient of drag force. Re x = u w x ν f is local R e according to the elongated velocity u w ( x ) .

4 G-FEM: A numerical method

Galerkin finite element technique [88] is used to do numerical computations for governing equations model. The following is a summary of FEM:

  1. On the ordinary term [χ e , χ e+1], the second order nonlinear terms are incorporated to give the powerless integral formulas with weighted remains.

  2. To determine the term of stiffness parameters, powerless residual terms are replaced by finite element formulas.

  3. To compute the rigidity factors, a normal term [χ e , χ e+1] is used, which is then applied to the cluster technique of equations.

  4. The collection of algebraic expressions obtained is linearized. To solve them further, an iterative technique is used with a 10−6 computational tolerance.

  5. A calculational domain is generated by modifying the interval [0, ∞) after identifying the greatest variable value

  6. Convergence is noticeable. To achieve decisive results, computations are done using a step size of Δ χ = 0.001.

Figure 2 depicts the G-FEM flow diagram.

Figure 2 Flow chart of G-FEM.
Figure 2

Flow chart of G-FEM.

5 Code verification

Rate of heat transfer is measured, and the obtained results from the current method are compared with the results from the literature [89,90]. In this way, it can be seen that the method employed is valid. Comparison of some validities among a few analyses is presented in Table 4; however, results obtained during the current study are very accurate.

Table 4

Comparing of − θ ′ ( 0 ) values with Pr , when A = 0 , ϕ = 0 , ϕ hnf = 0 , Q = 0 , E c = 0 , Λ = 0 , N r = 0 , S = 0 , and B i → 0

P r Ref. [89] Ref. [90] Present
72 × 10−2 0.80876122 0.80876181 0.80876181
1 × 100 1.00000000 1.00000000 1.00000000
3 × 100 1.92357431 1.92357420 1.92357420
7 × 100 3.07314679 3.07314651 3.07314651
10 × 100 3.72055436 3.72055429 3.72055429

Unsteadiness of controlling equations was solved by Das et al. [89] with the help of RK-Fehlberg method. Jamshed et al. [90] used KBM to find the solution of the current model. KBM provides better and more accurate solutions compared with other methods.

6 Entropy analysis

The entropy of the system is generally increased by porous media. Entropy formation of the nanofluids is described as [90]:

(6.1) E G = k hnf ¥ ∞ 2 ∂ ¥ ∂ y 2 + 16 3 σ ⁎ ¥ ∞ 3 κ ⁎ ν f ( ρ C p ) f ∂ ¥ ∂ y 2 + μ hnf ¥ ∞ ∂ v 1 ∂ y 2 + μ hnf v 1 2 k ¥ ∞ .

Entropy analysis has the following non-dimensional formula [91]:

(6.2) N G = ¥ ∞ 2 b 2 E G k f ( ¥ w − ¥ ∞ ) 2 .

By formula (3.2), the non-dimensional entropy formula is:

(6.3) N G = R e ϕ d ( 1 + N r ) θ ′ 2 + 1 ϕ a B r Ω ( f ″ 2 + K f ′ 2 ) ,

where R e represents the Reynolds number, Brinkmann number is represented by B r , and Ω symbolizes the dimensionless temperature gradient.

