Thermal characteristics of kerosene oil-based hybrid nanofluids (Ag-MnZnFe2O4): A comprehensive study

Hybrid nanofluids are new and most fascinating types of fluids that involve superior thermal characteristics. These fluids exhibit better heat-transfer performance as equated to conventional fluids. Our concern, in this paper, is to numerically interpret the kerosene oil-based hybrid nanofluids comprising dissimilar nanoparticles like silver (Ag) and manganese zinc ferrite (MnZnFe₂O₄). A numerical algorithm, which is mainly based on finite difference discretization, is developed to find the numerical solution of the problem. A numerical comparison appraises the efficiency of this algorithm. The effects of physical parameters are examined via the graphical representations in either case of nanofluids (pure or hybrid). The results designate that the porosity of the medium causes a resistance in the fluid flow. The enlarging values of nanoparticle volume fraction of silver sufficiently increase the temperature as well as velocity. It is examined here that mixture of hybrid nanoparticles (Ag-MnZnFe₂O₄) together with kerosene oil can provide assistance in heating up the thermal systems.

Introduction

Kerosene oil-based hybrid nanofluids can embellish the thermal characteristics; that is why these fluids have several uses in modern engineering and technology (Upreti et al., 2021; Yahya et al., 2022). The host or base fluid such as kerosene oil also plays an important role in augmentation of the heat-transfer performance rather than the nanoparticles. A combustible hydrocarbon-type liquid often obtained from petroleum can be referred to as kerosene oil, which is also known as paraffin or lamp oil. It is used as jet fuel in jet engines, as lighting and cooking fuel, as aviation fuel, as an oil-based paint, and in corrosion experiments. Due to these characteristics, we have chosen kerosene oil as the host fluid in the current analysis. To prepare the hybrid composition (Ahmad et al., 2021a), nanoparticles of manganese zinc ferrite and silver are mixed in kerosene oil. Silver is a metal or chemical element having the highest thermal and electrical conductivity as compared to other metals. It is usually found in Earth’s crust as a free element. Many substances are made of silver, such as ornaments, jewellery, utensils, solar panels, high-value tableware, and lead, and it is used in stained glass, catalysis of chemical reactions, window coatings, specialized mirrors, zinc refining, gold, and so forth. Manganese zinc ferrites belong to ferrite materials and exhibit high magnetic permeability (Ahmad et al., 2022a). These are widely used in noise filters, choke coils, transformers, and memory devices. Some recent investigations on nanofluids and hybrid nanofluids are discussed in reference articles (Abdal et al., 2021; Ahmad et al., 2021b; Zahid et al., 2021; Ayub et al., 2022; Nisar et al., 2022; Safdar et al., 2022).

Recently, many researchers have evaluated the thermal performance of usual and hybrid nanofluids numerically, theoretically, and experimentally. Dawar et al. (2022) investigated the kerosene oil and water-based hybrid nanofluid flow of copper and copper oxide nanoparticles. The magnetohydrodynamic effect was also taken into account, and the flow was taken over a bi-directional expanding surface. Comparative results of both hybrid nanofluids were established. The hybrid mixture of copper and aluminum oxide particles was prepared to form water-based hybrid nanofluid flow of Cu-Al₂O₃/water (Zainal et al., 2022). The outcomes of this study revealed that the Nusselt number got reduced when the values of slip parameter increased. Akhter et al. (2022) and Ali et al. (2022) numerically simulated the nanofluid and hybrid nanofluid flows using the quasilinearization technique, respectively. Ezhil et al. (2021) presented the analysis of ferrous oxide Fe₃O₄ and copper (Cu) taking ethylene glycol as the base fluid. Flow was assumed to be fully developed occurring over a stretching sheet. The same work was carried out by Unyong et al. (2022) taking the effects of an inclined magnetic field and partial slip.

