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CFD analysis of paraffin-based hybrid (Co–Au) and trihybrid (Co–Au–ZrO2) nanofluid flow through a porous medium

  • Dezhi Yang , Sohail Ahmad , Kashif Ali , Salem Algarni , Talal Alqahtani , Wasim Jamshed EMAIL logo , Syed M. Hussain , Kashif Irshad and Hijaz Ahmad
Published/Copyright: May 17, 2024
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 13 Issue 1

Abstract

Ternary hybrid nanofluids possess improved thermal characteristics, enhanced stability, better physical strength, and multi-functionality as compared to hybrid or usual nanofluids. The aim of the ongoing study is to explore the novel thermal attributes of hybrid and trihybrid nanofluids through a porous medium. Whereas the nano-composition of cobalt (Co), gold (Au), and zirconium oxide (ZrO2) make amalgamation in the paraffin (Pfin) which is a base fluid. This nano-composition of the proposed nanoparticles, specifically, subject to the base fluid Pfin has not been interpreted before. The analysis not only covers the features of trihybrid nanofluids (Co–Au–ZrO2–Pfin) but it also describes the characteristics of hybrid (Co–Au–Pfin) as well as pure nanofluids (Co–Pfin). An efficient numerical algorithm is developed for which the numerical simulations are carried out. The approximations are performed in MATLAB software using “Successive under Relaxation (SUR)” technique. A comparison, under certain limiting conditions, with the established results appraises the efficiency of the numerical code. The outcomes evidently designate that temperature raises with the change in thermal radiation and volume fraction of gold and zirconium oxide in either case of pure, hybrid, or ternary nanofluids. The concentration ϕ 3 of ZrO2 has a significant impact on Nusselt number rather than the concentration ϕ 1 of cobalt and ϕ 2 of gold. It has been comparatively noticed that the ternary nanofluids (Co–Au–ZrO2–Pfin) portray embellished and improvised thermal characteristics as compared to the other two cases.

Keywords: zirconium oxide; cobalt; gold; ternary hybrid nanofluids; paraffin; porous medium; SUR technique

1 Introduction

The fluids that are engineered in such a way that the solid fragments of metallic or non-metallic materials are dispersed in the base fluids can be referred to as the nanofluids. These fluids have the capacity to embellish the thermal conductivity of host liquids, and this particular property makes them considerable in several scientific zones. An enhancement in the thermal and physical properties of base fluids are due to the nanofluids [1,2,3,4,5]. The amalgamation of three distinct nanoparticles into the base liquids gives rise to the ternary case of nanofluids and this mixture is called trihybrid or ternary hybrid nanofluids. Using several kinds of nanoparticles, ternary hybrid nanofluids offer a framework for designing nanofluid properties, opening new opportunities for improved thermal, mechanical, and electrical capabilities in a variety of applications. Some potential utilizations of ternary, mono, and hybrid nanofluids are as follows: electronics cooling to reduce the risk of overheating [6]; solar thermal collectors by enhancing the absorption of solar radiation [7,8]; heat transfer enhancement in cooling systems, electronic devices, and heat exchangers (Panduro and Finotti [9]); and use in biomedical sciences like cancer therapy, tissue engineering and drug delivery [10,11]. The further prominent applications involve lubricants, engine cooling, oil recovery, and nuclear reactor cooling.

The current work reveals the novel features of three distinct nanoparticles, e.g., cobalt, gold, and zirconium oxide which combined make ternary hybrid nanofluids Co–Au–ZrO2/Pfin. Cobalt is a silvery-blue lustrous metal. It exhibits magnetic features, and is widely used in the preparation of magnets. Cobalt can produce power magnets when alloyed with nickel and aluminum. The recent uses of radioactive cobalt involve cancer treatment and food preservation. The other uses of cobalt alloys are jet and gas turbine generators, electroplating, and resistance to corrosion, and cobalt salt produces blue colors in pottery, glass, and paint. The cobalt, subject to different perspectives, has been investigated by several researchers. Rahman Salari [12] synthesized the tin dioxide (SnO2) and cobalt oxide (CO3) in the preparation of water-based nanofluid. They characterized the structural mechanism of nanoparticles by scanning, X-Ray diffraction, and Fourier transformation infrared spectroscopy. An investigation into the cobalt-based nanofluid with a concentration of 0.1–0.41 % was presented by Sekhar et al. [13]. The major aim, of their research, was to measure the conductivity of fluid as well as relative viscosity over a 30–60°C temperature range limit. Farooq et al. [14] comparatively analyzed the hybrid nanofluids Ag-COFe2O4 composed of silver and cobalt ferrite in the coexistence of magnetic field. Mathematical investigations were performed by Murtaza et al. [15] which incorporates the cobalt particles to synthesize the nanofluid with the impact of second-order slip and variable viscosity. Santhosh and Sivaraj [16] anticipated a hydro-magnetic flow inside a porous enclosure with mixed convective heat transfer. The enclosure contained base fluid (kerosene oil) and the ferromagnetic cobalt particles. Their results spotted that the blade-shaped cobalt nanoparticles had better effect on the heat transfer rather than the spherical-shaped cobalt nanoparticles. Mandal et al. [17] and Biswas et al. [18,19] examined the bio-convective flows through porous medium.

Gold is a chemical element and a precious metal having the symbol Au. In pure or natural form, it is a malleable, soft, dense, bright, ductile, and yellow-colored metal. In ancient times, gold was used as currency in the form of coins. Most of the gold in the world (78%) is used in jewelry. It is also used in electronics, medicine, and dentistry. Gold is most dense than all metals and good conductor of electricity as well as heat. The use of gold, in the thermal analysis, is found in many studies. Tsai et al. [20] analyzed various sized gold nanoparticles in an aqueous solution inside a circular heat pipe. The thermal resistance was noted to vary in the pipe with the change in the gold size of nanomaterial. The blood-based heat transfer micropolar nanofluid flow involving gold as nanoparticles was speculated by Khan et al. [21]. Several effects like microorganisms, Brownian motion, and chemically reactive activation energy were taken into consideration. Numerical studies of gold/water nanofluid and gold/blood nanofluid flow over a disk and within a permeable channel were studied by Magodora et al. [22] and Srinivas et al. [23], respectively. The work of Burgos et al. [24] described a statistical and experimental analysis of the gold nanoparticles on nanofluids stability and photothermal properties of the solar nanofluids.

The fusion-reduction process of zircon sand (zirconium silicate) gives rise to zirconia which is also recognized as zirconium di-oxide ZrO2. The ceramic industry encompasses the potential employments of ZrO2. This metal is inorganic in nature with better thermal and corrosion resistance, high refractory, and strong chemical inertness but low solubility and biocompatibility. Some recent investigations based on ZrO2 nanoparticles can be studied in various research works [25–29].

