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Analysis of pure nanofluid (GO/engine oil) and hybrid nanofluid (GO–Fe3O4/engine oil): Novel thermal and magnetic features

  • Sohail Ahmad EMAIL logo , Kashif Ali , Muhammad Ashraf , Hamiden Abd El-Wahed Khalifa , Fayza Abdel Aziz ElSeabee and El Sayed M. Tag El Din
Published/Copyright: October 14, 2022
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 11 Issue 1

Abstract

Hybrid nanofluids can provide better physical strength, thermal conductivity, and mechanical resistance in many thermodynamic systems than pure nanofluids. To establish the novel results, using superior types of hybrid nanoparticles like graphene oxide (GO) and iron oxide (Fe3O4) is the main focus of recent work. This study investigates the innovative thermal and magnetic features of both pure nanofluid GO/engine oil (EO) and hybrid nanofluid GO–Fe3O4 /EO under the simultaneous effects of induced as well as applied magnetic field. The chemical reaction phenomenon together with activation energy has also been taken into account. A novel algorithm based on order reduction and finite difference discretization is developed in order to numerically treat the problem. The efficiency of the code is appraised by a numerical comparison which is found to be in a good correlation with the existing results. From the consequences of this study, it is deduced that the reduction in induced magnetic field and fluid’s velocity (in case of either pure or hybrid nanofluid) is associated with the enlarging values of magnetic Prandtl number and induced magnetic field parameter. Further, activation energy is responsible for enhancement in concentration. The hybrid nano-composition of GO–Fe3O4/EO can provide the thermal stability, prevent the corrosion and make the liquid to stay in high temperature.

Keywords: graphene oxide; iron oxide; engine oil; activation energy; induced magnetic field

Nomenclature

B → 0

uniform magnetic field

c

stretching/shrinking constant

C

concentration of the fluid

C ∞

concentration far away from the sheet

C p hnf

specific heat of hybrid nanofluid

D B

diffusion coefficient

E ⁎

activation energy

H 1

induced magnetic field component along x-axis

H 2

induced magnetic component along y-axis

H e

magnetic field at the edge of boundary layer

k ∗

Darcy permeability

K r

rate constant of chemical reaction

k hnf

thermal conductivity of hybrid nanofluid

m 1

exponent fixed rate

T

temperature of the fluid

T ∞

temperature far away from the sheet

T w

fixed temperature at the surface

u

component of velocity along x-axis

v

component of velocity along y-axis

v 0

suction velocity (where v 0 > 0 )

υ hnf

kinematic viscosity of hybrid nanofluid

μ e

magnetic permeability

μ hnf

hybrid nanofluid viscosity

σ hnf

electrical conductivity of hybrid nanofluid

ρ hnf

density of hybrid nanofluid

1 Introduction

The combination of different nanoparticles possesses superior thermal features which have several practical employments in modern engineering and technology. Usually hybrid nanofluids are prepared by mixing two or more distinct nanoparticles with the base fluid. This combination yields a homogeneous compound which involves different characteristics as compared to individual nanoparticles. Metal base nanoparticles like aluminum oxide (Al2O3), cerium oxide (CeO2), zinc oxide (ZnO), titanium dioxide (TiO2), and iron oxide (Fe3O4) play a crucial role in augmentation of heat transfer in many systems. The iron oxide nanoparticles such as Fe3O4 are natural compounds which can also be synthesized in the laboratory. Due to their super magnetic properties, the magnetite particles Fe3O4 are used widely in magnetic ink and toner, rubber, plastic, paper, glass, ceramic glazes, and cosmetics as well as in textiles. In the same way, graphene oxide (GO) is a lightweight and thin nanomaterial or compound which is made of carbon, hydrogen, and oxygen. It is a promising nanomaterial having several applications in medicine and biotechnology for drug delivery, cancer treatment, and cellular imaging. The engine oil (EO) based hybrid nano-composite of Fe3O4 and GO might be of great interest in thermal heating and cooling systems.