Heat transmission and fluid flow in permeable media have gained utmost attention of researchers due to their practical employments. Flow of Williamson nanofluids over a horizontal sheet embedded in a porous medium taking the combined impact of Brownian motion and thermal radiation was studied by Mishra and Mathur (2020). A boundary layer flow involving gyrotactic microorganisms and nanofluids was examined by Elbashbeshy and Asker (2022). The nonlinear velocity caused the stretching of sheets, and the controlling parameters were discussed quantitatively. The characteristics of flow dynamics in porous media and in the presence of nanoparticles have substantial effects on heat-transfer effects (Dastvareh and Azaiez, 2017). In this paper, it was determined that nanoparticles decreased the viscosity distribution monotonically. Flow and heat transfer of ferro-nanofluids through Darcian porous media between channel walls were numerically simulated by Das et al. (2019). The heat-transfer rate at the upper channel wall was noticed to be increasing as compared to the lower wall. Flow of nanoparticles in the presence of peristaltic waves and porous media has been investigated by Kareem and Abdulhadi (2020). They achieved numerical results using the Mathematica 11 program. More recent numerical investigations on nanofluids can be found in Ahmed et al., 2017a; Ahmed et al., 2017b; Ahmed et al., 2018; Ahmed et al., 2020; Adnan et al., 2022a; Adnan et al., 2022e; Adnan et al., 2022f; Adnan et al., 2022b; Adnan et al., 2022d; and Adnan et al., 2022c.

In spite of so much efforts to explore and discover the new energy sources, still, struggle is continued. New types of hybrid nanocompositions are being introduced. The available literature evidently discloses that kerosene oil-based nanofluids and hybrid nanofluids consisting of silver (Ag) and manganese zinc ferrite (MnZnFe₂O₄) nanoparticles have not been numerically investigated yet. However, our analysis is a first effort to examine the nanocomposition of Ag-MnZnFe₂O₄-KO. The role of chemical reaction, suction, and porous media is also discussed in both pure and hybrid cases of nanofluids. Numerical solutions are found with the help of finite difference discretization via MATLAB. Thermal systems can manage and maintain their temperature and heat-transfer rate with the help of proposed hybrid compositions, for example, Ag-MnZnFe₂O₄-KO.

Problem formulation

The nanoparticles of silver (Ag) and manganese zinc ferrite (MnZnFe₂O₄) are mixed in kerosene oil to form the hybrid nanocomposite of Ag-MnZnFe₂O₄/kerosene oil. The x- and y-axes are taken in such a way that the fluid flowing along the x-axis and y-axis is vertical to the surface. Figure 1 demonstrates the structure of the extending surface. It is assumed that the fluid is flowing through a porous medium with the effect of chemical reaction.

FIGURE 1

FIGURE 1. Structure of the geometry.

The model governing equations have the following form (Ahmad et al., 2021c):

$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0(1)$

$u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}={\upsilon }_{hnf}\frac{{\partial }^{2}u}{\partial y^2}-\frac{{\mu }_{hnf}}{{\rho }_{hnf}{k}^{\ast }}u(2)$

$u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\frac{K_{hnf}}{{\left(\rho C_p\right)}_{hnf}}\frac{{\partial }^{2}T}{\partial y^2}(3)$

$u\frac{\partial C}{\partial x}+v\frac{\partial C}{\partial y}=D_B\frac{{\partial }^{2}C}{\partial y^2}-K_r(C-C_{\infty }).(4)$

The analogous boundary conditions (BCs) are

$\begin{array}{l}y=0:u(x,0)=U_w\left(x\right)=cx,T(x,0)=T_w,v(x,0)=-v_0,C(x,0)=C_w\\ y\to \infty :u(x,\infty )=0,T(x,\infty )=T_{\infty },C(x,\infty )=C_{\infty }\end{array}\}(5)$

The suction velocity is denoted by $v_0>0$. The notations $T_w$ and $T_{\infty }$ represent the temperatures at the surface boundary and away from the boundary. Likewise, the concentrations away from the boundary and at the boundary are respectively represented by $C_{\infty }$ and $C_w$. The surface is stretching with the velocity $U_w\left(x\right)=u(x,0)=cx$ The hybrid nanofluid is expressed by the notation $hnf$.