The ternary hybrid nanofluids subject to different physical conditions have been examined recently by the research community. Shao et al. [30] investigated the natural convection phenomenon inside a prismatic porous enclosure filled with ternary hybrid nanofluid having two hot movable baffles. The simulations were performed to look into the effects of length between baffles and Darcy number on the thermal characteristics of trihybrid nanofluids. Some limitations in the mono nanofluids and advantages of the ternary hybrid nanofluids were pointed out by Adun et al. [31] in a review analysis of ternary hybrid nanofluids. In their analysis, they discussed the heat transfer characteristics, thermophysical properties, stability, and synthesis of ternary hybrid nanofluids. Algehyne et al. [32] used the non-Fourier’s concept and variable diffusion to numerically elaborate the trihybrid nanofluids involving nanoparticles of magnesium oxide (MgO), cobalt ferrite (CoFe2O4), and titanium dioxide (TiO2). Their results spotted that hybrid and trihybrid case of nanofluids had a better efficiency for velocity propagation rate and fluid energy. The usages of three different types of nanoparticles (trihybrid case) and their importance in heat transport rate subject to dynamics of coolant in automobiles and fuel were prescribed by Elnaqeeb et al. [33]. The ternary nanofluid was prepared using the nano-composition of Ag–TiO2–Cu/water (Li et al. [34]). Some prominent effects like temperature jump and Troian and Thomson slip conditions were considered in the model problem. The RKF-45 methodology was incorporated to determine the approximate solution of the problems. It was examined (in this research) that the flow speed got reduced by the slip in the velocity. The recent works [35,36,37,38,39,40,41,42,43,44,45] further interpret the relevant studies. Some recent studies consisting of several trihybrid nanoparticles are portrayed in Table 1.

Table 1

Some recent studies consisting of several trihybrid nanoparticles

References Nanoparticles Base fluid Prominent effects
Abeer et al. [46] TiO2–CuO–Al2O3 Blood Ohmic heat, energy emission/absorption, nonlinear thermal radiation
Yaseen et al. [47] CNT–Cu–Al2O3 Water Second-degree thermal radiation, magnetic field
Cao et al. [48] CNTs–Go–Al Ethylene glycol Mixed convection, partial slip
Noreen et al. [49] SiO2–Fe3O4–Cu Kerosene oil Magnetohydrodynamics
Nabwey et al. [50] Ag–TiO2–Al2O3 Water Magnetic field, radiative heat flux

A survey of the existing literature portrays the fact that the nano-composition of trihybrid nanoparticles (as in the present study) is not interpreted yet. The proposed nanoparticles such as cobalt, gold, and zirconium oxide have special characteristics owing to their thermo-physical properties. Paraffin (Pfin) which is the base fluid, in the present case, often exists in both solid and liquid form, and involves a wide range of industrial and commercial applications like beauty products, heating oil, medicines, and candles. The aim of this study is to explore the new feature of Pfin-based ternary hybrid nanofluids Co–Au–ZrO2/Pfin incorporating the cobalt, gold, and zirconium oxide particles. The analysis is further extended to investigate the pure and hybrid case of nanofluids using Co/Pfin nanofluid and Co–Au/Pfin hybrid nanofluid.

2 Mathematical and physical aspects of the problem

A trihybrid nano-composition of zirconium oxide, cobalt, and gold nanoparticles is amalgamated in a host fluid to prepare the ternary hybrid nanofluids Co–Au–ZrO2–Pfin. The liquid form of Pfin, in the present case, is assumed to be the base fluid. Three cases of nanofluids such as:

i) Pure nanofluid which comprises of Cobalt–Pfin,

ii) Hybrid nanofluid which comprises of Cobalt–Gold–Pfin, and

iii) Trihybrid nanofluid which comprises of Cobalt–Gold–Zirconium oxide–Pfin

are incorporated to analyze their thermal performance. The y-axis and x-axis are, respectively, taken across and along the flow over a surface. The force B 0 is applied in the same direction for which the y-axis is taken (Figure 1).

Figure 1 The problem structure.
Figure 1

The problem structure.

Flow is occurring through a porous medium. The velocity U w ( x ) represents the rate at which the surface is being stretched. The vector form of the general nanofluid flow model involving heat and mass transfer characteristics is given below:

(1) ρ ∂ u ¯ ∂ t + ( u ¯ ⋅ ∇ ) u ¯ = − ∇ p + μ ∇ 2 u ¯ + ρ g , ρ C p ∂ T ∂ t + ( u ¯ ⋅ ∇ ) T = ∇ ⋅ ( k ∇ T ) + φ , ρ ∂ C ∂ t + ( u ¯ ⋅ ∇ ) C = ∇ ⋅ ( D ∇ C ) , ,

where u ¯ is the velocity vector field of the fluid, ρ is the fluid density, T is the temperature, C p is the specific heat capacity at constant pressure, φ represents any volumetric heat sources, t is the time, D is the mass diffusivity, μ is the dynamic viscosity of the fluid, g ¯ is the gravitational acceleration vector, k is the thermal conductivity, p is the pressure, and C is the concentration of the species.

The governing equations are followed by the recently established models [51,52,53] that describe the hybrid and trihybrid cases of nanofluids.

2.1 Momentum equation

The momentum equation of the problem can be given as

(2) u ∂ u ∂ x + v ∂ u ∂ y = υ Tnf ∂ 2 u ∂ y 2 − μ Tnf ρ Tnf k ⁎ u − σ Tnf ρ Tnf B 0 2 u ,

Equation (2) is the derived or modified form of the Navier–Stokes momentum equation which is interlinked with the Darcy’s law. This law basically governs the fluid’s movement through any porous material or media. The inter-connectivity of pores in a medium is recognized as permeability. The second last term in the above equation illustrates the Darcy’s law whereas the last term designates the applied magnetic field effect. The terms on the left-hand side of equation (2) represent the inertia forces. The basic task of these forces is to keep particles away from the layer. On the other hand, the first term υ Tnf ∂ 2 u ∂ y 2 on the right side of the same equation represents the viscous force that causes the smooth movement of the layers over one another. The terms in equation (2) can be communicated as follows:

ρ Tnf expresses the trihybrid nanofluid’s density
u symbolizes the horizontal velocity component
μ Tnf shows the viscosity of the trihybrid nanofluid
B 0 defines the magnetic field strength
k ⁎ demonstrates the permeability of the porous medium
v signifies the vertical component of velocity
σ Tnf expresses the electrical conductivity of the trihybrid nanofluid
v Tnf describes the trihybrid nanofluid’s kinematic viscosity

2.2 Energy equation

The thermal radiation effect is assumed in the energy equation that is given below:

(3) u ∂ T ∂ x + v ∂ T ∂ y = K Tnf ( ρ C p ) Tnf ∂ 2 T ∂ y 2 − 1 ( ρ C p ) Tnf ∂ Q R ∂ y ,

where the trihybrid nanofluid’s thermal diffusivity is denoted by α hnf , and the temperature of the fluid is represented by T . The first derivative terms like ∂ T ∂ x and ∂ T ∂ y of equation (3) describe the thermal convection whereas the term ∂ 2 T ∂ y 2 portrays the thermal diffusion. The diffusion occurs because of the differences in the surface temperature and the fluid's temperature. The terms ( ρ C p ) Tnf and K Tnf are used, respectively, for the heat capacity and thermal conductivity.