The involvement of magnetite nanoparticles in hybrid or non-hybrid nanofluids is important due to their super paramagnetic properties. In this regard, a lot of work has been performed by many researchers. A magnetized non-Darcy flow of hybrid nanofluid (MWCNT + Fe3O4/water) subject to convective boundary conditions was explored by Shah et al. [1]. The control volume finite element computational technique was adopted to determine the numerical solution. This thermally conductive flow was strengthened due to Lorentz force and porosity of the medium. Tekir et al. [2] investigated the water-based hybrid nanofluid flow involving Fe3O4 and copper (Cu) as nanoparticles. The flow was taken within a straight pipe under the effect of constant magnetic field. The range of parameters like Reynolds number and solid nanoparticles volume fraction was adjusted in such a way that increased Nusselt number may be obtained (e.g., 0 < φ < 0.02 and 994 < Re < 2,337). The features of mono nanofluid MnZnFe2O2/H2O as well as hybrid nanofluid MnZnFe2O2–NiZnFe2O2/H2O together with gyrotactic microorganisms were elaborated by Ahmad et al. [3]. In this study, it was found that the heat transfer rate increased significantly with the composition of zinc ferrites and motile gyrotactic microorganisms. The ferrofluid-based magnetite nanomaterials (Fe3O4) were evaluated in order to reduce the viscosity of oil ([4]). They utilized engine lubricant oil to synthesize the carrier fluid. Astafyev et al. [5] used the thermomagnetometric method to study the nickel–zinc ferrites taking different magnetic phase transitions.

Hemmat Esfe et al. [6] described the rheological behavior of hybrid nanofluid (MWCNT–Al2O3) based on temperature, volume fraction of nanoparticles, and shear rate to present an experimental correlation model. Vidhya et al. [7] experimentally and statistically reported the convective heat transfer performance of a cylindrical mesh-type heat pipe apparatus filled with ZrO2–CeO2/water–ethylene glycol nanofluids. Thermal conductivity and viscous properties of water-based SiO2–ND hybrid nanofluid were measured experimentally by Yalçın et al. [8]. The flow over a curved surface was interpreted by Mishra and Upreti [9] to check out the effects of ethylene glycol based hybrid nanofluids CoFe2O4–Fe3O4/water on heat transfer characteristics. Jan et al. [10] mixed the inorganic nanomaterials such as Cobalt (Co) and Fe3O4 to prepare the hybrid nano composition of Co–Fe3O4/C2H6O2–water. They found the numerical solution of the problem using BVP4c built in function in Mathematica. Magnetically driven flow of EO comprising Cu and titanium oxide was numerically examined by Ali et al. [11] by employing Quasi–linearization method. Yu et al. [12] used commercially available nanomatrerials e.g., H2C2O4·2H2O, NiSO4·6H2O, ZnSO4·7H2O, and FeSO4·7H2O to analyze their thermal properties. Their outcomes portrayed that the ferrites such as Ni–Zn demonstrated better magnetic properties which could be beneficial in microwave absorbers. An experimental study was presented by Azhagushanmugam et al. [13] in which the effect of nanoparticles nickel cobalt zinc ferrites (Ni–Co–ZnFe2O4) on concentration and magnetization was examined. Further recent investigations on mono and hybrid nanofluids can be seen in refs [14–20].

In order to initiate the chemical or biochemical processes, certain amount of energy is always required. A small quantity of energy which is required to accelerate the chemical reaction process is known as activation energy. Bestman [21] presented, for the first time, the idea of boundary layer flow consisting of activation energy. He adopted perturbation technique to numerically solve this problem. A numerical technique named RKF-45 was implemented by Ramesh and Madhukesh [22] and Madhukesh et al. [23] to numerically interpret the hybrid nanofluid flows through extendable slipped surface and circular cylinder, respectively. The flow of Williamson fluid involving Al2O3 and Cu under the heterogeneous and homogeneous chemical reactions was deliberated by Almaneea [24]. It was disclosed that the Cu–Williamson nanofluid was marginally affected by the Lorentz force as compared to Cu–Al2O3–Williamson hybrid nanofluid. Rekha et al. [25] proposed hybrid nanoparticles like aluminum alloys (AA7075 and AA7072) to prepare the water-based hybrid nanofluids. They investigated the flow and thermal features in the presence of activation energy by taking different geometries (plate, wedge, and cone).

The EO-based magnetized hybrid nanoparticles not only control the temperature but can also act as cooling fluid. The composition of GO–Fe3O4/EO can provide thermal stability, prevent corrosion, and make the liquid to stay in high temperature. The flow of EO together with hybrid nanoparticles (Fe3O4 and GO) might be used in engine cooling to maintain the viscosity-temperature properties, to protect against corrosion, and many more. Due to these interesting characteristics, we intend to investigate the novel aspects of the hybrid nanofluid which is GO–Fe3O4/EO in the present case. We distinguish our work from the existing literature as: (i) the combination of the proposed hybrid nanoparticles GO and Fe3O4 together with base fluid EO has not been reported yet; (ii) the simultaneous effect of induced as well as applied magnetic field has also been taken into account; (iii) our analysis covers the features of both GO/EO which is a mono nanofluid and GO–Fe3O4/EO which is a hybrid nanofluid; (iv) the role of suction, chemical reaction, and activation energy has also been discussed in either case of nanofluids.