Formation of pure (Ag/KO) and hybrid nanofluids (MnZnFe₂O₄-Ag/KO)

The hybrid nanocomposite MnZnFe₂O₄-Ag/KO can be achieved by mixing the nanoparticles of manganese zinc ferrite (MnZnFe₂O₄) and silver (Ag) in the kerosene oil (KO). Initially, the volume fraction of MnZnFe₂O₄ (${\varphi }_1$) is considered as 0.2 when resolved in the kerosene oil to form the pure nanofluid MnZnFe₂O₄/KO. Afterward, the particles of Ag (${\varphi }_2$) are inserted in this solution, which give rise to the hybrid nanofluids (MnZnFe₂O₄-Ag/KO). Thermal properties of manganese zinc ferrite, silver, and kerosene oil are specified in Table 1. Further characteristics like specific heat, thermal conductivity, and density (in both cases of nanofluids) are assumed to be the same as those taken by Ahmad et al. (2021d). The notation $s_2$ expresses the silver volume fraction, and $s_1$ is used for the volume fraction of manganese zinc ferrite. The host fluid kerosene oil is represented by f.

TABLE 1

TABLE 1. Thermal properties of silver, kerosene oil, and manganese zinc ferrite.

Dimensionless variables

The following dimensionless variables are introduced in order to convert partial differential equations (PDEs) into a dimensionless system of ordinary differential equations (ODEs):

$\xi =\sqrt{\frac{c}{{\upsilon }_f}}y,\psi =\sqrt{c{\upsilon }_f}xf\left(\xi \right),\theta \left(\xi \right)=\frac{T-T\infty }{T_w-T\infty },\varphi \left(\xi \right)=\frac{C-C_{\infty }}{C_w-C_{\infty }}(6)$

The continuity equation (Eq. 1) is identically satisfied by relation (6), and this relation renovates the system of Eqs. 2–4 in the form

$f^{\prime \prime \prime }={\mathrm{\Delta }}_1\left(f^{{\prime }^2}-f{f}^{\prime \prime }\right)+\epsilon f^{\prime }(7)$

$\frac{1}{\mathrm{Pr}}{\mathrm{\Delta }}_2{\theta }^{\prime \prime }+{\mathrm{\Delta }}_{3}f{\theta }^{\prime }=0(8)$

$\frac{1}{Sc}{\varphi }^{\prime \prime }+f{\varphi }^{\prime }-C_R\varphi =0(9)$

where

${\mathrm{\Delta }}_1={(1-{\varphi }_1)}^{2.5}{(1-{\varphi }_2)}^{2.5}\left[(1-{\varphi }_2)\left\{(1-{\varphi }_1)+{\varphi }_1\frac{{\rho }_{s_1}}{{\rho }_f}\right\}+{\varphi }_2\frac{{\rho }_{s_2}}{{\rho }_f}\right](10)$

${\mathrm{\Delta }}_2=\frac{K_{hnf}}{K_f}(11)$

${\mathrm{\Delta }}_3=\left[(1-{\varphi }_2)\left\{(1-{\varphi }_1)+{\varphi }_1\frac{{\left(\rho c_p\right)}_{s_1}}{{\left(\rho c_p\right)}_f}\right\}+{\varphi }_2\frac{{\left(\rho c_p\right)}_{s_2}}{{\left(\rho c_p\right)}_f}\right](12)$

The BCs (5) take the following form now:

$\begin{array}{l}\xi =0:f={\lambda }_S,f^{\prime }=1,\theta =1,\varphi =1,\\ \xi \to \infty :f^{\prime }\to 0,\theta \to 0,\varphi \to 0.\end{array}\}(13)$

Problem parameters

The problem parameters of dimensionless Eqs. 7–9 are identified as follows:

$S_c=\frac{{\upsilon }_f}{D_B}$ is the Schmidt number

${\lambda }_S=\frac{v_0}{\sqrt{c{\upsilon }_f}}$ is the suction parameter

$\mathrm{Pr}=\frac{{\mu }_f{\left(c_p\right)}_f}{k_f}$ is the Prandtl number

$\epsilon =\frac{{\upsilon }_f}{c{k}^{\ast }}$ is the porosity parameter

$C_R=\frac{K_r^2}{c}$ is the chemical reaction parameter

The relations for shear stress as well as Sherwood and Nusselt number are given by

${\mathrm{Re}}_x^{\frac{1}{2}}{C}_{fx}=\frac{f^{\prime \prime }\left(0\right)}{{(1-{\varphi }_1)}^{2.5}{(1-{\varphi }_2)}^{2.5}},S{h}_x{\mathrm{Re}}_x^{\frac{1}{2}}=-{\varphi }^{\prime }\left(0\right),N{u}_x{\mathrm{Re}}_x^{\frac{1}{2}}=-\frac{k_{hnf}}{k_f}{\theta }^{\prime }\left(0\right).(14)$

whereas the local Reynolds number is given as ${\mathrm{Re}}_x=\frac{U_{w}x}{{\upsilon }_f}$.