7 Results and discussion

The discussion is based on the numerical outcomes attained from the considered model that are itemized in the previous part. The implied parameters in this section are λ , A , K , ϕ , Λ , N r , B i , E c , Q , S , R e , and B r . Physical performance of dimensionless parameters including entropy, swiftness, and temperature is shown in Figures 3–22. Outcomes for Cu–EO conventional SBNF and GO–Cu/EO non-Newtonian SBHNF are attained. Coefficients of drag force along with temperature variations are described in Table 5. Following are default values λ = 0.1 , A = 0.2 , K = 0.1 , ϕ = 0.18 , ϕ H = 0.09 , Λ = 0.3 , n = 0.2 , Q = 0.3 , P r = 7.38 , N r = 0.3 , B i = 0.2 , E c = 0.2 , R e = 5 , B r = 5 , and S = 0.1 . The effects of Deborah number λ on temperature, entropy outlines, and swiftness of Cu–EO mono SBNF and GO–Cu/EO SBHNF are displayed in Figures 3–5. Calculations are accomplished for λ = 0.1 ,   0.2 ,   0.3 at orderly nanoparticles concentration of ϕ R = 0.09 , ϕ H = 0.09 , and ϕ = 0.18 . The swiftness is enhanced when values of λ are raised as shown in Figure 3. So the thickness of the impetus boundary layer is increased. Increment in λ resulted in reducing the velocity profile which caused the momentum of the border sheet to reduce. Motion of the fluid decreases due to resistance. At λ = 0.1 , GO–Cu/EO hybrid nanoliquid has a comparatively higher thickness of boundary-layer than the Cu–EO nanoliquid. The growing value of the resilience-stress variable resulted in increasing the heat in the boundary layer as shown in Figure 4. The rate of heat transfer, as depicted by Nusselt number, decreases for Cu–EO as well as for GO–Cu/EO. Increment in system entropy is observed with increase in the values of λ , as displayed in Figure 5. The behavioral shifts in the velocity and temperature of hybrid nanoliquid are seen in Figures 6 and 7. The amplitude of the resistive body force decreases with the increase in permeability, so a constant reduction in drag is confronted with fluid, and the flow decreases so that the speed in that borderline tends to zero. The vector K affects the nanofluid density directly by reducing the fluid temperature inside the border layer, leading to a reduction in the fluid permeability of the medium. Entropy of system likewise upsurges, in this case, Figure 8. Increment in variable K increases the heat transfer rate. The influence of nanoparticles size ϕ of mono-nanofluids and ϕ hnf of hybrid-nanofluids are depicted in Figures 9 and 10. Here ϕ R = 0.09 , so analysis is done for varied values of ϕ H . Increment in the values of ϕ and ϕ hnf resulted in the velocity profile of nanofluids decreasing. Meanwhile, a profile of temperature is observed to be elevated. The variable ϕ and ϕ hnf are representing solid nanoparticles volume inside basefluid. As there is a higher thermal conductance in solid-molecules than in traditional liquids, increment in the values of ϕ and ϕ hnf resulted in decreasing the velocity profile of the fluid as shown in Figure 9. Temperature profile in the boundary layer also increases. Figure 12 displays the thickness of the thermal boundary layer to increase with increment in the net thermal conductance of nanofluids. Temperature profile of hybrid nanofluids rises at a higher rate as compared with conventional nanofluids. Figure 11 illustrates that entropy is improved for larger solid nanomolecule sizes. For SBNF and SBHNF, Figures 12–14 show the effect of slippery parameter on the flowing, temperature, and entropy producing outlines, respectively. For the slippery behavior Λ , decreasing behavior in velocity is evident, as the slippery effect decelerated the fluid flowing. The thermal energy of the fluid has an opposite effect as nanofluid temperatures rise with an increase in the variable energy Figure 13. Owing to the increased slip parameter Λ , there is a reduction in the drag force between the fluid and its borders. From Figure 14, the entropy is decreased with rising values of Λ , it can be quickly remarked. Larger Λ values mean that the boundary-layer has a reduced velocity. This decreases the velocity in exchange for reducing the frictional forces within fluid friction, which also reduces frictional irreversibility. Thus, its relation to entropy is reduced by entropy, which reduces the entropy of the system. Figure 15 illustrates how the thermal radiation variable impacts the thermal outlines of SBNF and SBHNF, which shows that the nanofluid temperatures are increased for increasing amounts of N r = 0.1 , 0.3 , 0.5 . The increased heating rate behavior as shown in Table 5 would also contribute to an improvement in thermal rendering and efficacy. If the temperature is boosted, the thickness of the thermal boundary-layer is enhanced. This is because there is a higher heat fluxing. Moreover, heat dissipative transfer E c is the kinetic energy to the gap ratio to the boundary-layer enthalpy. Higher value of E c indicates greater kinetic energy, meanwhile, the friction causes heating on the sheet, which resulted in raising the temperature of the liquid. Figure 17 shows the improvement in temperature with increasing values of E c . The increment in N r and E c parameters can be seen in Figures 16 and 18, respectively on the entropy distribution. According to Table 5, the rate of heat transfer increases for N r and E c in both nanofluids (GO–Cu/EO and Cu–EO), while the gradient of the velocity profile is constant at the plate. Thermal efficiency of the system has a vital role in the shape of nanoparticles. According to the researchers, the surface area of nanoparticles has a major role in increasing or decreasing the heat transfer rate. Analysis is done on the effect of solid nanoparticles on the temperature and system entropy. Figures 19 and 20 show the findings for five different shapes of the nanoparticle. Figure 19 shows the values of the shape-factor while using a different shape. The temperature is boosted for an increased amount of m as seen in Figure 20. In addition, for m = 3 , i.e., spherical nanoparticles, the lowest interface temperature is noticed. It is the result of the net surface area of the sphere along with the highest heat transfer rate of fluid into the inner fluid from the surface. This is also verified by the surface heat transmission coefficient in Table 5. In Figure 22, entropy is boosted with increasing values of m . In the spherical-shaped particles, it is obvious that entropy has the smallest rate. Lastly, Reynolds R e and Brinkmann B r numbers’ impacts are provided on entropy production. The R e value raises the entropy to depend on the outcomes. The interpretation: the inertial forces overpower viscid effects when the R e values are high. As seen in Figure 21, the thermal scheme production of entropy thus boosts. The effect of B r on entropy is shown in Figure 22, where the increase in B r increased the entropy production. The fact is that the rise in B r means more heat is dissipated than heat is carried on the surface and entropy is augmented.