2 Formulation of model problem

The composition of GO and magnetic Fe3O4 is used in EO to prepare hybrid nano-composite of GO–Fe3O4/EO. The components of induced magnetic field are represented by H → 1 and H → 2 while H → = ( H → 1 , H → 2 ) is the induced magnetic field vector. The y-axis is vertical to the surface, while direction of flow is along the x-axis. The structure of extending surface is shown in Figure 1. The concentration and temperature, away from surface of sheet, are expressed as C ∞ and T ∞ , respectively. Likewise, C w and T w denote, respectively, the concentration and temperature on the surface boundary. The applied magnetic field B 0 is assumed normal to the surface (parallel to the y-axis). The surface is being stretched with a velocity U w ( x ) . The activation energy term is also included in the concentration.

Figure 1 Structure of the geometry.
Figure 1

Structure of the geometry.

Taking into consideration the above suppositions, the flow model governing equations have the form [26,27]:

(1) ∂ u ∂ x + ∂ v ∂ y = 0 ,

(2) u ∂ u ∂ x + v ∂ u ∂ y = υ hnf ∂ 2 u ∂ y 2 − σ hnf ρ hnf B 0 2 u + μ e 4 π ρ hnf H 1 ∂ H 1 ∂ x + H 2 H 1 ∂ y − μ e H e 4 π ρ hnf ∂ H e ∂ x ,

(3) u ∂ H 1 ∂ x + v H 1 ∂ y = H 1 ∂ u ∂ x + H 2 ∂ u ∂ y + 1 4 π ρ hnf μ e ∂ 2 H 1 ∂ y 2 ,

(4) u ∂ T ∂ x + v ∂ T ∂ y = K hnf ( ρ C p ) hnf ∂ 2 T ∂ y 2 ,

(5) u ∂ C ∂ x + v ∂ C ∂ y = D B ∂ 2 C ∂ y 2 − K r 2 ( C − C ∞ ) T T ∞ m 1 exp − E ⁎ k ⁎ T ,

The supposed boundary conditions at the sheet surface and far away from the surface are:

(6) y = 0 : u ( x , 0 ) = c x = U w ( x ) , T ( x , 0 ) = T w , C ( x , 0 ) = C w , v ( x , 0 ) = − v 0 , ∂ H 1 ∂ y = H 2 = 0 y → ∞ : u ( x , ∞ ) = 0 , T ( x , ∞ ) = T ∞ , H 1 = H 2 = 0 , C ( x , ∞ ) = C ∞ ,

In the above relations, the velocity v 0 > 0 represents the suction, the temperature T w is noted on the boundary of the sheet and T ∞ is the temperature away from the boundary. In the same way, C ∞ and C w represent the concentrations at y → ∞ and y = 0 , respectively. The velocity U w ( x ) = u ( x , 0 ) = c x is specified for the extending surface. The induced magnetic field components are expressed by H → 1 and H → 2 taken along and across the sheet, respectively. The subscript hnf signifies the hybrid nanofluid. The other terms involved in the system of equations (1)–(6) are specified in the nomenclature.

2.1 Preparation of pure (GO/EO) and hybrid nanofluids (Fe3O4–GO/EO)

The nano sized fragments of Fe3O4 and GO are mixed in the EO in order to prepare the hybrid mixture of Fe3O4–GO/EO. The nanoparticles volume fraction Fe3O4 ( ϕ 1 ) is taken as 0.3 initially which is resolved in the base liquid (EO). After that amalgamation of GO ( ϕ 2 ) in the solution of Fe3O4/EO leads toward the formation of hybrid nanofluids (Fe3O4–GO/EO). The fixed value of volume fraction Fe3O4 (e.g., ϕ 1 = 0.3 ) is taken throughout hereafter. The thermal properties of Fe3O4, GO, and EO are identified in Table 1. We have used these properties while analyzing the thermal and magnetic aspects of the problem. Further properties such as density, electrical conductivity, thermal conductivity, and specific heat (in either case of nanofluids) are taken from our earlier work (Ahmad et al. [28]). The notation s 1 signifies the nanoparticles volume fraction of Fe3O4 and s 2 is used for GO volume fraction. Whereas f is used for base fluid which is EO in the present case.