The term Q R expresses the radiation heat flux which is often known as thermal radiation (in the dynamical problems). On the other side, thermal radiation is followed by the Rosseland’s approximation (Sheikholeslami et al. [54,55]). By incorporating this approximation to simplify Q R , we have

(4) q r = − 4 σ 3 k 0 ∂ T 4 ∂ y ,

where the mean absorption coefficient as well as the Stefan–Boltzmann constant is, respectively, represented by k 0 and σ . In order to linearize T 4 given in equation (4), we use the following relation:

(5) T 4 = 4 T ∞ 3 T − 3 T ∞ 4 ,

Using relations (3) and (4), equation (3) attains the form

(6) u ∂ T ∂ x + v ∂ T ∂ y = K Tnf ( ρ C p ) Tnf ∂ 2 T ∂ y 2 + 16 σ 0 T ∞ 3 3 k 0 ( ρ C p ) Tnf ∂ 2 T ∂ y 2 ,

2.3 Concentration equation

The species that are assumed to be chemically reactive are also involved in the mixture of Pfin-based trihybrid nanofluids. Due to the involvement of species, the flow will definitely contain the mass transfer phenomenon. The concentration C having unit mol/m 3 , in this way, comprises of the homogeneous mixture. However, an irreversible and homogeneous reaction occurs in the flow because of the species involvement. Using these premises, the concentration equation is given by

(7) u ∂ C ∂ x + v ∂ C ∂ y = D B ∂ 2 C ∂ y 2 − K r ( C − C ∞ ) ,

where D B and K r depict the mass diffusivity and chemical reaction rate constant. The term K r basically determines the rate at which the chemical reaction occurs. It can be concluded from the last term (with negative sign) in the above equation that the chemical reaction tends to deteriorate the species in the flow.

2.4 Boundary conditions

The proposed boundary constraints at y = 0 and y → ∞ have the form [56]

(8) T ( x , 0 ) = T w , v ( x , 0 ) = − v 0 , u ( x , 0 ) = U w ( x ) = c x , C ( x , 0 ) = C w a t y = 0 T ( x , ∞ ) = T ∞ , u ( x , ∞ ) = 0 , C ( x , ∞ ) = C ∞ at y → ∞ ,

whereas the suction having velocity v 0 occurs at v 0 > 0 . The temperatures T ∞ and T w are specified at y → ∞ and y = 0 , respectively. In the same manners, C w and C ∞ are the concentrations at the surface and apart from the surface. The velocity for which the surface stretches is U ( x , 0 ) = U w ( x ) = c x .

2.5 Thermo-physical characteristics of pure, hybrid, and trihybrid nanofluids

The combination of Co, Ag, and ZrO2 nanoparticles is taken with 0.1 volume fraction each. The ternary nanofluid (Co–Au–ZrO2–Pfin) is prepared by the addition of Co ( ϕ 1 ), Ag ( ϕ 2 ), and ZrO2 ( ϕ 3 ) nanoparticles in the host liquid which is Pfin in the present case. The basic physical properties of the nanofluids in pure, hybrid, and trihybrid cases (engaged from the standard literature [57,58]) are portrayed in Tables 2 and 3.

Table 2

Mathematical relations for electrical and thermal conductivities of nanofluids

Nanofluids Electrical conductivity Thermal conductivity
Pure nanofluid σ nf σ f = 1 + 3 ( σ ‒ 1 ) ϕ ( σ + 2 ) ‒ ( σ ‒ 1 ) ϕ , where σ = σ s σ f k nf k f = k s + ( n ‒ 1 ) k f ‒ ϕ ( k f ‒ k s ) k s + ( n ‒ 1 ) k f + ϕ ( k f ‒ k s )
Hybrid nanofluid σ hnf σ bf = σ s 2 + 2 σ bf ‒ 2 ϕ 2 ( σ bf ‒ σ s 2 ) σ s 2 + 2 σ bf + ϕ 2 ( σ bf ‒ σ s 2 ) , where σ bf σ f = σ s 1 + 2 σ f ‒ 2 ϕ 2 ( σ f ‒ σ s 1 ) σ s 1 + 2 σ f + ϕ 2 ( σ f ‒ σ s 1 ) k hnf k bf = k s 2 + ( n ‒ 1 ) k bf ‒ ϕ 2 ( n ‒ 1 ) ( k bf ‒ k s 2 ) k s 2 + ( n ‒ 1 ) k bf + ϕ 2 ( k bf ‒ k s 2 ) , where k bf k f = k s 1 + ( n ‒ 1 ) k f ‒ ϕ 1 ( k f ‒ k s 1 ) k s 1 + ( n ‒ 1 ) k f + ϕ 1 ( k f ‒ k s 1 )
Trihybrid nanofluid σ Tnf σ hnf = ( 1 + 2 ϕ 3 ) σ s 3 + ( 1 ‒ 2 ϕ 3 ) σ hnf ( 1 ‒ ϕ 3 ) σ s 3 + ( 1 + ϕ 3 ) σ hnf k Tnf k hnf = k s 3 + 2 k hnf ‒ 2 ϕ 3 ( k hnf ‒ k s 3 ) k s 3 + 2 k hnf + ϕ 3 ( k hnf ‒ k s 3 ) '
σ hnf σ nf = ( 1 + 2 ϕ 2 ) σ s 2 + ( 1 ‒ 2 ϕ 2 ) σ nf ( 1 ‒ ϕ 2 ) σ s 2 + ( 1 + ϕ 2 ) σ nf , k hnf k nf = k s 2 + 2 k nf ‒ 2 ϕ 2 ( k nf ‒ k s 2 ) k s 2 + 2 k nf + ϕ 2 ( k nf ‒ k s 2 ) '
σ nf σ f = ( 1 + 2 ϕ 1 ) σ s 1 + ( 1 ‒ 2 ϕ 1 ) σ f ( 1 ‒ ϕ 1 ) σ s 1 + ( 1 + ϕ 1 ) σ f , k nf k f = k s 1 + 2 k f ‒ 2 ϕ 1 ( k f ‒ k s 1 ) k s 1 + 2 k f + ϕ 1 ( k f ‒ k s 1 ) '
Table 3

Mathematical relations for viscosity and density of nanofluids

Nanofluids Viscosity Density
Pure nanofluid μ nf = μ f ( 1 ‒ ϕ ) 2.5 ρ nf = ( 1 ‒ ϕ ) ρ f + ϕ ρ s
Hybrid nanofluid μ hnf = μ f ( 1 ‒ ϕ 1 ) 2.5 ( 1 ‒ ϕ 2 ) 2.5 ρ hnf = { ( 1 ‒ ϕ 2 ) [ ( 1 ‒ ϕ 1 ) ρ f + ϕ 1 ρ s 1 ] } + ϕ 2 ρ s 2
Trihybrid nanofluid μ Tnf = μ f ( 1 ‒ ϕ 1 ) 2.5 ( 1 ‒ ϕ 2 ) 2.5 ( 1 ‒ ϕ 3 ) 2.5 ρ Thf = ( 1 ‒ ϕ 3 ) ( 1 ‒ ϕ 2 ) [ ( 1 ‒ ϕ 1 ) ρ f + ϕ 1 ρ s 1 ] + ϕ 2 ρ s 2 + ϕ 3 ρ s 3

The subscripts in the above Tables like Tnf , hnf , nf , f, s 1 , s 2 , and s 3 illustrate the ternary nanofluid, hybrid nanofluid, pure nanofluid, base fluid, solid nanoparticles of cobalt, gold, and zirconium oxide, respectively. Heat capacity in ternary case of nanofluids can be given as

(9) ( ρ C p ) Thf = ( 1 − ϕ 3 ) { ( 1 − ϕ 2 ) [ ( 1 − ϕ 1 ) ( ρ C p ) f + ϕ 1 ( ρ C p ) s 1 ] + ϕ 2 ( ρ C p ) s 2 } + ϕ 3 ( ρ C p ) s 3 .