Figure 3 Velocity variation vs λ \lambda .
Figure 3

Velocity variation vs λ .

Figure 4 Temperature variation vs λ \lambda .
Figure 4

Temperature variation vs λ .

Figure 5 Entropy variation vs λ \lambda .
Figure 5

Entropy variation vs λ .

Figure 6 Velocity change with K K .
Figure 6

Velocity change with K .

Figure 7 Temperature change with K K .
Figure 7

Temperature change with K .

Figure 8 Entropy variations against K K .
Figure 8

Entropy variations against K .

Figure 9 Velocity variation vs ϕ \phi and ϕ hnf {\phi }_{\text{hnf}} .
Figure 9

Velocity variation vs ϕ and ϕ hnf .

Figure 10 Temperature variations with ϕ \phi and ϕ hnf {\phi }_{\text{hnf}} .
Figure 10

Temperature variations with ϕ and ϕ hnf .

Figure 11 Entropy variations with ϕ \phi and ϕ hnf {\phi }_{\text{hnf}} .
Figure 11

Entropy variations with ϕ and ϕ hnf .

Figure 12 Velocity variations with Λ \text{&#x039B;} .
Figure 12

Velocity variations with Λ .

Figure 13 Temperature variations with Λ \text{&#x039B;} .
Figure 13

Temperature variations with Λ .

Figure 14 Entropy variations with Λ \text{&#x039B;} .
Figure 14

Entropy variations with Λ .

Figure 15 Temperature variations vs N r {N}_{\text{r}} .
Figure 15

Temperature variations vs N r .

Figure 16 Entropy variations vs N r {N}_{\text{r}} .
Figure 16

Entropy variations vs N r .

Figure 17 Temperature variations vs E c {E}_{\text{c}} .
Figure 17

Temperature variations vs E c .

Figure 18 Entropy variations vs E c {E}_{\text{c}} .
Figure 18

Entropy variations vs E c .

Figure 19 Temperature variations with m m .
Figure 19

Temperature variations with m .

Figure 20 Entropy variations with variable m m .
Figure 20

Entropy variations with variable m .

Figure 21 Entropy variations vs R e {R}_{\text{e}} .
Figure 21

Entropy variations vs R e .

Figure 22 Entropy variations vs B r {B}_{\text{r}} .
Figure 22

Entropy variations vs B r .

Table 5

Values of C f Re x 1 / 2 and Nu x Re x − 1 / 2 for P r = 6 , 450 and n = 0.2

λ S K ϕ ϕ H Λ E c N r B i C f Re x 1 2 Cu–EO C f Re x 1 2 GO–Cu/EO N u Re x − 1 2 Cu–EO N u Re x − 1 2 GO–Cu/EO
0.1 0.1 0.1 0.18 0.09 0.3 0.2 0.3 0.2 1.1833 1.2678 0.1412 0.1623
0.2 0.1602 1.2589 0.1203 0.1564
0.3 0.1487 1.2321 0.1134 0.1461
0.1 1.1833 1.2678 0.1412 0.1623
0.2 1.1920 1.2701 0.1648 0.1789
0.3 1.2161 1.3054 0.1787 0.1831
0.1 1.1833 1.2678 0.1412 0.1623
0.3 1.5055 1.6088 0.1283 0.1290
0.4 1.7526 1.8692 0.1267 0.1273
0.09 0.1721 — 0.0978 —
0.15 0.1765 — 0.1129 —
0.18 1.1833 — 0.1412 —
0.0 — 0.1721 — 0.0978
0.06 — 1.1860 — 0.1344
0.09 — 1.2678 — 0.1623
0.1 2.0156 2.2401 0.1609 0.1984
0.2 1.2316 2.1945 0.1588 0.1793
0.3 1.1833 1.2678 0.1412 0.1623
0.1 1.1833 1.2678 0.1335 0.1407
0.2 1.1833 1.2678 0.1412 0.1623
0.3 1.1833 1.2678 0.1612 0.1820
0.1 1.1833 1.2678 0.1298 0.1450
0.3 1.1833 1.2678 0.1412 0.1623
0.5 1.1833 1.2678 0.1553 0.1756
0.1 1.1833 1.2678 0.1288 0.1356
0.2 1.1833 1.2678 0.1412 0.1623
0.3 1.1833 1.2678 0.1618 0.1829