Table 1

Thermal properties of graphene oxide, EO and Fe3O4

Properties GO (s 2) EO (f) Fe3O4(s 1)
k (W/mK) 5,000 0.144 9.7
σ (s/m) 1.1 × 10−5 2.1 × 10−12 0.74 × 106
C p (J/kgK) 717 1,910 670
ρ (kg/m 3 ) 1,800 884 5,180

2.2 Dimensionless variables

We transmute the governing equations into dimensionless form by means of the following similarity variables:

(7) η = c υ f y , ψ = c υ f x f ( η ) , θ ( η ) = T − T ∞ T w − T ∞ , H 1 = H ∗ x g ′ ( η ) , ϕ ( η ) = C − C ∞ C w − C ∞ , H 2 = − c υ f g ( η ) .

The relation (7) identically satisfies the continuity equation (1) and converts the equations (2)–(5) into the following form:

(8) f ′ ″ = Δ 1 ( f ′ 2 − f f ″ ) + Δ 2 M 0 f ′ + β Δ 0 ( g ′ 2 − g g ″ − 1 ) ,

(9) λ 0 Δ 0 g ′ ″ + f g ″ − g f ″ = 0 ,

(10) 1 Pr Δ 3 θ ″ + Δ 4 f θ ′ = 0 ,

(11) 1 Sc ϕ ″ + f ϕ ′ − σ ( 1 + δ θ ) m 1 exp − E a 1 + δ θ ϕ = 0 ,

where

(12) Δ 0 = 1 ( 1 − ϕ 2 ) ( 1 − ϕ 1 ) + ϕ 1 ρ s 1 ρ f + ϕ 2 ρ s 2 ρ f ,

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

(14) Δ 2 = ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 σ hnf σ f ,

(15) Δ 3 = K hnf K f ,

(16) Δ 4 = ( 1 − ϕ 2 ) ( 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 ,

We have adopted almost similar process to formulate the relations (12)–(16) as in the references [29,30]. The boundary conditions given in (6) now become:

(17) ξ = 0 : f = S 0 , f ′ = 1 , θ = 1 , ϕ = 1 , H = 0 , ξ → ∞ : f ′ → 0 , θ → 0 , ϕ → 0 , H = 1 . .

2.3 The preeminent parameters

The preeminent parameters which are involved in the equations (8)–(11) and boundary conditions (17) are mentioned in Table 2.

Table 2

The preeminent parameters

δ = T w − T ∞ T ∞ Temperature difference parameter S 0 = v 0 c υ f Suction parameter
M 0 2 = σ f B 0 2 c ρ f Magnetic interaction parameter Pr = μ f ( c p ) f k f Prandtl number
C R = K r 2 c Chemical reaction rate constant β = μ e 4 π ρ f H ∗ c 2 Induced magnetic field parameter where H ∗ is the strength of uniformly induced magnetic field
λ 0 = η 0 υ Reciprocal magnetic Prandtl number where η 0 = 1 4 π ρ f μ e is the magnetic diffusivity E 0 = E ⁎ k ⁎ T ∞ Activation energy parameter
Sc = υ f D B Schmidt number

Further physical quantities, which belong to engineering interests such as Nusselt number, surface drag, and Sherwood number, are portrayed as:

(18) Nu x Re x 1 2 = − k hnf k f θ ′ ( 0 ) , Re x 1 2 C f x = f ″ ( 0 ) ( 1 − ϕ 1 ) 2.5 ( 1 − ϕ 2 ) 2.5 , Sh x Re x 1 2 = − ϕ ′ ( 0 ) ,

Whereas the relation given by Re x = U w x υ f represents the local Reynolds number.

3 Numerical scheme based on order reduction and finite difference discretization

The analytical solution of the nonlinear coupled differential equations (8)–(11) is not only difficult to find out but it might also consume an enormous time. However, numerical solution is the choice to develop the outcomes of the problem under consideration. A typical way is to alter the system in the 1st order system of ordinary differential equations whose solution might be determined using common numerical schemes. But, in this way, an inadequacy seems to appear in the case of missing conditions. The solution diverges sometimes even for precise guesses of missing conditions (e.g., initial or boundary conditions). The strong dependence of the iterative process on the boundary conditions may be one of the reasons of this inconsistency. On the other hand, boundary conditions located at infinity can also interrupt the numerical solution. However, some efficient numerical technique is essentially required to tackle such types of troubles. The order reduction (e.g., z = f ′ = d f d η ) together with finite difference discretization is adopted in our work to determine the numerical solution of the problem.