2.6 Non-dimensional variables and equations

Following non-dimensional variables have been taken into consideration to change the governing equations into ordinary ones [59]:

(10) u = c x f ′ ( ξ ) , ξ = c υ f y , y = c υ f f ( ξ ) , θ ( ξ ) = T − T ∞ T w − T ∞ , ϕ ( ξ ) = C − C ∞ C w − C ∞ .

Employing the above relations in equations (2)–(4), we get

(11) f ‴ = Δ 0 + Δ 1 ( f ′ 2 − f f ″ ) + P 0 f ′ + Δ 2 M 0 f ′ ,

(12) 1 Pr K Tnf K f + 4 3 R d θ ″ + Δ 4 f θ ′ = 0 ,

(13) 1 Sc ϕ ″ + f ϕ ′ − K c ϕ = 0 ,

where

(14) Δ 0 = ( 1 − ϕ 3 ) ( 1 − ϕ 2 ) ( 1 + 2 ϕ 3 ) σ s 3 + ( 1 − 2 ϕ 3 ) σ s f + ϕ 2 ( 1 − ϕ 3 ) σ s 3 + ( 1 + ϕ 3 ) σ f + ϕ 3 ρ s 3 ρ f − 1 ,

(15) Δ 1 = ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 ( 1 − ϕ 3 ) 2.5 ( 1 − ϕ 2 ) ( 1 − ϕ 1 ) + ϕ 1 ρ s 1 ρ f + ϕ 2 ρ s 2 ρ f + ϕ 3 ρ s 3 ρ f ,

(16) Δ 2 = ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 ( 1 − ϕ 3 ) 2.5 σ Tnf σ f ,

(17) Δ 3 = K Tnf K f + 4 3 R d ,

(18) Δ 4 = ( 1 − ϕ 2 ) ( 1 − ϕ 3 ) ( 1 − ϕ 1 ) + ϕ 1 ( ρ c p ) s 1 ( ρ c p ) f + ϕ 2 ( ρ c p ) s 2 ( ρ c p ) f + ϕ 3 ( ρ c p ) s 3 ( ρ c p ) f ,

Boundary conditions (5), in the light of (6), take new form as follows:

(19) ξ = 0 f = S , f ′ = 1 , θ = 1 , ϕ = 1 , ξ → ∞ f ′ → 0 , θ → 0 , ϕ → 0 .

where S uc = v 0 c υ f denotes the suction phenomenon.

2.7 Problem parameters

The preeminent parameters can be specified as follows:

ϕ 1 is the nanoparticles volume concentration of cobalt
M 0 2 = σ f B 0 2 c ρ f is the magnetic interaction parameter
C h R = K r x U w is the chemical reaction parameter
Por = υ f c k ⁎ is the porosity parameter
ϕ 2 is the nanoparticles volume concentration of gold
Pr = μ f ( c p ) f k f is the Prandtl number
T Rad = 4 σ 0 T ∞ 3 k 0 k f is the thermal radiation parameter
Sc 0 = υ f D B is the Schmidt number
ϕ 1 is the nanoparticles volume concentration of zirconium oxide

The prime quantities of the engineering applications may be described as

(20) Re x 1 2 C f x = f ″ ( 0 ) ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 ( 1 − ϕ 3 ) 2.5 , Nu x Re x 1 2 = − k Tnf k f θ ′ ( 0 ) , Sh x Re x 1 2 = − ϕ ′ ( 0 ) .

The Reynolds number in the above equation is described by the relation Re x = U w x υ f . The properties of the base fluid as well as three different nanoparticles are specified in Table 4.

Table 4

Thermal properties of Pfin, cobalt, gold, and zirconium oxide

Properties Paraffin (Pfin) ( f ) Cobalt ( Co ) ( s 1 ) Gold (Au) ( s 2 ) Zirconium oxide (ZrO2) ( s 3 )
σ ( s/m ) 1.6 × 10−14 1.602 × 107 4.5 × 107 2.4 × 10−6
k ( W / m K ) 0.23 100 320 1.7
ρ ( kg / m 3 ) 802 8,900 19,300 5,680
C p ( J/kg K ) 2,320 420 129.1 502

The local thermo-fluid flow behavior (in terms of streamline and isotherms) is portrayed in Figures 2 and 3.

Figure 2 Streamlines for the flow when Pr = 6.2, Sc = 1.5, and M = 5.
Figure 2

Streamlines for the flow when Pr = 6.2, Sc = 1.5, and M = 5.

Figure 3 Isotherm for the temperature distribution when Pr = 6.2, Sc = 1.5, and M = 5.
Figure 3

Isotherm for the temperature distribution when Pr = 6.2, Sc = 1.5, and M = 5.

3 Solution methodology

The analytical solution of equations (11)–(13) might be so much complicated as these equations are not only coupled but also highly nonlinear. A suitable numerical technique may be the better choice to find the approximate solutions of the problem. However, Successive over Relaxation Method which is based on Gauss–Seidel iteration method is incorporated for the purpose of simulation analysis. This technique involves a relaxation factor for which the required convergence can be attained. This factor accelerates the convergence, and takes the value which is (in general) less than 1. The smaller steps or step sizes, in this method, leads toward the final solution. To initiate the iterative procedure, we set the equations (11)–(13) as follows:

(21) f ( i ) = ( W / A 0 ) ⁎ ( A 1 ⁎ p ( i + 1 ) + A 2 ⁎ p ( i − 1 ) + A 3 ) + ( 1 − W ) ⁎ f ( i ) , θ ( i ) = ( W / B 0 ) ⁎ ( B 1 ⁎ θ ( i + 1 ) + B 2 ⁎ θ ( i − 1 ) + B 3 ) + ( 1 − W ) ⁎ θ ( i ) , ϕ ( i ) = ( W / C 0 ) ⁎ ( C 1 ⁎ ϕ ( i + 1 ) + C 2 ⁎ ϕ ( i − 1 ) + C 3 ) + ( 1 − W ) ⁎ ϕ ( i ) .

where W is the relaxation factor such that W < 1 . Table 5 provides a comparison which validates the results and assures the accuracy of the numerical procedure. The main steps of the adopted methodology are mentioned in the flow chart diagram (Figure 4). The numerical uncertainty analysis is presented in Table 6. Numerical values of f ( η ) corresponding to the step size h can be analyzed from this table.

Table 5

A heat transfer rate comparison when Prandtl number changes and ϕ 1 = ϕ 2 = ϕ 3 = 0

Pr Devi and Devi [60] Ahmad et al. [61] Khan and Pop [62] Present results
2 0.91135 0.91045 0.9113 0.91045
7 1.89540 1.89083 1.8954 1.89083
20 3.35390 3.35271 3.3539 3.35271
Figure 4 Flow chart diagram for numerical scheme.
Figure 4

Flow chart diagram for numerical scheme.

