Thermal Analysis on Kerosene Oil-Based Two Groups of Ternary Hybrid Nanoparticles (CNT-Gr-Fe 3 O 4 and MgO-Cu-Au) Mix Flow over a Bidirectional Stretching Sheet: A Comparative Approach

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Introduction
Nanoliquid is a colloidal combination of regular liquids with particles by a diameter of nanometers.Tese particles are used to improve the thermal characteristics of common liquids with poor thermal conductivities.Te most recent generations have employed numerous cutting-edge approaches to increase heat transfer rates to reach various rates of thermal capabilities.To accomplish this, improving heat conductivity is essential.In the end, various attempts to improve thermal conductivity were made by spreading larger thermally conductive solid components throughout the fuids.Various studies on nanofuids have been conducted to meet the demands of commercial applications.Nanofuids may quench the demand of energy utilization experts and scientists, but a better sort of fuid is still under investigation.To address them, better nanofuid forms with a higher thermal conductivity than nanofuid, such as "hybrid nanofuid" have arisen.Tese types of nanoparticles have high thermal properties.When we mix these types of nanoparticles, we get better thermal conductivity.Because of this, the current work's main objective is to increase heat rate transmission using a ternary hybrid nanofuid.
Nanofuid is utilized in a variety of industrial and nanotechnological techniques, including heat transfer systems, electronic device cooling, nuclear reactors, vehicle cooling, and vehicle thermal management, among others, to solve realworld challenges.Magnetic nanofuids are also useful for a wide range of other uses, including the treatment of wounds, the opening of blocked arteries, therapy for cancer, and magnetic resonance imaging.Ahmad et al. [1] explored the augmentation of Go/kerosene oil and Gr-silver/kerosene oil hybrid nanoliquids in the existence of an applied magnetic feld if the liquids stream across a porous medium through a stretched surface.Kerosene oil-(Ko-) based hybrid nanofuid, a particular diathermal oil, was the subject of an examined by Anwar et al. [2].Te needed hybrid nanoliquid is created by the hybridization of MgO and silica nanoparticles.By creating a new combination of nanoparticles known as triple particles, Bilal et al. [3] explained the hydrothermal properties of water in this article.Two distinct kinds of groups are taken into account for this purpose: one with lower densities (CNT, Gr, and aluminum oxide) and the other with a greater density (CuO, Cu, and Ag).Elnaqeeb et al. [4] looked into the process of transport of water carrying lesser densities of tiny particles (such as CNT, Gr, and Al 2 O 3 ) and signifcant higher densities of tiny particles (such as CuO, Cu, and Ag) of diferent kinds with a rectangular closed feld.Deionized water-(DIW-) based Al 2 O 3 and MWCNT mix nanoliquids were studied by Giwa et al. [5] to determine how temperatures and mass ratios of particles afected the fuids' viscosity and electrical conductivity.Huminic and Huminic [6] investigated the heat transmission capabilities and level of thermodynamic irreversibility of the two kinds of hybrid nanofuids, specifcally MWCNT-Fe 3 O 4 /water and ND-Fe 3 O 4 /water, utilized in a fattened tube.A pair of emphasize based on water nanofuids, a mix nanoliquid, and thermal radiation in a triple mixed nanofuid was studied by Jakeer et al. [7] to determine how nonlinear Darcy-Forchheimer afected the electromagneto hydrodynamic fow of these fuids on a sheet that was stretched.One of the non-Newtonian fuid classes that established the properties of yield stress was the Casson liquid model.In real life, Casson fuid is frequently utilized in things like jelly, honey, sauce, concentrated fruit juices, and soup.Additionally, it has a wide range of applications in the domains of industries that advance daily.Te non-Newtonian fuid presents a signifcantly more difcult study due to its dynamics, complexity, and interactions.Krishna [8] established with using into consideration account the impacts of heat generation and viscous dissipation, the impact of Newtonian heat on unstable an infnitely oscillating vertically plate attached to a porous medium is used to accomplish MHD free convective fow of a radiate and chemically reacting Casson mixed nanoliquid.
Majeed et al. [9] investigated the non-Newtonian (Casson) tiny liquids models: two-dimensional bioconvection MHD stream and warm transmission.To simulate the MHD Casson in two dimensions stream across a linearly extending/ contracting sheet given the convective boundary conditions and suction, and radiation impacts, Mousavi et al. [10] investigated the thermal efciency of a mix of water/MgO-Ag nanoliquid.Mahanta and Shaw [11] explored a porous, linear extended sheet is passed by a 3D Casson fuid in this issue using magneto hydrodynamics (MHD).Electromagnetic waves transmit energy or heat through a process called thermal radiation.When there is a signifcant variation in temperature between the boundary surfaces and the surrounding fuid, radiation parameter is crucial.Radiative infuences are important in physics and engineering.When completing tasks involving high temperatures and space technology, consideration of radiation heat transfer's impacts on diverse fows is crucial.In addition, the impacts of radiation are crucial for observing heat transfer in the polymer sectors, where heat regulating components have a minimal impact on the fnal product's quality.Te implications of radiation on airplanes, gas turbines, spacecraft, liquid