3.1 Discretization model

Initially, we reduced the order of equations (8) and (9) by substituting z = f ′ = d f d ξ and s = g ′ = d g d ξ , respectively, and obtained

(19) z ″ = Δ 1 ( z 2 − f z ′ ) + P 0 z + Δ 2 M 0 z + β Δ 0 ( g ′ 2 − g g ″ − 1 ) ,

(20) λ 0 Δ 0 s ″ + f s ′ − g z ′ = 0 .

In the same way, dimensionless energy and concentration equations (10) and (11) are

(21) 1 Pr Δ 3 θ ″ + Δ 4 f θ ′ = 0 ,

(22) 1 Sc ϕ ″ + f ϕ ′ − σ ( 1 + δ θ ) m 1 exp − E a 1 + δ θ ϕ = 0 .

Now after using finite differences in the above equations, we obtain the following discretized equations:

(23) z i − 1 ( 2 − h Δ 1 f i ) + z i + 1 ( 2 + h Δ 1 f i ) − z i [ 4 + 2 h 2 ( Δ 1 z i + Δ 2 M 0 + P 0 ) ] + A 3 = 0 ,

where

(24) A 3 = − β Δ 0 1 2 ( g i + 1 − g i − 1 ) 2 − 2 g i ( g i + 1 − 2 g i + g i − 1 ) − 2 h 2 ,

(25) θ i − 1 2 Pr Δ 3 − h f i Δ 4 + θ i + 1 2 Pr Δ 3 + h f i Δ 4 − 4 Pr Δ 3 θ i = 0 ,

(26) s i − 1 ( 2 λ 0 Δ 0 − h f i ) − 4 λ 0 Δ 0 s i − 2 g i ( f i + 1 − 2 f i + f i − 1 ) + s i − 1 ( 2 λ 0 Δ 0 + h f i ) = 0 ,

(27) 4 + 2 h 2 S c C R e E 0 / 1 + δ θ ( i ) ( 1 + δ ) θ i m 1 ϕ i + ϕ i − 1 2 − h Sc f i + ϕ i + 1 2 − h Sc f i = 0 ,

We numerically solve the discretized equations (23)–(27). In our earlier work [31,32], we successfully implemented this technique to solve the complex nonlinear problems. The structure of this method (Figure 2) is such that it provides quick convergence and better execution.

Figure 2 Structure of numerical algorithm.
Figure 2

Structure of numerical algorithm.

4 Comparison and error analysis

A numerical comparison, under certain conditions, is illustrated in Table 3. The comparison is found to be in good correlation with earlier ones and it appraises the efficiency of the code. Table 3 also predicts that an increase in heat transfer rate, for simple Newtonian case, is due to an increase in the values of the Prandtl number.

Table 3

Change in heat transfer for different Prandtl numbers when ϕ 1 = ϕ 2 = 0

Pr Devi and Devi [33] Ali et al. [34] Present results
2 0.91135 0.91045 0.91045
7 1.89540 1.89083 1.89083
20 3.35390 3.35271 3.35271
70 — 6.47814 6.47814

The convergence as well as error analysis is portrayed in Tables 4 and 5. These tables not only demonstrate the convergence and error analysis but also appraise the efficiency of code.

Table 4

Convergence of numerical results for f ( η ) with step-size η for β 0 = 0.1 , S 0 = 0.8 , λ 0 = 3 , M 0 = 2 , Pr = 6.135 , δ = 4 , m 0 = 3 , ϕ 2 = 0.08 , ϕ 1 = 0.3 , σ 0 = 6 , E 0 = 2 , Sc = 1

η f ( η )
h = 0.07 h/2 = 0.035 h/4 = 0.0175 h/8 = 0.00825
0 0.80000000 0.80000000 0.80000000 0.80000000
0.7 1.12768459 1.12760689 1.12758767 1.12758288
1.4 1.18113888 1.18101728 1.18098709 1.18097956
2.1 1.18812018 1.18798486 1.18795126 1.18794287
2.8 1.18789295 1.18775271 1.18771789 1.18770920
3.5 1.18696821 1.18682553 1.18679011 1.18678127
4.2 1.18626526 1.18612106 1.18608527 1.18607634
4.9 1.18581247 1.18566728 1.18563126 1.18562226
5.6 1.18553611 1.18539032 1.18535414 1.18534512
6.3 1.18538022 1.18523418 1.18519791 1.18518886
7.0 1.18532408 1.18517832 1.18514204 1.18513298
Table 5