8 Final results and future guidance

In the current analysis, a permeable stretched surface was carried out to calculate the boundary-layer flow of non-Newtonian EO based on Cu and GO hybrid nanofluids. The KBM was employed in an investigation in the presence of porous regime, viscidness dissipative flowing, form, entropy, and thermal radiative impact. The above procedure has the following summary:

  1. The temperature profile is raised with λ , K , ϕ , ϕ hnf , E c , B i , and N r parameters, while it is declined with Λ .

  2. Velocity is diminished with a swelling impact of λ , ϕ , and ϕ hnf .

  3. Entropy is raised with augmentation in λ , A , K , ϕ , E c B i , N r , S > 0 , B r , and R e , while it is diminished with the increment in Λ , hence the thermal efficiency of the model is enhanced.

  4. For sphere-shaped nanosolid-particles, the utmost heat transport is seen, while for lamina-shaped nanosolid-particles, a lower heat transport is noticed.

  5. According to the current study, Cu-GO/EO hybrid nanofluid is more eminent than Cu/EO in heat transmission.

The results of this analysis can be used as guidance for future research, in which thermal efficacy can be calculated by using various kinds of mixture of non-Newtonian nanoliquids (i.e,. Casson, Falkner–Skan, micropolar, Eyring–Powell, etc.). Furthermore, equations may be generalized to include the effects of the viscidity based on temperature, porousness depending on temperatures, and magneto multi-dimensional slippery flowing.

Acknowledgment

Taif University Researchers Supporting Project number (TURSP-2020/319), Taif University, Taif, Saudi Arabia.

  1. Funding information: Taif University.

  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.

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Received: 2021-12-17
Revised: 2022-02-13
Accepted: 2022-02-16
Published Online: 2022-03-11