Numerical scheme based on finite difference discretization

Finding the analytical solution of the coupled Eqs. 7–9 may be so much time-consuming as these equations are not only higher-order but also highly nonlinear. However, we require some persuasive numerical technique which could be employed to determine the solution of the problem. Therefore, we adopt a finite difference methodology in order to find the numerical solution of the problem under consideration. The different numerical methods (to solve such types of dynamical problems) that we adopted in our earlier work can be seen in reference articles (Ahmad et al., 2021e; Ahmad et al., 2021f; Jamshed. et al., 2021; Ahmad et al., 2022b). We describe the structure of this methodology in the following flow chart diagram (Figure 2).

FIGURE 2

FIGURE 2. Flow chart of the numerical method.

Results and discussion

This section depicts the analysis of mono (Ag/kerosene oil) and hybrid (Ag-MnZnFe₂O₄/kerosene oil) cases of nanofluids. The nanocomposites of silver (Ag) into the kerosene oil give rise to the mono nanofluid, whereas the amalgamation of manganese zinc ferrite and silver produces the hybrid mixture. The effects of physical parameters are deliberated via the graphs and tables. Table 2 portrays a comparison which is found to be in a good correlation with the existing outcomes under limiting cases.

TABLE 2

TABLE 2. Change in heat-transfer rate for different Prandtl numbers when ${\varphi }_1={\varphi }_2=0$.

We assign fixed values to the parameters such as $\mathrm{Pr}=6.135$. The other specified values which have been used in finding the numerical solution are

$\epsilon =4,{\varphi }_1=0.2,Sc=2.5,{\varphi }_2=0.05,{\lambda }_s=1.5,C_R=4.$

The change in surface drag ${\mathrm{Re}}_x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{C}_f$ and Nusselt number ${\mathrm{Re}}_x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}N{u}_x$ against porosity parameter $\epsilon$ can be observed from Table 3. An increase in the values of porosity parameter tends to enhance the skin friction, but its effect is to deteriorate the rate of heat transfer. The fluid flow is resisted by the porosity of the medium due to which the velocity of the fluid reduces (see Figure 3). The Prandtl number tends to deteriorate the temperature as shown in Figure 4.

TABLE 3

TABLE 3. Impact of porosity parameter on ${\mathrm{Re}}_x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{C}_f$ and ${\mathrm{Re}}_x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}N{u}_x$.

FIGURE 3

FIGURE 3. Variation in velocity with $\epsilon$.

FIGURE 4

FIGURE 4. Variation in temperature with $pr$.

Thermal characteristics in either case of nanofluids are affected by the volume fraction ${\varphi }_2$ of silver nanoparticles. The required outcomes can be attained by suitably taking the volume fractions of nanoparticles. It is comparatively noticed from Figure 5 that the temperature increases rapidly in the case of the hybrid composition Ag-MnZnFe₂O₄/KO rather than the composition of Ag/KO when we increase the volume concentration ${\varphi }_2$. In the same way, the velocity of the fluid accelerates quickly in the hybrid case of the nanofluid as pictured in Figure 6. The impact of both volume fraction ${\varphi }_2$ and the Prandtl number $\mathit{Pr}$ is to escalate the Nusselt number ${\mathrm{Re}}_x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}N{u}_x$ for both pure and hybrid nanofluids (see Table 4).

FIGURE 5

FIGURE 5. Variation in temperature with ${\varphi }_2$.

FIGURE 6

FIGURE 6. Variation in velocity with ${\varphi }_2$.

TABLE 4

TABLE 4. Impact of nanoparticle volume fraction and Prandtl number on ${\mathrm{Re}}_x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}N{u}_x$.