metal fuids, and solar radiation are also pertinent.Mandal and Pal [12] studied the steady twodimensional magneto hydrodynamic nature of stream and heat exchange of the Darcy-Forchheimer non-Newtonian (cross) mix nanoliquid made of Go/kerosene oil and Go-Ag/kerosene oil passing by the permeable medium through a stretch sheet.Nayak et al. [13] examined a three-dimensional GO-MoS 2 /Casson combined nanofuid stream over two parallel plates is studied to determine how the magnetic feld, nonlinear radiation impact, heat absorption, and viscous dissipation afect it.Nasir et al. [14] examined how radiation impression afected the fow of water-based nano, mix, and triple mix nanofuids under a couple stress on a sheet that was stretched.SiO 2 , TiO Te thermodifusion and difusion thermo impacts on Casson nanoliquid moving in a perpendicular system under the infuence of radiation impact were studied by Patil et al. [15].Titania-ethylene glycol nanofuid (TiO 2 /EG NF) fow through a wedge with nanoparticle aggregation efect was investigated by Kumar Rawat et al. [16].Tis fow occurred in the presence of suction/injection efects, mixed convection, thermal radiation, porous media, and nonuniform heat source/sink.Te exchange of mass and energy processes of a 3D triple hybrid nanoliquid stream through a porous medium in the direction of an expanding surface were investigated by Ramzan et al. [17].Te impacts of thermos difusion and difusion thermo factors on the characteristics of a hybrid nanoliquid stream between the electric conductivity of two plates in parallel with depending on temperature were looked at by Revathi et al. [18].Reddy et al. [19] quantitatively evaluated the impact of updated the energy fux of Fourier on the energy transmission characteristics of a mix nanoliquid made of MgO, magnetite (Fe 3 O 4 ) as tiny particles, and ethylene glycol (Eg) as an ordinary liquid.Te efects of the Cattaneo-Christov model (CC model) and quadratic thermal radiation with convective boundary conditions on ternary hybrid nanofuid (TiO 2 -SiO 2 -MoS 2 /kerosene oil) fow across a spinning disc were investigated by Singh et al. [20].Shaheen et al. [21] investigated the impact of varied parameters on the fow of a hazy Casson nanofuid in three dimensions (3D) across a deformable surface with two directions combined the energy of Arrhenius activation and chemical reaction.Sayed and Hosham [22] researched the moveable reactions of streamline sequences with their splitting in a peristaltic stream channel to transmit heat.Tis kind showed a porous flled tapering asymmetric microchannel carrying a Casson incompressible mix nanoliquid Au-Cu/blood.Sarada et al. [23] explored the movement of a curved stretched sheet with activation energy across a tripartite cross nanofuid graphene-CNT-silver with water original fuid.Te experiment by Sandeep et al. [24] was carried out to consider the novel relevance of the nonlinear thermal radiation infuence on the magneto hydrodynamic movement of the Casson mix nanoliquid induced through a curved, extending surface.Using the legendre wavelet collocation technique (LWCT), Gupta et al. [25] investigated the computational solution of magnetised GP-MoS 2 /C 2 H 6 O 2 -H 2 O unsteady fow across a stretching surface.Upreti et al. [26] examined the nature of heat and mass transfer on a Casson nanofuid fowing in three dimensions over a Riga plate with a changed magnetic feld, thermophoresis, and Brownian motion.Te Casson nanofuid contains gyrotactic microorganisms.Ullah et al. [27] studied the Casson hybrid nanofuid (HN) (ZnO-Ag/Casson fuid), which is electrically conductive and fows stably along a twodirectional stretchy sheet when a changing magnetic fux is applied.On a Riga plate with suction and injection implications, Zari et al. [28] explored the Casson nanofuid formulation due to Marangoni convection.Graphene oxide (GO) is the hard nanoparticles, and water and kerosene oil are used as the regular base fuids for nanoparticles.Te efect of cross difusion features in combined convection radiation Casson liquid stream on an exponential heated sheet was investigated by Zaigham Zia et al. [29].
Ahmed et al. [30] studied the heat transfer development in a square heat exchanger under constant heat fux conditions with the turbulent fow of innovative metal oxide-based ternary composite nanofuids of ZnO + Al 2 O 3 + TiO 2 /DW at varied weight percent concentrations (0.025, 0.05, 0.075, and 0.1).Mousavi et al. [31] explained the efects of nanoparticle volume concentration and temperature on the thermophysical characteristics and the rheological behaviour of water-based CuO/MgO/TiO 2 ternary hybrid nanofuids.An inclined catheterized artery with several stenoses and wall slip was examined by Dolui et al. [32] using ternary hybrid nanoparticles (Cu-Ag-Au).Nasir et al. [33]  Inspired by the literature listed above, this work's primary objective is to fll this gap.Te authors examined 3D non-Newtonian steady radiative MHD Casson ternary hybrid nanofuids fow across a dually stretch sheet with heat generation/absorption and viscous dissipation.For this aim, two ternary nanoparticles, namely, (CNT, graphene, and Fe 3 O 4 ) and (MgO, Cu, and Au) are mixed with the base fuid kerosene oil.Te results are generated using the bvp4c application.However, research into this fow over a dually stretching sheet has not yet started.We can be confdent that the results of our computational work are applied to any real-time issues in a variety of thermal engineering felds, including energy production, heating and cooling systems, and the design of new thermal systems and medical science such as cancer therapy and industries.