Change in error for f ( η ) with step-size η for β 0 = 0.1 , S 0 = 0.8 , λ 0 = 3 , M 0 = 2 , Pr = 6.135 , δ = 4 , m 0 = 3 , ϕ 2 = 0.08 , ϕ 1 = 0.3 , σ 0 = 6 , E 0 = 2 , S c = 1

(Absolute change in error with step-size h) × 10−3
η h to h/2 h/2 to h/4 h/4 to h/8
0 0 0 0
0.7 0.0777 0.0192 0.0047
1.4 0.1216 0.0301 0.0075
2.1 0.1353 0.0336 0.0083
2.8 0.1402 0.0348 0.0086
3.5 0.1426 0.0354 0.0088
4.2 0.1442 0.0357 0.0089
4.9 0.1451 0.0360 0.0089
5.6 0.1457 0.0361 0.0090
6.3 0.1460 0.0362 0.0090
7.0 0.1457 0.0362 0.0090

5 Results and discussion

The main focus, in this section, is to explore the novel aspects of the prime parameters for the flow of usual as well as hybrid case of nanofluids. The pure nanofluid case is assumed by taking the nanocomposites of GO with the base fluid which is EO in the present case. Likewise, hybrid case of nanofluids (e.g., GO–Fe3O4/EO) is also taken into account. In this way, features of both pure and hybrid case of nanofluids are covered in this work. Assigning distinct values to the parameters, instead of particular values, may provide better results in factual applications of the work. The specified values of parameters in the numerical calculations are: Pr = 6.135 , δ = 4 , m 0 = 3 , Sc = 1 and the other values are given in Tables 6 and 7.

Table 6

Change in Re x 1 / 2 C f and Re x − 1 / 2 Nu x for GO / EO and GO − Fe 3 O 4 / EO

Values of parameters Shear stresses Nusselt numbers
β 0 S 0 λ 0 M 0 GO/EO GO − Fe 3 O 4 / EO GO / EO GO − Fe 3 O 4 / EO
0.3 0.8 3 1.2 −2.63194 −5.75363 5.66258 7.81165
0.6 −2.91135 −6.00177 5.62881 7.78157
0.9 −3.21293 −6.26116 5.58908 7.74856
1.2 −3.54698 −6.53337 5.53938 7.71197
0.3 1.5 3 1.2 −3.15478 −6.84054 9.52567 12.77747
2.0 −3.55727 −7.69149 12.31918 16.42816
2.5 −3.97801 −8.59631 15.09426 20.10754
3.0 −4.41304 −9.54678 17.83080 23.78906
0.3 0.8 0.3 1.2 −2.33067 −5.31521 5.70340 7.87497
0.5 −2.45395 −5.42635 5.68749 7.86184
0.7 −2.51665 −5.50215 5.67898 7.85169
0.9 −2.55301 −5.55778 5.67392 7.84364
0.3 0.8 3 0 −2.07525 −4.15984 5.70846 7.95729
4 −5.62316 −13.10718 5.46481 7.33720
8 −10.31007 −24.26423 5.27579 6.97005
12 −14.83891 −35.03407 5.16745 6.78365
Table 7

Change in Re x − 1 / 2 Nu x and Re x − 1 / 2 Sh x for GO/EO and GO − Fe 3 O 4 / EO

Values of parameters Nusselt numbers Sherwood numbers
ϕ 2 ϕ 1 C R E 0 GO/EO GO − Fe 3 O 4 / EO GO/EO GO − Fe 3 O 4 / EO
0.03 0.3 6 2 5.65065 7.82174 — —
0.06 5.66274 7.81962
0.09 5.67559 7.81842
0.12 5.68948 7.81843
0.08 0.1 6 2 6.32993 6.46176 — —
0.2 7.05333 7.17728
0.3 7.82612 8.00156
0.4 8.67174 8.99314
0.08 0.3 0 2 1.11473 1.14216
1 5.79774 7.08680
3 11.44395 12.96163
5 15.09251 16.59830
0.08 0.3 6 3 14.67421 16.30981
5 11.19862 13.09641
7 8.22614 10.21281
9 5.90833 7.72788

The impact of induced magnetic field parameter β 0 is portrayed in Figure 3 which describes the variation in velocity and induced magnetic field of pure GO–EO nanofluid and hybrid GO–Fe3O4/EO nanofluid. An induced magnetism can be generated in hybrid nanofluids by the magnetic dipole due to which induced current will vary. This phenomenon tends to reduce the induced magnetic field as well as velocity. This nature of the parameter β 0 makes the hybrid nanofluid (GO–Fe3O4/EO) much useful in photo-catalytic and semiconductors technology. Figure 4 shows the appearance of velocity F ′ ( ξ ) and temperature θ ( ξ ) (as a function of η ) for distinct values of suction parameter. These figures evidently reveal that the velocity as well as temperature of the fluid turns toward reduction in either case of nanofluid (pure and hybrid case).