© 2022 Jamel Bouslimi et al., published by De Gruyter

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

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https://doi.org/10.1515/ntrev-2022-0070
Keywords for this article
Sutterby hybrid nanofluid; entropy generation; viscous dissipation; finite element; shaped-factor
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Theoretical and experimental investigation of MWCNT dispersion effect on the elastic modulus of flexible PDMS/MWCNT nanocomposites
  3. Mechanical, morphological, and fracture-deformation behavior of MWCNTs-reinforced (Al–Cu–Mg–T351) alloy cast nanocomposites fabricated by optimized mechanical milling and powder metallurgy techniques
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  5. Glutathione-loaded non-ionic surfactant niosomes: A new approach to improve oral bioavailability and hepatoprotective efficacy of glutathione
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  8. Research on a mechanical model of magnetorheological fluid different diameter particles
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  10. Investigative properties of CeO2 doped with niobium: A combined characterization and DFT studies
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  12. N/S co-doped CoSe/C nanocubes as anode materials for Li-ion batteries
  13. Synergistic effects of halloysite nanotubes with metal and phosphorus additives on the optimal design of eco-friendly sandwich panels with maximum flame resistance and minimum weight
  14. Octreotide-conjugated silver nanoparticles for active targeting of somatostatin receptors and their application in a nebulized rat model
  15. Controllable morphology of Bi2S3 nanostructures formed via hydrothermal vulcanization of Bi2O3 thin-film layer and their photoelectrocatalytic performances
  16. Development of (−)-epigallocatechin-3-gallate-loaded folate receptor-targeted nanoparticles for prostate cancer treatment
  17. Enhancement of the mechanical properties of HDPE mineral nanocomposites by filler particles modulation of the matrix plastic/elastic behavior
  18. Effect of plasticizers on the properties of sugar palm nanocellulose/cinnamon essential oil reinforced starch bionanocomposite films
  19. Optimization of nano coating to reduce the thermal deformation of ball screws
  20. Preparation of efficient piezoelectric PVDF–HFP/Ni composite films by high electric field poling
  21. MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon
  22. Effects of nano-SiO2 modification on rubberised mortar and concrete with recycled coarse aggregates
  23. Mechanical and microscopic properties of fiber-reinforced coal gangue-based geopolymer concrete
  24. Effect of morphology and size on the thermodynamic stability of cerium oxide nanoparticles: Experiment and molecular dynamics calculation
  25. Mechanical performance of a CFRP composite reinforced via gelatin-CNTs: A study on fiber interfacial enhancement and matrix enhancement
  26. A practical review over surface modification, nanopatterns, emerging materials, drug delivery systems, and their biophysiochemical properties for dental implants: Recent progresses and advances
  27. HTR: An ultra-high speed algorithm for cage recognition of clathrate hydrates
  28. Effects of microalloying elements added by in situ synthesis on the microstructure of WCu composites
  29. A highly sensitive nanobiosensor based on aptamer-conjugated graphene-decorated rhodium nanoparticles for detection of HER2-positive circulating tumor cells
  30. Progressive collapse performance of shear strengthened RC frames by nano CFRP
  31. Core–shell heterostructured composites of carbon nanotubes and imine-linked hyperbranched polymers as metal-free Li-ion anodes
  32. A Galerkin strategy for tri-hybridized mixture in ethylene glycol comprising variable diffusion and thermal conductivity using non-Fourier’s theory
  33. Simple models for tensile modulus of shape memory polymer nanocomposites at ambient temperature
  34. Preparation and morphological studies of tin sulfide nanoparticles and use as efficient photocatalysts for the degradation of rhodamine B and phenol
  35. Polyethyleneimine-impregnated activated carbon nanofiber composited graphene-derived rice husk char for efficient post-combustion CO2 capture
  36. Electrospun nanofibers of Co3O4 nanocrystals encapsulated in cyclized-polyacrylonitrile for lithium storage
  37. Pitting corrosion induced on high-strength high carbon steel wire in high alkaline deaerated chloride electrolyte
  38. Formulation of polymeric nanoparticles loaded sorafenib; evaluation of cytotoxicity, molecular evaluation, and gene expression studies in lung and breast cancer cell lines
  39. Engineered nanocomposites in asphalt binders
  40. Influence of loading voltage, domain ratio, and additional load on the actuation of dielectric elastomer
  41. Thermally induced hex-graphene transitions in 2D carbon crystals
  42. The surface modification effect on the interfacial properties of glass fiber-reinforced epoxy: A molecular dynamics study
  43. Molecular dynamics study of deformation mechanism of interfacial microzone of Cu/Al2Cu/Al composites under tension
  44. Nanocolloid simulators of luminescent solar concentrator photovoltaic windows
  45. Compressive strength and anti-chloride ion penetration assessment of geopolymer mortar merging PVA fiber and nano-SiO2 using RBF–BP composite neural network
  46. Effect of 3-mercapto-1-propane sulfonate sulfonic acid and polyvinylpyrrolidone on the growth of cobalt pillar by electrodeposition