The variation in temperature and velocity for diverse values of the suction parameter can be examined from Figures 7, 8. Both the temperature $\theta \left(\xi \right)$ and velocity $F^{\prime }\left(\xi \right)$ turn toward reduction (in both cases of nanofluids) with the effect of suction. Figure 9 illustrates the influence of the chemical reaction parameter on concentration in either case of the nanofluid. A decreasing trend is noticed in the concentration profile, which shows that the chemical reaction parameter $C_R$ causes a substantial decrease in the concentration.

FIGURE 7

FIGURE 7. Variation in temperature with ${\lambda }_s$

FIGURE 8

FIGURE 8. Variation in velocity with ${\lambda }_s$.

FIGURE 9

FIGURE 9. Variation in concentration with $C_R$.

The mass-transfer rate increases with an increase in the values of $C_R$ as observed in Table 6. It has also been deduced from Table 5 that the suction parameter ${\lambda }_S$ marginally enhances the heat-transfer rate in the case of the hybrid nanofluid Ag-MnZnFe₂O₄/KO rather than the usual case of the nanofluid Ag/KO.

TABLE 5

TABLE 5. Impact of activation energy and chemical reaction on ${\mathrm{Re}}_x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}S{h}_x$.

Conclusion

Specific rate of heat transfer plays an important role in many engineering systems as it can affect the quality of the product. A certain or specific heat-transfer rate is essentially required in many energy systems, for example, metal expulsion, nuclear system cooling, refrigeration, thermal storage, cooling generator, and so on. The amalgamation of manganese zinc ferrites (MnZnFe₂O₄) and silver (Ag) in kerosene oil can provide assistance in increasing the heat-transfer rate. The main results of this study are listed as follows:

a) The nanoparticle volume fraction of silver (${\varphi }_2$) tends to elevate the velocity and temperature of Ag/KO as well as Ag-MnZnFe₂O₄/KO, which are mono and hybrid cases of nanofluids, respectively.

b) The fluid motion and temperature are reduced due to the suction phenomenon. On the other hand, the surface drag got increased with suction for both cases of nanofluids.

c) The heat-transfer rate is an increasing function of Prandtl number, whereas the temperature is decelerated with the effect of Prandtl number.

d) The concentration profile seems to be falling down with an increase in the chemical reaction parameter.

e) The porosity of the medium resists the flow in either case of nanofluids, for example, the pure or hybrid case.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Funding

The authors are grateful to the Deanship of Scientific Research, Islamic University of Madinah, Ministry of Education, KSA, for supporting this research work through a research project grant under Research Group Program/1/804.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

References

Abdal, S., Habib, U., Siddique, I., Akgül, A., and Ali, B. (2021). Attribution of multi-slips and bioconvection for micropolar nanofluids transpiration through porous medium over an extending sheet with PST and PHF conditions. Int. J. Appl. Comput. Math. 7 (6), 235. doi:10.1007/s40819-021-01137-9

CrossRef Full Text | Google Scholar

Adnan, , , Ashraf, W., Khan, I., and Andualem, M. (2022a). Thermal transport investigation and shear drag at solid-liquid interface of modified permeable radiative-SRID subject to Darcy-Forchheimer fluid flow composed by γ-nanomaterial. Sci. Rep. 12, 3564. doi:10.1038/s41598-022-07045-2

PubMed Abstract | CrossRef Full Text | Google Scholar

Adnan, , , Ashraf, W., Khan, I., Shemseldin, M. A., and Mousa, A. A. A. (2022c). Numerical energy storage efficiency of MWCNTs-Propylene Glycol by inducing thermal radiations and combined convection effects in the constitutive model. Front. Chem. 10, 879276. doi:10.3389/fchem.2022.879276

PubMed Abstract | CrossRef Full Text | Google Scholar

Adnan, , , Ashraf, W., Khan, U., Al-Johani, A. S., Ahmed, N., Mohyud-Din, S. T., et al. (2022b). Impact of freezing temperature (Tfr) of Al2O3 and molecular diameter (H2O)d on thermal enhancement in magnetized and radiative nanofluid with mixed convection. Sci. Rep. 12, 703. doi:10.1038/s41598-021-04587-9

CrossRef Full Text | Google Scholar

Adnan, , , Khan, U., Ahmed, N., Mohyud-Din, S. T., Alharbi, S. O., and Khan, I. (2022d). Thermal improvement in magnetized nanofluid for multiple shapes nanoparticles over radiative rotating disk. Alexandria Eng. J. 61 (3), 2318–2329. doi:10.1016/j.aej.2021.07.021