Figure 3 Change in (a) velocity and (b) induced magnetic field with β 0 {\beta }_{0} .
Figure 3

Change in (a) velocity and (b) induced magnetic field with β 0 .

Figure 4 Change in (a) velocity and (b) temperature with S 0 {S}_{0} .
Figure 4

Change in (a) velocity and (b) temperature with S 0 .

Table 6 portrays the change in Nusselt numbers and Shear stresses against various parameters for both cases of nanofluids e.g., pure and hybrid nanofluid case. It has been noticed here that both the shear stress and Nusselt number tend toward enhancement due to the suction on the surface. Suction phenomenon generates a frictional force between fluid’s particles and surface due to which shear rate increases in both cases of nanofluids. The optimal solution interrupts when we assign large values to the suction parameter. However, the small values of this parameter (i.e., S u c < 1.0 ) lead the solution toward the stability and we obtain better convergence. The heat transport rate decreases steadily with the impact of applied magnetic field but its effect is to marginally increase the shear rate on the sheet surface. The hybrid nanofluid GO–Fe3O4/EO has a substantial effect on shear stress with the effect of applied magnetic field as compared to usual nanofluid which can be evidently observed from Table 6. The surface drag Re x 1 / 2 C f seems to increase and that of Nusselt number Re x − 1 / 2 Nu x decrease provided the values of magnetic Prandtl number and induced magnetic field parameter β 0 increase, respectively (Table 6). Both these parameters act parallel to each other in case of their effects on shear rates and heat transfer rates. A significant change in the values of Nusselt number is noticed with the effect of suction parameter whereas the other parameters have low effect on it.

The increasing values of the magnetic Prandtl number λ 0 cause a substantial reduction in the velocity and induced magnetic field for both the usual and hybrid case of nanofluids, as shown in Figure 5a and b. The magnetic field strength reduces with lower magnetic diffusivity which mainly causes the reduction in induced magnetic field and velocity. It has been noticed from the consequences of Figure 6a and b that the influence of magnetic field M 0 is to dissuade the velocity and to escalate the temperature for same grid size ( η ). The magnetic retardation force caused by the Lorentz force tends to raise the temperature and ultimately increases the thermal boundary layer thickness. Contrarily, it causes diminution in the thickness of momentum boundary. It is important to mention here that the hybrid nanofluid GO–Fe3O4/EO performs well in case of temperature enhancement as compared to mono nanofluid GO/EO.

Figure 5 Change in (a) velocity and (b) induced magnetic field with λ 0 {\lambda }_{0} .
Figure 5

Change in (a) velocity and (b) induced magnetic field with λ 0 .

Figure 6 Change in (a) velocity and (b) temperature with M 0 {M}_{0} .
Figure 6

Change in (a) velocity and (b) temperature with M 0 .

The GO nanoparticles volume fraction ϕ 2 and Fe3O4 nanoparticles volume fraction ϕ 1 have a significant impact on the thermal features of both pure and hybrid nanofluids. Obviously, the base fluids enriched with the nanoparticles can embellish the thermal characteristics in many industrial applications. However, the desired heat transfer rate can be achieved by the amalgamation of hybrid nano-composites into the base liquids. The hybrid nano-composites GO–Fe3O4 /EO increase temperature more rapidly whereas mono nano-composites GO/EO ( ϕ 2 ) has low effect on temperature as pictured in Figure 7a. It has been comparatively noticed from Figure 7a and b that the solid nanoparticles volume fraction ϕ 1 of Fe3O4 nanoparticles increases temperature more efficiently than solid nanoparticles volume fraction ϕ 2 of GO nanoparticles. In Figure 7b, it is important to mention that ϕ 2 = 0 for pure nanofluid case GO/EO whereas ϕ 2 = 0.3 in hybrid case GO–Fe3O4 /EO.

Figure 7 Change in temperature with (a) volume fraction ϕ 2 {\phi }_{2} and (b) volume fraction ϕ 1 {\phi }_{1} .
Figure 7

Change in temperature with (a) volume fraction ϕ 2 and (b) volume fraction ϕ 1 .