Table 6

Numerical values of f ( η ) corresponding to the step size h

η f ( η ) Change in error in f ( η )
h = 0.05 h 2 = 0.025 h 4 = 0.0125 From h to h 2 From h 2 to h 4
0.5 0.34974940 0.34889300 0.34867867 0.000856788 2.1433085 × 10−4
1.0 0.43469733 0.43345392 0.43314171 0.001243410 3.1220685 × 10−4
1.5 0.46581887 0.46441823 0.46406630 0.001400644 3.5192816 × 10−4
2.0 0.47945838 0.47798565 0.47761552 0.001472729 3.7012717 × 10−4
2.5 0.48610751 0.48459873 0.48421951 0.001508775 3.7922471 × 10−4
3.0 0.48958050 0.48805259 0.48766854 0.001527911 3.8405277 × 10−4
3.5 0.49146811 0.48992968 0.48954298 0.001538424 3.8670473 × 10−4
4.0 0.49249417 0.49094998 0.49056183 0.001544180 3.8815634 × 10−4
4.5 0.49300307 0.49145602 0.49106714 0.001547047 3.8887926 × 10−4
5.0 0.49315526 0.49160735 0.49121825 0.001547906 3.8909581 × 10−4

4 Results and discussion

In this section, the numerical consequences of the preeminent parameters are discussed by the physical interpretations of the graphs and tables. The flow and thermal characteristics of the pure nanofluid Co − Pfin , hybrid nanofluid Co − Au − Pfin , and trihybrid nanofluid Co − Au − ZrO 2 − Pfin are elaborated in this study. An asymptotic behavior (in graphical profiles) is achieved by appropriately choosing the step sizes. Assigning the suitable dimensionless values to the parameters might provide better consequences in factual employments of the work rather than proposing the fluid characteristics and particular domains [63,64]. According to these lines, the simulation process is carried out using T Rad = 0.2 , Sc 0 = 1.5 , M 0 = 2 , Ch R = 4 , Por = 2 , Pr = 6.135 , and ϕ 1 = ϕ 2 = ϕ 3 = 0.1 unless otherwise apportioned.

Figures 5 and 6 are depicted to elucidate the velocity F ′ ( η ) and temperature θ ( η ) for three cases of nanofluids with change in magnetic interaction parameter M 0 . The first case indicates the pure nanofluids Co–Pfin ( ϕ 1 = 0.1 and ϕ 2 = ϕ 3 = 0.1 ), the second one represents the hybrid nanofluid Co–Au–Pfin ( ϕ 1 = ϕ 2 = 0.1 and ϕ 3 = 0 ), and the third one is for the ternary case of nanofluids Co–Au–ZrO2–Pfin ( ϕ 1 = ϕ 2 = ϕ 3 = 0.1 ). The velocity is decreased and the temperature is increased by the magnetic field. The applied magnetic field is one of the factors which originates the Lorentz force. When the magnetic and electric field interact during the motion of an electrically conducting fluid, then it gives rise to the Lorentz force. The retarding force, in the present case, increases when the levels (values) of magnetic field parameter are increased. Subsequently, the fluid velocity decreases and the temperature of fluid increases with the magnetic field.

Figure 5 Velocity F ′ ( η ) F^{\prime} (\eta ) for three cases of nanofluids with change in M 0 {M}_{0} .
Figure 5

Velocity F ′ ( η ) for three cases of nanofluids with change in M 0 .

Figure 6 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in M 0 {M}_{0} .
Figure 6

Temperature θ ( η ) for three cases of nanofluids with change in M 0 .

The dimensionless velocity as well as temperature profile is appeared in Figures 7 and 8. In either case of nanofluids, velocity is reduced by the porosity of the medium but the temperature of fluid tends to increase with this parameter. A declination in the velocity is associated with the pores size within the permeable media. In this case, fluid faces resistance when it passes through the pores. An important fact noted is that the smaller values of porosity parameter interrupt the solution. This fact may be attributed because of the involvement of three distinct types of nanoparticles which require large pore size to pass through them. However, we assigned large values to the porosity parameter unless otherwise optimal state of solution does not achieve.

Figure 7 Velocity F ( η ) F(\eta ) for three cases of nanofluids with change in Por \text{Por} .
Figure 7

Velocity F ( η ) for three cases of nanofluids with change in Por .

Figure 8 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in Por \text{Por} .
Figure 8

Temperature θ ( η ) for three cases of nanofluids with change in Por .

It is noted from Tables 7 and 8 that the porosity parameter has dominant effect on the skin friction as compared to the magnetic parameter. Both these parameters tend to upsurge the shear stress but deteriorate the heat transfer rate in either case of nanofluids (usual, hybrid, and ternary nanofluid). It is better to mention that material porosity has higher influence on the skin friction as compared to the magnetic field parameter. On the other hand, both these parameters insert low effect on the Nusselt number.

Table 7

Skin frictions for three cases of nanofluids with change in Por and M 0

Parameters Skin frictions
Por M 0 Pure nano Hybrid nano Trihybrid nano
20 −6.8745974 −9.4005197 −11.9779623
40 −9.0386709 −12.1977051 −15.6280456
60 −10.7246677 −14.3779038 −18.4707024
0 −3.9669009 −5.3127986 −6.2827091
1 −4.2398968 −6.2006625 −8.3972919
2 −5.2138095 −8.3124442 −12.6196198
Table 8

Nusselt numbers for three cases of nanofluids with change in Por and M 0

Parameters Nusselt numbers
Por M 0 Pure nano Hybrid nano Trihybrid nano
20 3.4789813 3.7523867 4.0469349
40 3.3750103 3.6295708 3.9041364
60 3.3118644 3.5568421 3.8212620
0 3.6586039 4.0123214 4.4044729
1 3.6336487 3.9515072 4.2484228
2 3.5794819 3.8121882 4.01805868

The consequences of Figure 9 articulate that the temperature decreases with an increase in the dimensionless values of Prandtl number. It may have happened due to the relatively high thermal diffusivity of fluid as equated to kinematic viscosity. Variation in the temperature θ ( η ) for three (usual, hybrid, and ternary) cases of nanofluids with change in thermal radiation T Rad , volume fraction ϕ 2 of gold, and volume fraction ϕ 3 of zirconium oxide is portrayed in Figures 10–12. The temperature profiles seem to be increasing with these three parameters in all cases of nanofluids. Out of three heat transfer modes, thermal radiation is one of them whereas the other two are convection and conduction. When the thermal radiation emitted from the source is absorbed by the fluid, then it would definitely elevate the temperature. The trihybrid nano case is more prominent in order to enhance the temperature throughout the flow regime. The amalgamation of three distinct nanoparticles in base fluid exhibits improved overall thermal characteristics as related to the single or binary components nanofluids. This is the reason that we have noticed high temperature in ternary nanofluid case other than the mono or hybrid case.

Figure 9 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in Pr \text{Pr} .
Figure 9

Temperature θ ( η ) for three cases of nanofluids with change in Pr .

Figure 10 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in T Rad {T}_{\text{Rad}} .
Figure 10

Temperature θ ( η ) for three cases of nanofluids with change in T Rad .

Figure 11 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in ϕ 2 {\phi }_{2} .
Figure 11

Temperature θ ( η ) for three cases of nanofluids with change in ϕ 2 .

Figure 12 Temperature θ ( η ) \theta (\eta ) for three cases of nanofluids with change in ϕ 3 {\phi }_{3} .
Figure 12

Temperature θ ( η ) for three cases of nanofluids with change in ϕ 3 .

Heat transfer rate is increased by the volume fraction of gold (Au), Prandtl number (Pr), and volume fraction of zirconium oxide (ZrO2) (Table 9). However, a decrease in the Nusselt number is observed when the thermal radiation parameter T Rad is increased. It is noticeable that trihybrid nanofluids (Co–Au–ZrO2–Pfin) have marginally increased heat transmission rate as compared to the other two cases. If we comparatively analyze the impact of ϕ 2 and ϕ 3 , which are, respectively, nanoparticles volume fractions of gold and zirconium oxide on the Nusselt number, then we conclude that the volume fraction of ZrO2 has a significant impact on Nu.