CrossRef Full Text | Google Scholar

Adnan, , , Khan, U., Ahmed, N., Mohyud-Din, S. T., Alsulami, M. D., and Khan, I. (2022e). A novel analysis of heat transfer in the nanofluid composed by nanodimaond and silver nanomaterials: Numerical investigation. Sci. Rep. 12, 1284. doi:10.1038/s41598-021-04658-x

PubMed Abstract | CrossRef Full Text | Google Scholar

Adnan, , , Murtaza, R., Hussain, I., Rehman, Z., Khan, I., and Andualem, M. (2022f). Thermal enhancement in Falkner-Skan flow of the nanofluid by considering molecular diameter and freezing temperature. Sci. Rep. 12, 9415. doi:10.1038/s41598-022-13423-7

PubMed Abstract | CrossRef Full Text | Google Scholar

Ahmad, S., Akhter, S., and Shahid, M. I. (2022). Novel thermal aspects of hybrid nanofluid flow comprising of Manganese zinc ferrite MnZnFe₂O₄, Nickel zinc ferrite NiZnFe₂O₄ and motile microorganisms. Ain Shams Eng. J. 13 (5), 101668. doi:10.1016/j.asej.2021.101668

CrossRef Full Text | Google Scholar

Ahmad, S., Ali, K., Ahmad, S., and Cai, J. (2021). Numerical study of lorentz force interaction with micro structure in channel flow. Energies 14 (14), 4286. doi:10.3390/en14144286

CrossRef Full Text | Google Scholar

Ahmad, S., Ali, K., and Ashraf, M. (2021). MHD flow of Cu-Al2O3/water hybrid nanofluid through a porous media. J. Por. Media 24 (7), 61–73. doi:10.1615/JPorMedia.2021036704

CrossRef Full Text | Google Scholar

Ahmad, S., Ali, K., Faridi, A. A., and Ashraf, M. (2021). Novel thermal aspects of hybrid nanoparticles Cu-TiO2 in the flow of Ethylene Glycol. Int. Commun. Heat. Mass Transf. 129, 105708. doi:10.1016/j.icheatmasstransfer.2021.105708

CrossRef Full Text | Google Scholar

Ahmad, S., Ali, K., Nisar, K. S., Faridi, A. A., Khan, N., Jamshed, W., et al. (2021). Features of Cu and TiO2 in the flow of engine oil subject to thermal jump conditions. Sci. Rep. 11, 19592. doi:10.1038/s41598-021-99045-x

PubMed Abstract | CrossRef Full Text | Google Scholar

Ahmad, S., Ali, K., Rizwan, M., and Ashraf, M. (2021). Heat and mass transfer attributes of copper-aluminum oxide hybrid nanoparticles flow through a porous medium. Case Stud. Therm. Eng. 25, 100932. doi:10.1016/j.csite.2021.100932

CrossRef Full Text | Google Scholar

Ahmad, S., Ashraf, M., and Ali, K. (2021). Simulation of thermal radiation in a micropolar fluid flow through a porous medium between channel walls. J. Therm. Anal. Calorim. 144 (3), 941–953. doi:10.1007/s10973-020-09542-w

CrossRef Full Text | Google Scholar

Ahmad, S., Younis, J., Ali, K., Rizwan, M., Ashraf, M., and Abd El Salam, M. A. (2022). Impact of swimming gyrotactic microorganisms and viscous dissipation on nanoparticles flow through a permeable medium: A numerical assessment. J. Nanomater. 2022, 1–11. doi:10.1155/2022/4888128

CrossRef Full Text | Google Scholar

Ahmed, N., Abbasi, A., Khan, U., and Mohyud-Din, S. T. (2018). Thermal radiation effects on flow of Jeffery fluid in converging and diverging stretchable channels. Neural Comput. Applic. 30, 2371–2379. doi:10.1007/s00521-016-2831-5

CrossRef Full Text | Google Scholar

Ahmed, N., Adnan, , Khan, U., Mohyud-Din, S. T., and Manzoor, R. (2017). Influence of viscous dissipation on a copper oxide nanofluid in an oblique channel: Implementation of the KKL model. Eur. Phys. J. Plus 132, 237. doi:10.1140/epjp/i2017-11504-y