  47. Dynamics of convective slippery constraints on hybrid radiative Sutterby nanofluid flow by Galerkin finite element simulation
  48. Preparation of vanadium by the magnesiothermic self-propagating reduction and process control
  49. Microstructure-dependent photoelectrocatalytic activity of heterogeneous ZnO–ZnS nanosheets
  50. Cytotoxic and pro-inflammatory effects of molybdenum and tungsten disulphide on human bronchial cells
  51. Improving recycled aggregate concrete by compression casting and nano-silica
  52. Chemically reactive Maxwell nanoliquid flow by a stretching surface in the frames of Newtonian heating, nonlinear convection and radiative flux: Nanopolymer flow processing simulation
  53. Nonlinear dynamic and crack behaviors of carbon nanotubes-reinforced composites with various geometries
  54. Biosynthesis of copper oxide nanoparticles and its therapeutic efficacy against colon cancer
  55. Synthesis and characterization of smart stimuli-responsive herbal drug-encapsulated nanoniosome particles for efficient treatment of breast cancer
  56. Homotopic simulation for heat transport phenomenon of the Burgers nanofluids flow over a stretching cylinder with thermal convective and zero mass flux conditions
  57. Incorporation of copper and strontium ions in TiO2 nanotubes via dopamine to enhance hemocompatibility and cytocompatibility
  58. Mechanical, thermal, and barrier properties of starch films incorporated with chitosan nanoparticles
  59. Mechanical properties and microstructure of nano-strengthened recycled aggregate concrete
  60. Glucose-responsive nanogels efficiently maintain the stability and activity of therapeutic enzymes
  61. Tunning matrix rheology and mechanical performance of ultra-high performance concrete using cellulose nanofibers
  62. Flexible MXene/copper/cellulose nanofiber heat spreader films with enhanced thermal conductivity
  63. Promoted charge separation and specific surface area via interlacing of N-doped titanium dioxide nanotubes on carbon nitride nanosheets for photocatalytic degradation of Rhodamine B
  64. Elucidating the role of silicon dioxide and titanium dioxide nanoparticles in mitigating the disease of the eggplant caused by Phomopsis vexans, Ralstonia solanacearum, and root-knot nematode Meloidogyne incognita
  65. An implication of magnetic dipole in Carreau Yasuda liquid influenced by engine oil using ternary hybrid nanomaterial
  66. Robust synthesis of a composite phase of copper vanadium oxide with enhanced performance for durable aqueous Zn-ion batteries
  67. Tunning self-assembled phases of bovine serum albumin via hydrothermal process to synthesize novel functional hydrogel for skin protection against UVB
  68. A comparative experimental study on damping properties of epoxy nanocomposite beams reinforced with carbon nanotubes and graphene nanoplatelets
  69. Lightweight and hydrophobic Ni/GO/PVA composite aerogels for ultrahigh performance electromagnetic interference shielding
  70. Research on the auxetic behavior and mechanical properties of periodically rotating graphene nanostructures
  71. Repairing performances of novel cement mortar modified with graphene oxide and polyacrylate polymer
  72. Closed-loop recycling and fabrication of hydrophilic CNT films with high performance
  73. Design of thin-film configuration of SnO2–Ag2O composites for NO2 gas-sensing applications
  74. Study on stress distribution of SiC/Al composites based on microstructure models with microns and nanoparticles
  75. PVDF green nanofibers as potential carriers for improving self-healing and mechanical properties of carbon fiber/epoxy prepregs
  76. Osteogenesis capability of three-dimensionally printed poly(lactic acid)-halloysite nanotube scaffolds containing strontium ranelate
  77. Silver nanoparticles induce mitochondria-dependent apoptosis and late non-canonical autophagy in HT-29 colon cancer cells
  78. Preparation and bonding mechanisms of polymer/metal hybrid composite by nano molding technology
  79. Damage self-sensing and strain monitoring of glass-reinforced epoxy composite impregnated with graphene nanoplatelet and multiwalled carbon nanotubes
  80. Thermal analysis characterisation of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: An optimal thermal application
  81. Pyrene-functionalized halloysite nanotubes for simultaneously detecting and separating Hg(ii) in aqueous media: A comprehensive comparison on interparticle and intraparticle excimers
  82. Fabrication of self-assembly CNT flexible film and its piezoresistive sensing behaviors
  83. Thermal valuation and entropy inspection of second-grade nanoscale fluid flow over a stretching surface by applying Koo–Kleinstreuer–Li relation
  84. Mechanical properties and microstructure of nano-SiO2 and basalt-fiber-reinforced recycled aggregate concrete
  85. Characterization and tribology performance of polyaniline-coated nanodiamond lubricant additives
  86. Combined impact of Marangoni convection and thermophoretic particle deposition on chemically reactive transport of nanofluid flow over a stretching surface
  87. Spark plasma extrusion of binder free hydroxyapatite powder
  88. An investigation on thermo-mechanical performance of graphene-oxide-reinforced shape memory polymer
  89. Effect of nanoadditives on the novel leather fiber/recycled poly(ethylene-vinyl-acetate) polymer composites for multifunctional applications: Fabrication, characterizations, and multiobjective optimization using central composite design