Table 9

Nusselt numbers for three cases of nanofluids with change in Pr , T Rad , ϕ 2 , and ϕ 3

Parameters Nusselt numbers
Pr T Rad ϕ 2 ϕ 3 Pure nano Hybrid nano Trihybrid nano
6 3.5503990 3.9176022 4.2716610
7 4.1056182 4.5105642 4.9120449
8 4.6482035 5.0936047 5.5424835
0.2 3.6261513 3.9982474 4.3586809
0.4 3.1291554 3.5723390 3.9657133
0.6 2.7500112 3.2314996 3.6414327
0.1 3.4390635 3.9982474 4.3586809
0.2 3.7764852 4.3068073 4.6556849
0.3 4.1151896 4.6151008 4.9393795

Figures 13 and 14 portray the concentration profiles ϕ ( η ) against the parameter of chemical reaction Ch R and the Schmidt number Sc 0 . Both the profiles are noticed to be decelerating with the prominent effects of Ch R and the Schmidt number Sc 0 . This fact may be attributed to the reason that the mass diffusivity is reduced by the Schmidt number as well as chemical reaction parameter. Hence, concentration is decreased in the flow regime. One of the other reasons is the viscous diffusion which increases when Sc 0 increases and, consequently, concentration is declined. It can be revealed from Table 10 that the mass transfer rate is significantly increased in all (pure, hybrid, and trihybrid) cases of nanofluids with the effects of chemical reaction parameter and Schmidt number. Effects of different prime parameters on the flow dynamics can be studied from previous literature [65,66,67,68,69,70,71,72,73,74,75,76].

Figure 13 Concentration ϕ ( η ) \phi (\eta ) for three cases of nanofluids with change in Ch R {\text{Ch}}_{\text{R}} .
Figure 13

Concentration ϕ ( η ) for three cases of nanofluids with change in Ch R .

Figure 14 Concentration ϕ ( η ) \phi (\eta ) for three cases of nanofluids with change in Sc 0 {\text{Sc}}_{\text{0}} .
Figure 14

Concentration ϕ ( η ) for three cases of nanofluids with change in Sc 0 .

Table 10

Sherwood numbers for three cases of nanofluids with change in Ch R and Sc 0

Parameters Sherwood numbers
Ch R Sc 0 Pure nano Hybrid nano Trihybrid nano
1 4.4429811 4.7350108 4.8865235
3 8.3545029 8.6694166 8.8258259
6 12.0034633 12.3101431 12.4624268
0.3 3.4616350 3.7456153 3.8991065
0.6 5.5712367 5.8910443 6.0536072
0.9 7.2066153 7.5271109 7.6868220

5 Conclusion

The appropriate combination of nanoparticles in trihybrid nanofluids is mainly based on the specific properties and desired applications. For instance, some of the nanoparticles enhance the heat transfer characteristics and some types of nano-sized particles might deliver improved thermal conductivity. An effort is taken out to examine the change in flow and thermal features of the problem for three cases of nanofluids: (i) pure nanofluids, (ii) hybrid nanofluids, and (iii) ternary hybrid nanofluids. The nano-composition of three distinct particles (ternary case of nanofluids) can lead toward the higher thermal conductivity, embellished heat transfer efficiency and the other required features. The current work aims to investigate the features of Pfin-based trihybrid nanofluids which consist of cobalt, gold, and zirconium oxide nanoparticles. The main consequences of the present work are enlisted below

  1. The trihybrid nanofluids (Co–Au–ZrO2–Pfin) have marginally increased the heat transfer rate as compared to the other two cases, e.g., pure and hybrid nanofluid case.

  2. The porosity as well as magnetic interaction parameter tends to upsurge the shear stress but deteriorate the heat transfer rate in usual, hybrid, and ternary case of nanofluids.

  3. In either case of nanofluids, velocity is reduced by the porosity of the medium but the temperature of fluid tends to increase with this parameter.

  4. The temperature profiles seem to be increasing with the change (increase) in thermal radiation T Rad , volume fraction ϕ 2 of gold, and volume fraction ϕ 3 of zirconium oxide.

  5. The velocity of fluid decreases whereas the temperature increases due to the magnetic field in all cases.

  6. The volume fraction ϕ 3 of ZrO2 has a significant impact on Nusselt number rather than ϕ 2 which is volume fraction of gold (Au).

  7. The prominent effects of chemical reaction Ch R and the Schmidt number Sc 0 cause a deceleration in the concentration of hybrid and ternary hybrid nanofluids.

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through small group Research Project under grant number RGP.1/97/44.

  1. Funding information: The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through small group Research Project under grant number RGP.1/97/44.

  2. Author contributions: D.Y. and S.A. formulated the problem. K.A. and W.J. solved the problem. D.Y., S.A., K.A., S.A., T.A., W.J., S.M.H., K.I., and H.A. computed and scrutinized the results. 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.

  4. Data availability statement: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Received: 2023-10-02
Revised: 2024-03-18
Accepted: 2024-04-08
Published Online: 2024-05-17