CrossRef Full Text | Google Scholar

Ahmed, N., Adnan, , Khan, U., and Mohyud-Din, S. T. (2020). Modified heat transfer flow model for SWCNTs-H2O and MWCNTs-H2O over a curved stretchable semi infinite region with thermal jump and velocity slip: A numerical simulation. Phys. A Stat. Mech. its Appl. 545, 123431. doi:10.1016/j.physa.2019.123431

CrossRef Full Text | Google Scholar

Ahmed, N., Adnan, , Khan, U., Mohyud-Din, S. T., and Suat Erturk, V. S. (2017). Influence of thermal and concentration gradients on unsteady flow over a stretchable surface. Results Phys. 7, 3153–3162. doi:10.1016/j.rinp.2017.08.034

CrossRef Full Text | Google Scholar

Akhter, S., Ahmad, S., and Ashraf, M. (2022). Cumulative impact of viscous dissipation and heat generation on MHD Darcy-Forchheimer flow between two stretchable disks: Quasi linearization technique. J. Sci. Arts 22 (1), 219–232. doi:10.46939/J.Sci.Arts-22.1-c01

CrossRef Full Text | Google Scholar

Ali, K., Faridi, A. A., Ahmad, S., Jamshed, W., Khan, N., and Alam, M. M. (2022). Quasi-linearization analysis for heat and mass transfer of magnetically driven 3rd-grade (Cu-TiO2/engine oil) nanofluid via a convectively heated surface. Int. Commun. Heat Mass Transf. 135, 106060. doi:10.1016/j.icheatmasstransfer.2022.106060

CrossRef Full Text | Google Scholar

Ayub, R., Ahmad, S., Ahmad, S., Akhtar, Y., Alam, M. M., and Mahmoud, O. (2022). Numerical assessment of dipole interaction with the single-phase nanofluid flow in an enclosure: A pseudo-transient approach. Materials 15, 2761. doi:10.3390/ma15082761

PubMed Abstract | CrossRef Full Text | Google Scholar

Das, S., Tarafdar, B., Jana, R. N., and Makinde, O. D. (2019). Magnetic ferro-nanofluid flow in a rotating channel containing darcian porous medium considering induced magnetic field and Hall currents. Spec. Top. Rev. Porous Media 10 (4), 357–383. doi:10.1615/SpecialTopicsRevPorousMedia.2019028377

CrossRef Full Text | Google Scholar

Dastvareh, B., and Azaiez, J. (2017). Instabilities of nanofluid flow displacements in porous media. Phys. Fluids 29, 044101. doi:10.1063/1.4978890

CrossRef Full Text | Google Scholar

Dawar, A., Islam, S., and Shah, Z. (2022). A comparative analysis of the performance of magnetised copper-copper oxide/water and copper-copper oxide/kerosene oil hybrid nanofluids flowing through an extending surface with velocity slips and thermal convective conditions. Int. J. Ambient Energy, 1–19. doi:10.1080/01430750.2022.2063387

CrossRef Full Text | Google Scholar

Elbashbeshy, E. M. A., and Asker, H. G. (2022). Fluid flow over a vertical stretching surface within a porous medium filled by a nanofluid containing gyrotactic microorganisms. Eur. Phys. J. Plus 137, 541. doi:10.1140/epjp/s13360-022-02682-y

CrossRef Full Text | Google Scholar

Ezhil, K., Thavada, S. K., and Ramakrishna, S. B. (2021). MHD slip flow and heat transfer of Cu-Fe3O4/Ethylene glycol-based hybrid nanofluid over a stretching surface. Biointerface Res. Appl. Chem. 11 (4), 11956–11968. doi:10.33263/BRIAC114.1195611968

CrossRef Full Text | Google Scholar

Jamshed., W., Baleanu, D., Nasir, N. A. A. M., Shahzad, F., Nisar, K. S., Shoaib, M., et al. (2021). The improved thermal efficiency of Prandtl-eyring hybrid nanofluid via classical keller box technique. Sci. Rep. 11, 23535. doi:10.1038/s41598-021-02756-4

PubMed Abstract | CrossRef Full Text | Google Scholar

Kareem, R. S., and Abdulhadi, A. M. (2020). Effect of MHD and porous media on nanofluid flow with heat transfer: Numerical treatment. J. Adv. Res. Fluid Mech. Therm. Sci. 63 (2), 317–328.