The analysis of heat and mass transfer rates for several parameters like nanoparticles volume fraction, activation energy, and chemical reaction parameter is provided in Table 7. The nanoparticles volume fraction ϕ 2 shows a reduction in heat transfer rate when hybrid case of nanofluids (GO–Fe3O4/EO) is considered but it causes an enhancement in the rate of heat transfer in case of pure nanofluid (GO/EO). It is worth observing here that heat transfer rate reduces gradually for GO–Fe3O4 /EO with the effect of volume fraction ϕ 2 whereas heat transfer rates elevate in case of GO/EO. In the same way, the effect of solid nanoparticles volume fraction ϕ 1 of Fe3O4 is to enhance the heat transfer rate in both the cases of nanofluids. However, it is concluded that the mixture of hybrid nano-composites such as GO and Fe3O4 together with EO can be used as coolant/heating agents to cool down or heat up the systems. Therefore, the present results may be applied (with caution) to thermal cooling/heating systems. The heat transfer rate over a surface is important in order to attain the required consequences. The impact of activation energy is to devaluate the rate of mass transfer but contrarily the chemical reaction parameter sufficiently enhances the mass transfer rate on the surface of sheet, as depicted in Table 7. The increasing values of activation energy parameter modify the Arrhenius function which causes a reduction in mass transfer.

The concentration curves, against chemical reaction and activation energy parameter, demonstrate an adversative trend for hybrid and usual case of nanofluids with EO as host fluid (Figure 8a and b). The minimum amount of energy required to accelerate a chemical reaction process is known as activation energy. However, the inflate concentration is associated with the large values of activation energy E 0 . This fact is attributed by the Arrhenius equation which states that the higher will be the activation energy, the higher will be the concentration. On the opposite side, the chemical reaction parameter causes a deceleration in the concentration. Flow is more concentrated for GO–Fe3O4/EO as equated to GO/EO.

Figure 8 Change in concentration with (a) chemical reaction parameter and (b) activation energy.
Figure 8

Change in concentration with (a) chemical reaction parameter and (b) activation energy.

6 Conclusion

Some industrial and engineering processes e.g., nuclear system cooling, metal expulsion, cooling generator, solar heating, thermal storage, refrigeration, and so forth demand a specific rate of heat which could not affect the ultimate quality or final worth of the product. Heat transfer rate can be managed using hybrid mixture of Fe3O4 and GO in EO which can provide assistance in acquiring better quality products at low cost. Moreover, use of induced magnetic field not only regulates the flow but it also controls the variation in the flow. In the same way, magnetic effect maintains the thermal properties in several dynamical phenomena. We have investigated, in the recent work, the thermal and flow features of mono nanofluid GO/EO and hybrid nanofluid Fe3O4–GO/EO under the induced magnetic field environment. Finite difference discretization together with order reduction method is used to acquire the simulated outcomes. The prime findings of the problem under consideration may be listed as follows:

  • The magnetic Prandtl number λ 0 causes a substantial reduction in the induced magnetic field and velocity for both GO/EO (nanofluid case) and Fe3O4–GO/EO (hybrid nanofluid case).

  • Both the shear stress and Nusselt number tend toward enhancement on the surface due to the suction whereas temperature and fluid motion decreased in the flow regime with suction phenomenon.

  • An increase in the concentration is due to the effect of activation energy whereas the decrease in concentration is due to chemical reaction.

  • The temperature seems to be elevating but Nusselt number decreases with the impact of applied magnetic field.

  • The nanoparticles volume fraction ϕ 2 causes an enhancement in the rate of heat transfer in case of pure nanofluid (GO/EO) but it shows a reduction in heat transfer rate in the case of hybrid nanofluids (GO–FE3O4/EO).

  • The temperature is accelerated with the effect of volume fraction ϕ 2 of GO in case of usual and hybrid nanofluids.

Acknowledgments

The researchers would like to thank the Deanship of Scientific Research, Qassim University for funding the publication of this project.

  1. Funding information: The project was funded by the Deanship of Scientific Research, Qassim 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.

  4. Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2022-05-28
Revised: 2022-08-26
Accepted: 2022-09-16
Published Online: 2022-10-14

© 2022 Sohail Ahmad et al., published by De Gruyter

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

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  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
https://doi.org/10.1515/ntrev-2022-0486
Keywords for this article
graphene oxide; iron oxide; engine oil; activation energy; induced magnetic field
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  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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