© 2024 the author(s), published by De Gruyter

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

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  15. Time-dependent Darcy–Forchheimer flow of Casson hybrid nanofluid comprising the CNTs through a Riga plate with nonlinear thermal radiation and viscous dissipation
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https://doi.org/10.1515/ntrev-2024-0024
Keywords for this article
zirconium oxide; cobalt; gold; ternary hybrid nanofluids; paraffin; porous medium; SUR technique
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Tension buckling and postbuckling of nanocomposite laminated plates with in-plane negative Poisson’s ratio
  3. Polyvinylpyrrolidone-stabilised gold nanoparticle coatings inhibit blood protein adsorption
  4. Energy and mass transmission through hybrid nanofluid flow passing over a spinning sphere with magnetic effect and heat source/sink
  5. Surface treatment with nano-silica and magnesium potassium phosphate cement co-action for enhancing recycled aggregate concrete
  6. Numerical investigation of thermal radiation with entropy generation effects in hybrid nanofluid flow over a shrinking/stretching sheet
  7. Enhancing the performance of thermal energy storage by adding nano-particles with paraffin phase change materials
  8. Using nano-CaCO3 and ceramic tile waste to design low-carbon ultra high performance concrete
  9. Numerical analysis of thermophoretic particle deposition in a magneto-Marangoni convective dusty tangent hyperbolic nanofluid flow – Thermal and magnetic features
  10. Dual numerical solutions of Casson SA–hybrid nanofluid toward a stagnation point flow over stretching/shrinking cylinder
  11. Single flake homo p–n diode of MoTe2 enabled by oxygen plasma doping
  12. Electrostatic self-assembly effect of Fe3O4 nanoparticles on performance of carbon nanotubes in cement-based materials
  13. Multi-scale alignment to buried atom-scale devices using Kelvin probe force microscopy
  14. Antibacterial, mechanical, and dielectric properties of hydroxyapatite cordierite/zirconia porous nanocomposites for use in bone tissue engineering applications
  15. Time-dependent Darcy–Forchheimer flow of Casson hybrid nanofluid comprising the CNTs through a Riga plate with nonlinear thermal radiation and viscous dissipation
  16. Durability prediction of geopolymer mortar reinforced with nanoparticles and PVA fiber using particle swarm optimized BP neural network
  17. Utilization of zein nano-based system for promoting antibiofilm and anti-virulence activities of curcumin against Pseudomonas aeruginosa
  18. Antibacterial effect of novel dental resin composites containing rod-like zinc oxide
  19. An extended model to assess Jeffery–Hamel blood flow through arteries with iron-oxide (Fe2O3) nanoparticles and melting effects: Entropy optimization analysis
  20. Comparative study of copper nanoparticles over radially stretching sheet with water and silicone oil
  21. Cementitious composites modified by nanocarbon fillers with cooperation effect possessing excellent self-sensing properties
  22. Confinement size effect on dielectric properties, antimicrobial activity, and recycling of TiO2 quantum dots via photodegradation processes of Congo red dye and real industrial textile wastewater
  23. Biogenic silver nanoparticles of Moringa oleifera leaf extract: Characterization and photocatalytic application
  24. Novel integrated structure and function of Mg–Gd neutron shielding materials
  25. Impact of multiple slips on thermally radiative peristaltic transport of Sisko nanofluid with double diffusion convection, viscous dissipation, and induced magnetic field
  26. Magnetized water-based hybrid nanofluid flow over an exponentially stretching sheet with thermal convective and mass flux conditions: HAM solution
  27. A numerical investigation of the two-dimensional magnetohydrodynamic water-based hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles over a heated surface
  28. Development and modeling of an ultra-robust TPU-MWCNT foam with high flexibility and compressibility
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  30. Polymer nanocomposite for protecting photovoltaic cells from solar ultraviolet in space
  31. Study on the mechanical properties and microstructure of recycled concrete reinforced with basalt fibers and nano-silica in early low-temperature environments
  32. Synergistic effect of carbon nanotubes and polyvinyl alcohol on the mechanical performance and microstructure of cement mortar
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  34. Forced convective tangent hyperbolic nanofluid flow subject to heat source/sink and Lorentz force over a permeable wedge: Numerical exploration
  35. Physiochemical and electrical activities of nano copper oxides synthesised via hydrothermal method utilising natural reduction agents for solar cell application
  36. A homotopic analysis of the blood-based bioconvection Carreau–Yasuda hybrid nanofluid flow over a stretching sheet with convective conditions
  37. In situ synthesis of reduced graphene oxide/SnIn4S8 nanocomposites with enhanced photocatalytic performance for pollutant degradation
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  40. The LyP-1 cyclic peptide modified mesoporous polydopamine nanospheres for targeted delivery of triptolide regulate the macrophage repolarization in atherosclerosis
  41. Synergistic effect of hydroxyapatite-magnetite nanocomposites in magnetic hyperthermia for bone cancer treatment
  42. The significance of quadratic thermal radiative scrutinization of a nanofluid flow across a microchannel with thermophoretic particle deposition effects
  43. Ferromagnetic effect on Casson nanofluid flow and transport phenomena across a bi-directional Riga sensor device: Darcy–Forchheimer model
  44. Performance of carbon nanomaterials incorporated with concrete exposed to high temperature
  45. Multicriteria-based optimization of roller compacted concrete pavement containing crumb rubber and nano-silica
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  49. Improved mechanical properties of graphene-modified basalt fibre–epoxy composites
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  51. Green synthesis of Vitis vinifera extract-appended magnesium oxide NPs for biomedical applications
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  53. Heat convection and irreversibility of magneto-micropolar hybrid nanofluids within a porous hexagonal-shaped enclosure having heated obstacle
  54. Numerical simulation and optimization of biological nanocomposite system for enhanced oil recovery
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  72. Shell-core-structured electrospinning film with sequential anti-inflammatory and pro-neurogenic effects for peripheral nerve repairment
  73. Flow and heat transfer insights into a chemically reactive micropolar Williamson ternary hybrid nanofluid with cross-diffusion theory
  74. One-pot fabrication of open-spherical shapes based on the decoration of copper sulfide/poly-O-amino benzenethiol on copper oxide as a promising photocathode for hydrogen generation from the natural source of Red Sea water
  75. A penta-hybrid approach for modeling the nanofluid flow in a spatially dependent magnetic field
  76. Advancing sustainable agriculture: Metal-doped urea–hydroxyapatite hybrid nanofertilizer for agro-industry
  77. Utilizing Ziziphus spina-christi for eco-friendly synthesis of silver nanoparticles: Antimicrobial activity and promising application in wound healing
  78. Plant-mediated synthesis, characterization, and evaluation of a copper oxide/silicon dioxide nanocomposite by an antimicrobial study
  79. Effects of PVA fibers and nano-SiO2 on rheological properties of geopolymer mortar
  80. Investigating silver and alumina nanoparticles’ impact on fluid behavior over porous stretching surface
  81. Potential pharmaceutical applications and molecular docking study for green fabricated ZnO nanoparticles mediated Raphanus sativus: In vitro and in vivo study
  82. Effect of temperature and nanoparticle size on the interfacial layer thickness of TiO2–water nanofluids using molecular dynamics
  83. Characteristics of induced magnetic field on the time-dependent MHD nanofluid flow through parallel plates
  84. Flexural and vibration behaviours of novel covered CFRP composite joints with an MWCNT-modified adhesive
  85. Experimental research on mechanically and thermally activation of nano-kaolin to improve the properties of ultra-high-performance fiber-reinforced concrete
  86. Analysis of variable fluid properties for three-dimensional flow of ternary hybrid nanofluid on a stretching sheet with MHD effects
  87. Biodegradability of corn starch films containing nanocellulose fiber and thymol
  88. Toxicity assessment of copper oxide nanoparticles: In vivo study
  89. Some measures to enhance the energy output performances of triboelectric nanogenerators
  90. Reinforcement of graphene nanoplatelets on water uptake and thermomechanical behaviour of epoxy adhesive subjected to water ageing conditions
  91. Optimization of preparation parameters and testing verification of carbon nanotube suspensions used in concrete
  92. Max-phase Ti3SiC2 and diverse nanoparticle reinforcements for enhancement of the mechanical, dynamic, and microstructural properties of AA5083 aluminum alloy via FSP
  93. Advancing drug delivery: Neural network perspectives on nanoparticle-mediated treatments for cancerous tissues