Google Scholar

Khan, W. A., and Pop, I. (2010). Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53, 2477–2483. doi:10.1016/j.ijheatmasstransfer.2010.01.032

CrossRef Full Text | Google Scholar

Mishra, S. R., and Mathur, P. (2020). Williamson nanofluid flow through porous medium in the presence of melting heat transfer boundary condition: Semi-analytical approach. Mmms 17 (1), 19–33. doi:10.1108/MMMS-12-2019-0225

CrossRef Full Text | Google Scholar

Nisar, K. S., Faridi, A. A., Ahmad, S., Khan, N., Ali, K., Jamshed, W., et al. (2022). Cumulative impact of micropolar fluid and porosity on mhd channel flow: A numerical study. Coatings 12, 93. doi:10.3390/coatings12010093

CrossRef Full Text | Google Scholar

Safdar, R., Jawad, M., Hussain, S., Imran, M., Akgül, A., and Jamshed, W. (2022). Thermal radiative mixed convection flow of MHD Maxwell nanofluid: Implementation of buongiorno's model. Chin. J. Phys. 77, 1465–1478. doi:10.1016/j.cjph.2021.11.022

CrossRef Full Text | Google Scholar

Unyong, B., Vadivel, R., Govindaraju, M., Anbuvithya, R., and Gunasekaran, N. (2022). Entropy analysis for ethylene glycol hybrid nanofluid flow with elastic deformation, radiation, non-uniform heat generation/absorption, and inclined Lorentz force effects. Case Stud. Therm. Eng. 30, 101639. doi:10.1016/j.csite.2021.101639

CrossRef Full Text | Google Scholar

Upreti, H., Pandey, A. K., and Kumar, M. (2021). Assessment of entropy generation and heat transfer in three-dimensional hybrid nanofluids flow due to convective surface and base fluids. J. Porous Media 24 (3), 35–50. doi:10.1615/JPorMedia.2021036038

CrossRef Full Text | Google Scholar

Yahya, A. U., Siddique, I., Jarad, F., Salamat, N., Abdal, S., Hamed, Y. S., et al. (2022). On the enhancement of thermal transport of Kerosene oil mixed TiO2 and SiO2 across Riga wedge. Case Stud. Therm. Eng. 34, 102025. doi:10.1016/j.csite.2022.102025

CrossRef Full Text | Google Scholar

Zahid, M., Asjad, M. I., Hussain, S., and Akgül, A. (2021). Nonlinear magnetohydrodynamic flow of nanofluids across a porous matrix over an extending sheet with mass transpiration and bioconvection. Heat. Transf. 50 (8), 7588–7603. doi:10.1002/htj.22244

CrossRef Full Text | Google Scholar

Zainal, N. A., Nazar, R., Naganthran, K., and Pop, I. (2022). Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point. Appl. Math. Mech.-Engl. Ed. 43, 547–556. doi:10.1007/s10483-022-2823-6

CrossRef Full Text | Google Scholar

Nomenclature

${\rho }_{hnf}$ Density of the hybrid nanofluid

$v$ Component of velocity along the $y$-axis

${\sigma }_{hnf}$ Electrical conductivity of the hybrid nanofluid

$k^{\ast }$ Darcy permeability

$v_0$ Suction velocity (where $v_0>0$)

$C_{p_{hnf}}$ Specific heat of the hybrid nanofluid

$u$ Component of velocity along the $x$-axis

$K_r$ Rate constant of chemical reaction

$k_{hnf}$ Thermal conductivity of the hybrid nanofluid

$c$ Stretching/shrinking constant

${\upsilon }_{hnf}$ Kinematic viscosity of the hybrid nanofluid

$T$ Temperature of the fluid

${\mu }_{hnf}$ Hybrid nanofluid viscosity

$T_{\infty }$ Temperature far away from the sheet

$C$ Concentration of the fluid

$T_w$ Fixed temperature at the surface

$D_B$ Diffusion coefficient

$C_{\infty }$ Concentration far away from the sheet