Mathematical Formulation
We have supposed three-dimensional, time-independent, viscous, incompressible boundary layer MHD non-Newtonian Casson ternary hybrid nanofuids fow over a bidirectional stretching sheet.Te fuid layer's stretching velocities along the x and y axes adjacent to the horizontal surfaces are u w (x) � ax and v w (x) � by, correspondingly.Te wall temperature and concentration are T w and C w , consequently (see Figure 1).Additionally, the following fow presumptions are noted for the present analysis: (i) Two ternary nanoparticles: one kind is CNT, graphene, and Fe 3 O 4 , and the other is MgO, Cu, and Au (ii) Base fuid-kerosene oil (iii) Radiation impact, magnetic parameter, viscous dissipation, and heat source/sink Non-Newtonian Casson fuid's constitutional relationships are used [8,12,13] where π � e mn e mn and e mn is the (m, n) T portion relating to rate of deformation, π is the multiple of the sections of defacement amount, π c is essential value of the multiply founded by fuid with non-Newtonian behaviour, μ B is the non-Newtonian fuid's plastic moveable viscosity, and τ y is yield stress for the fuid.Te continuity, motion, temperature, and concentration hybrid nanofuids controlling boundary layer equations are expressed as follows [3]: Equation of continuity is stated as follows: Equation of motion is stated as follows: Equation of temperature is stated as follows: Journal of Engineering Equation of concentration is stated as follows: ( Te associate borderline circumstances are composed by the following equation [3,4]: Te motion coefcient in x and y consistent coordinates, indicated by u and v, serially, where the fuid temperature is T (Kelvin − K) and β is several the shear thinning Casson fuid.Furthermore, hbnf denotes hybrid nanofuid, bf indicates base fluid, (ρC p ) hbnf stands for the hybrid nanofuid's capability for heat, B 0 (Tesla-T) denotes the power of the magnetic impact, σ hbnf depicts the electrical conductivity of the hybrid nanoliquid, k hbnf stands for the hybrid nanoliquid thermal conductivity, ρ hbnf depicts the density of the mixed nanofuid, μ hbnf denotes the dynamic viscosity of mix nanoliquid, z w is suction rate, Q 0 stands inside heat source (> 0)/sink (< 0) amount, D m denotes difusivity, the chemical reactive parameter defne as k 1 , C is the concentration, C p is the heat capacity at stable pressure, and C s represents for the concentration susceptibility.
Here, ϕ 1 represents the concentration of frst nanoparticles, ϕ 2 is the volume fraction of second nanoparticles, ϕ 3 denotes the volume fraction of third nanoparticles, and nf denotes the nanoparticles.Electrical conductivity, dynamic viscosity, density, and thermal conductivity of the original fuid denotes k bf , μ bf , ρ bf , and σ bf serially.In light of this, Table 1 provides details on the operating pure fuid and ternary nanostructures (see Table 2).
In energy equation ( 4), the Rosseland term, where q r denotes the fux of radiant heat and is determined using the Rosseland estimation, corresponds to thermal radiation [9,11,14,15,24].
where k * stands for the coefcient of mean absorption and σ is the Stefan-Boltzmann constant.Currently, utilizing the Taylor series T 4 as the reference at a position T ∞ and neglecting the approximate greater-order expressions and we can get the fnal form listed below: Inscribe the T 4 as a liner relation of temperature with Taylor series extension about T ∞ and disregarding superior expressions, we obtain the following equation: In the recent situation, by using the following transformations listed as follows [3], equations that are dimensional are transformed into nondimensional equations.
where the primes represent diferentiation of the pseudosimilarity variables.
Te nondimensional form of equations is obtained by applying transformations, and it is as follows: With suitable boundary circumstances, Te expressions used to indicate the presence of dimensionless limitations in equations ( 10)-( 14) are the non − Newtonian Casson parameter (β), magnetic parameter or Hartmann parameter (M), chemical reaction (Kr), Eckert number (Ec), Soret impact (Sr), Schmidt number(Sc), Prandtl parameter (Pr), radiation parameter (Nr), Dufour impact (Du), nondimensional suction parameter (f w ), ratio of stretching speed (c), and heat generation/absorption (Q).Tese factors are listed numerically as follows: Journal of Engineering Te dimensional form of the skin friction factors along the x and y directions are shown as follows: 2.1.2.Heat Transfer Rate.Te Nusselt number along the x and y directions are cleared like Nu x � xq w /k bf (T w − T ∞ ), Nu y � yq w /k bf (T w − T ∞ ), where q w is signifes heat fux, which is described asfollows:

Mass Transfer rate.
A Sherwood parameter (Sh) that is assumed yields the quantity of mass movement.Tis is defned as Sh x � xq m /D m (C w − C ∞ ), the mass transfer amount at the wall is q m , which is described as follows: Terefore, in terms of equations ( 16)-( 18), the following nondimensional quantities are obtained: , where Re x � ax 2 /v bf and Re y � b 2 y 2 /av bf are the Reynolds numbers in the x and y directions, respectively.[3,4,7].

Flowchart.
Te fowchart of Bvp4c function is as follows.

Code Validation.
Te use of comparison to recent research is used to validate the current fndings.Comparing the known study consistencies is presented in Table 3.For the present analysis, however, extremely precise results are obtained.

Journal of Engineering
Figures 3 and 4 show the velocity profles in horizontal and vertical directions alongside the diferent value of Casson fuid parameter β for both ternary groups I and II.When we increase the value of the Casson fuid parameter, velocities signifcantly decrease for ternary group II in comparison to ternary group I due to a greater reduction in the thickness of the boundary layer for ternary group II.In Figures 5 and 6, the declines velocity f′(η) and g ′ (η) are displayed with rising magnetic parameter.Te Lorentz force increases due to an increasing magnetic parameter, which increases the resistance in the fuid, so the velocity decreases more for ternary group II than for ternary group I. Since Lorenz force is inversely proportional to electrical conductivity, for ternary group II, the electrical conductivity is lower than for ternary group I.
Sketches of both Figures 7 and 8 are used to explain how suction velocity (f w ) afects the horizontal velocity (f ′ ) and vertical velocity (g ′ ).It is observed that as the value of suction velocity rises, the motion distribution declines due to the given relation f w � − z w / ��� � aϑ bf  for both ternary groups.Furthermore, from Figures 9 and 10, it is concluded that a larger value of the stretching ratio parameter narrows the thermal and concentration distributions for both ternary groups I and II.For ternary groups I and II, Figure 11 depicts how the temperature grows as the amount of the radiation parameter Nr rises.Te coefcient of heat absorption decreases as thermal radiation increases, raising the fuid temperature.As a result, because of the greater amount of heat transmitted there due to better radiation, the area's temperature increases.As can be illustrated from Figure 12, temperature distribution diminishes as the Prandtl number enhances for ternary groups I and II.We know that the