  90. Design selection for a hemispherical dimple core sandwich panel using hybrid multi-criteria decision-making methods
  91. Improving tensile strength and impact toughness of plasticized poly(lactic acid) biocomposites by incorporating nanofibrillated cellulose
  92. Green synthesis of spinel copper ferrite (CuFe2O4) nanoparticles and their toxicity
  93. The effect of TaC and NbC hybrid and mono-nanoparticles on AA2024 nanocomposites: Microstructure, strengthening, and artificial aging
  94. Excited-state geometry relaxation of pyrene-modified cellulose nanocrystals under UV-light excitation for detecting Fe3+
  95. Effect of CNTs and MEA on the creep of face-slab concrete at an early age
  96. Effect of deformation conditions on compression phase transformation of AZ31
  97. Application of MXene as a new generation of highly conductive coating materials for electromembrane-surrounded solid-phase microextraction
  98. A comparative study of the elasto-plastic properties for ceramic nanocomposites filled by graphene or graphene oxide nanoplates
  99. Encapsulation strategies for improving the biological behavior of CdS@ZIF-8 nanocomposites
  100. Biosynthesis of ZnO NPs from pumpkin seeds’ extract and elucidation of its anticancer potential against breast cancer
  101. Preliminary trials of the gold nanoparticles conjugated chrysin: An assessment of anti-oxidant, anti-microbial, and in vitro cytotoxic activities of a nanoformulated flavonoid
  102. Effect of micron-scale pores increased by nano-SiO2 sol modification on the strength of cement mortar
  103. Fractional simulations for thermal flow of hybrid nanofluid with aluminum oxide and titanium oxide nanoparticles with water and blood base fluids
  104. The effect of graphene nano-powder on the viscosity of water: An experimental study and artificial neural network modeling
  105. Development of a novel heat- and shear-resistant nano-silica gelling agent
  106. Characterization, biocompatibility and in vivo of nominal MnO2-containing wollastonite glass-ceramic
  107. Entropy production simulation of second-grade magnetic nanomaterials flowing across an expanding surface with viscidness dissipative flux
  108. Enhancement in structural, morphological, and optical properties of copper oxide for optoelectronic device applications
  109. Aptamer-functionalized chitosan-coated gold nanoparticle complex as a suitable targeted drug carrier for improved breast cancer treatment
  110. Performance and overall evaluation of nano-alumina-modified asphalt mixture
  111. Analysis of pure nanofluid (GO/engine oil) and hybrid nanofluid (GO–Fe3O4/engine oil): Novel thermal and magnetic features
  112. Synthesis of Ag@AgCl modified anatase/rutile/brookite mixed phase TiO2 and their photocatalytic property
  113. Mechanisms and influential variables on the abrasion resistance hydraulic concrete
  114. Synergistic reinforcement mechanism of basalt fiber/cellulose nanocrystals/polypropylene composites
  115. Achieving excellent oxidation resistance and mechanical properties of TiB2–B4C/carbon aerogel composites by quick-gelation and mechanical mixing
  116. Microwave-assisted sol–gel template-free synthesis and characterization of silica nanoparticles obtained from South African coal fly ash
  117. Pulsed laser-assisted synthesis of nano nickel(ii) oxide-anchored graphitic carbon nitride: Characterizations and their potential antibacterial/anti-biofilm applications
  118. Effects of nano-ZrSi2 on thermal stability of phenolic resin and thermal reusability of quartz–phenolic composites
  119. Benzaldehyde derivatives on tin electroplating as corrosion resistance for fabricating copper circuit
  120. Mechanical and heat transfer properties of 4D-printed shape memory graphene oxide/epoxy acrylate composites
  121. Coupling the vanadium-induced amorphous/crystalline NiFe2O4 with phosphide heterojunction toward active oxygen evolution reaction catalysts
  122. Graphene-oxide-reinforced cement composites mechanical and microstructural characteristics at elevated temperatures
  123. Gray correlation analysis of factors influencing compressive strength and durability of nano-SiO2 and PVA fiber reinforced geopolymer mortar
  124. Preparation of layered gradient Cu–Cr–Ti alloy with excellent mechanical properties, thermal stability, and electrical conductivity
  125. Recovery of Cr from chrome-containing leather wastes to develop aluminum-based composite material along with Al2O3 ceramic particles: An ingenious approach
  126. Mechanisms of the improved stiffness of flexible polymers under impact loading
  127. Anticancer potential of gold nanoparticles (AuNPs) using a battery of in vitro tests
  128. Review Articles
  129. Proposed approaches for coronaviruses elimination from wastewater: Membrane techniques and nanotechnology solutions
  130. Application of Pickering emulsion in oil drilling and production
  131. The contribution of microfluidics to the fight against tuberculosis
  132. Graphene-based biosensors for disease theranostics: Development, applications, and recent advancements
  133. Synthesis and encapsulation of iron oxide nanorods for application in magnetic hyperthermia and photothermal therapy
  134. Contemporary nano-architectured drugs and leads for ανβ3 integrin-based chemotherapy: Rationale and retrospect
  135. State-of-the-art review of fabrication, application, and mechanical properties of functionally graded porous nanocomposite materials