  94. PEG-PLGA core–shell nanoparticles for the controlled delivery of picoplatin–hydroxypropyl β-cyclodextrin inclusion complex in triple-negative breast cancer: In vitro and in vivo study
  95. Conduction transportation from graphene to an insulative polymer medium: A novel approach for the conductivity of nanocomposites
  96. Review Articles
  97. Developments of terahertz metasurface biosensors: A literature review
  98. Overview of amorphous carbon memristor device, modeling, and applications for neuromorphic computing
  99. Advances in the synthesis of gold nanoclusters (AuNCs) of proteins extracted from nature
  100. A review of ternary polymer nanocomposites containing clay and calcium carbonate and their biomedical applications
  101. Recent advancements in polyoxometalate-functionalized fiber materials: A review
  102. Special contribution of atomic force microscopy in cell death research
  103. A comprehensive review of oral chitosan drug delivery systems: Applications for oral insulin delivery
  104. Cellular senescence and nanoparticle-based therapies: Current developments and perspectives
  105. Cyclodextrins-block copolymer drug delivery systems: From design and development to preclinical studies
  106. Micelle-based nanoparticles with stimuli-responsive properties for drug delivery
  107. Critical assessment of the thermal stability and degradation of chemically functionalized nanocellulose-based polymer nanocomposites
  108. Research progress in preparation technology of micro and nano titanium alloy powder
  109. Nanoformulations for lysozyme-based additives in animal feed: An alternative to fight antibiotic resistance spread
  110. Incorporation of organic photochromic molecules in mesoporous silica materials: Synthesis and applications
  111. A review on modeling of graphene and associated nanostructures reinforced concrete
  112. A review on strengthening mechanisms of carbon quantum dots-reinforced Cu-matrix nanocomposites
  113. Review on nanocellulose composites and CNFs assembled microfiber toward automotive applications
  114. Nanomaterial coating for layered lithium rich transition metal oxide cathode for lithium-ion battery
  115. Application of AgNPs in biomedicine: An overview and current trends
  116. Nanobiotechnology and microbial influence on cold adaptation in plants
  117. Hepatotoxicity of nanomaterials: From mechanism to therapeutic strategy
  118. Applications of micro-nanobubble and its influence on concrete properties: An in-depth review
  119. A comprehensive systematic literature review of ML in nanotechnology for sustainable development
  120. Exploiting the nanotechnological approaches for traditional Chinese medicine in childhood rhinitis: A review of future perspectives
  121. Twisto-photonics in two-dimensional materials: A comprehensive review
  122. Current advances of anticancer drugs based on solubilization technology
  123. Recent process of using nanoparticles in the T cell-based immunometabolic therapy
  124. Future prospects of gold nanoclusters in hydrogen storage systems and sustainable environmental treatment applications
  125. Preparation, types, and applications of one- and two-dimensional nanochannels and their transport properties for water and ions
  126. Microstructural, mechanical, and corrosion characteristics of Mg–Gd–x systems: A review of recent advancements
  127. Functionalized nanostructures and targeted delivery systems with a focus on plant-derived natural agents for COVID-19 therapy: A review and outlook
  128. Mapping evolution and trends of cell membrane-coated nanoparticles: A bibliometric analysis and scoping review
  129. Nanoparticles and their application in the diagnosis of hepatocellular carcinoma
  130. In situ growth of carbon nanotubes on fly ash substrates
  131. Structural performance of boards through nanoparticle reinforcement: An advance review
  132. Reinforcing mechanisms review of the graphene oxide on cement composites
  133. Seed regeneration aided by nanomaterials in a climate change scenario: A comprehensive review
  134. Surface-engineered quantum dot nanocomposites for neurodegenerative disorder remediation and avenue for neuroimaging
  135. Graphitic carbon nitride hybrid thin films for energy conversion: A mini-review on defect activation with different materials
  136. Nanoparticles and the treatment of hepatocellular carcinoma
  137. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part II
  138. Highly safe lithium vanadium oxide anode for fast-charging dendrite-free lithium-ion batteries
  139. Recent progress in nanomaterials of battery energy storage: A patent landscape analysis, technology updates, and future prospects
  140. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part II
  141. Calcium-, magnesium-, and yttrium-doped lithium nickel phosphate nanomaterials as high-performance catalysts for electrochemical water oxidation reaction
  142. Low alkaline vegetation concrete with silica fume and nano-fly ash composites to improve the planting properties and soil ecology
  143. Mesoporous silica-grafted deep eutectic solvent-based mixed matrix membranes for wastewater treatment: Synthesis and emerging pollutant removal performance
  144. Electrochemically prepared ultrathin two-dimensional graphitic nanosheets as cathodes for advanced Zn-based energy storage devices
  145. Enhanced catalytic degradation of amoxicillin by phyto-mediated synthesised ZnO NPs and ZnO-rGO hybrid nanocomposite: Assessment of antioxidant activity, adsorption, and thermodynamic analysis
  146. Incorporating GO in PI matrix to advance nanocomposite coating: An enhancing strategy to prevent corrosion
  147. Synthesis, characterization, thermal stability, and application of microporous hyper cross-linked polyphosphazenes with naphthylamine group for CO2 uptake
  148. Engineering in ceramic albite morphology by the addition of additives: Carbon nanotubes and graphene oxide for energy applications
  149. Nanoscale synergy: Optimizing energy storage with SnO2 quantum dots on ZnO hexagonal prisms for advanced supercapacitors
  150. Aging assessment of silicone rubber materials under corona discharge accompanied by humidity and UV radiation
  151. Tuning structural and electrical properties of Co-precipitated and Cu-incorporated nickel ferrite for energy applications
  152. Sodium alginate-supported AgSr nanoparticles for catalytic degradation of malachite green and methyl orange in aqueous medium
  153. An environmentally greener and reusability approach for bioenergy production using Mallotus philippensis (Kamala) seed oil feedstock via phytonanotechnology
  154. Micro-/nano-alumina trihydrate and -magnesium hydroxide fillers in RTV-SR composites under electrical and environmental stresses
  155. Mechanism exploration of ion-implanted epoxy on surface trap distribution: An approach to augment the vacuum flashover voltages
  156. Nanoscale engineering of semiconductor photocatalysts boosting charge separation for solar-driven H2 production: Recent advances and future perspective
  157. Excellent catalytic performance over reduced graphene-boosted novel nanoparticles for oxidative desulfurization of fuel oil
  158. Special Issue on Advances in Nanotechnology for Agriculture
  159. Deciphering the synergistic potential of mycogenic zinc oxide nanoparticles and bio-slurry formulation on phenology and physiology of Vigna radiata
  160. Nanomaterials: Cross-disciplinary applications in ornamental plants
  161. Special Issue on Catechol Based Nano and Microstructures
  162. Polydopamine films: Versatile but interface-dependent coatings
  163. In vitro anticancer activity of melanin-like nanoparticles for multimodal therapy of glioblastoma
  164. Poly-3,4-dihydroxybenzylidenhydrazine, a different analogue of polydopamine
  165. Chirality and self-assembly of structures derived from optically active 1,2-diaminocyclohexane and catecholamines
  166. Advancing resource sustainability with green photothermal materials: Insights from organic waste-derived and bioderived sources
  167. Bioinspired neuromelanin-like Pt(iv) polymeric nanoparticles for cancer treatment
  168. Special Issue on Implementing Nanotechnology for Smart Healthcare System
  169. Intelligent explainable optical sensing on Internet of nanorobots for disease detection
  170. Special Issue on Green Mono, Bi and Tri Metallic Nanoparticles for Biological and Environmental Applications
  171. Tracking success of interaction of green-synthesized Carbopol nanoemulgel (neomycin-decorated Ag/ZnO nanocomposite) with wound-based MDR bacteria
  172. Green synthesis of copper oxide nanoparticles using genus Inula and evaluation of biological therapeutics and environmental applications
  173. Biogenic fabrication and multifunctional therapeutic applications of silver nanoparticles synthesized from rose petal extract
  174. Metal oxides on the frontlines: Antimicrobial activity in plant-derived biometallic nanoparticles
  175. Controlling pore size during the synthesis of hydroxyapatite nanoparticles using CTAB by the sol–gel hydrothermal method and their biological activities
  176. Special Issue on State-of-Art Advanced Nanotechnology for Healthcare
  177. Applications of nanomedicine-integrated phototherapeutic agents in cancer theranostics: A comprehensive review of the current state of research
  178. Smart bionanomaterials for treatment and diagnosis of inflammatory bowel disease
  179. Beyond conventional therapy: Synthesis of multifunctional nanoparticles for rheumatoid arthritis therapy
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