Journal of Engineering
Prandtl parameter is the ratio of kinematic viscosity to temperature difusivity.Since the mass and temperature difusivities of nanoparticles decrease as Pr grows, the temperature of the fuid decreases.Te impact of the Eckert number Ec on θ(η) is apparent in Figure 13.Due to the enhancement in Eckert number, the process of converting mechanical energy into heat energy becomes quicker, due to which the temperature of the fuid rises.Te Eckert number explains the connection between the fow of kinetic energy and the change in heat enthalpy.It indicates that as Eckert number grows, the hybrid nanofuids kinetic energy increases.Additionally, the average kinetic energy is a prevalent defnition of temperature.Because of this, increasing the Eckert number enhances the temperature for ternary groups I and II. Figure 14 shows the drop in concentration with increasing values of the chemical reaction.Also, there are no signifcant diferences in the levels of the concentration graphs for both the ternary groups.Te diminishing efect of Sc on the concentration distribution is shown in

Journal of Engineering
Figure 15.Tis is because as the Schmidt number (Sc) increases, viscous difusion increases, causing particles to travel wider and the convection potential to increase.Also, the concentration level decrease for both ternary groups.Te infuence of Du on the thermal feld is exposed in Figure 16.Te temperature feld enlarges for greater values of Du for ternary groups I and II.Tis can be explained as an enlargement in the Dufour efect due to an enhancement in the concentration gradient and the rate of mass difusion.As a result of which the heat transfer rate associated with the particles increases.Also, the thermal profle improves.Figure 17 displays how the concentration profle changes due to the Soret impact Sr. as the Soret number enlarges, the mass difusion caused by temperature distribution also rises, which accelerates the rate of mass transport from the surface, so concentration increases for both ternary groups.Figure 18 illustrates how the thermal profle enlarges with the rising value of heat generation/  Tables 4 and 5 express the rates of skin friction (x and y directions), heat transportation, and mass transport.When Journal of Engineering 11 ternary groups I and II.Tables 3 and 4    Journal of Engineering Y-axis velocity (m•s − 1 ) w:

Figure 5 :Figure 6 :
Figure 5: Velocity distribution in x direction for magnetic parameter M.

3 Figure 9 :
Figure 9: Temperature distribution for suction velocity f w .
2 , and Al 2 O 3 nanoparticles are combined with the base fuid H 2 O to form the triple hybrid nanofuid (SiO 2 + TiO 2 + Al 2 O 3 /H 2 O).

Table 1 :
Te thermophysical properties of the hybrid nanofuid Using the bvp4c method, equations are made simpler.All numerical data and graph are drawn using MATLAB software, which is explained in tables and graphs.Te fowchart of the bvp4c method is presented in Figure
M � 8, f w � 0.3, Nr � 1, Kr � Ec � Du � 0.5, Sc � 0.7, Q � Sr � 0.1, c � 4, Pr � 21, and ϕ 1 � ϕ 2 � 0.15, ϕ 3 � 0.01 for both ternary groups, the skin friction rate in x and y directions are enhanced by the rising Casson fuid parameter, while the opposite impact is shown for the magnetic impact and suction velocity.Te rate of heat transfer grows with rising radiation impact and Prandtl number, while the opposite efect is seen for Eckert number, Dufour impact, and heat source/sink.For both ternary groups, Sherwood number rises with enhancing Schmidt number, chemical reaction, and volume fraction of Fe 3 O 4 and MgO.Furthermore, the Sherwood number decays when the Soret efect increases.