  136. Insights on magnetic spinel ferrites for targeted drug delivery and hyperthermia applications
  137. A review on heterogeneous oxidation of acetaminophen based on micro and nanoparticles catalyzed by different activators
  138. Early diagnosis of lung cancer using magnetic nanoparticles-integrated systems
  139. Advances in ZnO: Manipulation of defects for enhancing their technological potentials
  140. Efficacious nanomedicine track toward combating COVID-19
  141. A review of the design, processes, and properties of Mg-based composites
  142. Green synthesis of nanoparticles for varied applications: Green renewable resources and energy-efficient synthetic routes
  143. Two-dimensional nanomaterial-based polymer composites: Fundamentals and applications
  144. Recent progress and challenges in plasmonic nanomaterials
  145. Apoptotic cell-derived micro/nanosized extracellular vesicles in tissue regeneration
  146. Electronic noses based on metal oxide nanowires: A review
  147. Framework materials for supercapacitors
  148. An overview on the reproductive toxicity of graphene derivatives: Highlighting the importance
  149. Antibacterial nanomaterials: Upcoming hope to overcome antibiotic resistance crisis
  150. Research progress of carbon materials in the field of three-dimensional printing polymer nanocomposites
  151. A review of atomic layer deposition modelling and simulation methodologies: Density functional theory and molecular dynamics
  152. Recent advances in the preparation of PVDF-based piezoelectric materials
  153. Recent developments in tensile properties of friction welding of carbon fiber-reinforced composite: A review
  154. Comprehensive review of the properties of fly ash-based geopolymer with additive of nano-SiO2
  155. Perspectives in biopolymer/graphene-based composite application: Advances, challenges, and recommendations
  156. Graphene-based nanocomposite using new modeling molecular dynamic simulations for proposed neutralizing mechanism and real-time sensing of COVID-19
  157. Nanotechnology application on bamboo materials: A review
  158. Recent developments and future perspectives of biorenewable nanocomposites for advanced applications
  159. Nanostructured lipid carrier system: A compendium of their formulation development approaches, optimization strategies by quality by design, and recent applications in drug delivery
  160. 3D printing customized design of human bone tissue implant and its application
  161. Design, preparation, and functionalization of nanobiomaterials for enhanced efficacy in current and future biomedical applications
  162. A brief review of nanoparticles-doped PEDOT:PSS nanocomposite for OLED and OPV
  163. Nanotechnology interventions as a putative tool for the treatment of dental afflictions
  164. Recent advancements in metal–organic frameworks integrating quantum dots (QDs@MOF) and their potential applications
  165. A focused review of short electrospun nanofiber preparation techniques for composite reinforcement
  166. Microstructural characteristics and nano-modification of interfacial transition zone in concrete: A review
  167. Latest developments in the upconversion nanotechnology for the rapid detection of food safety: A review
  168. Strategic applications of nano-fertilizers for sustainable agriculture: Benefits and bottlenecks
  169. Molecular dynamics application of cocrystal energetic materials: A review
  170. Synthesis and application of nanometer hydroxyapatite in biomedicine
  171. Cutting-edge development in waste-recycled nanomaterials for energy storage and conversion applications
  172. Biological applications of ternary quantum dots: A review
  173. Nanotherapeutics for hydrogen sulfide-involved treatment: An emerging approach for cancer therapy
  174. Application of antibacterial nanoparticles in orthodontic materials
  175. Effect of natural-based biological hydrogels combined with growth factors on skin wound healing
  176. Nanozymes – A route to overcome microbial resistance: A viewpoint
  177. Recent developments and applications of smart nanoparticles in biomedicine
  178. Contemporary review on carbon nanotube (CNT) composites and their impact on multifarious applications
  179. Interfacial interactions and reinforcing mechanisms of cellulose and chitin nanomaterials and starch derivatives for cement and concrete strength and durability enhancement: A review
  180. Diamond-like carbon films for tribological modification of rubber
  181. Layered double hydroxides (LDHs) modified cement-based materials: A systematic review
  182. Recent research progress and advanced applications of silica/polymer nanocomposites
  183. Modeling of supramolecular biopolymers: Leading the in silico revolution of tissue engineering and nanomedicine
  184. Recent advances in perovskites-based optoelectronics
  185. Biogenic synthesis of palladium nanoparticles: New production methods and applications
  186. A comprehensive review of nanofluids with fractional derivatives: Modeling and application
  187. Electrospinning of marine polysaccharides: Processing and chemical aspects, challenges, and future prospects
  188. Electrohydrodynamic printing for demanding devices: A review of processing and applications
  189. Rapid Communications
  190. Structural material with designed thermal twist for a simple actuation
  191. Recent advances in photothermal materials for solar-driven crude oil adsorption
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