Effect of asymmetrical heat rise/fall on the film flow of magnetohydrodynamic hybrid ferrofluid

The movement of the ferrous nanoparticles is random in the base fluid, and it will be homogeneous under the enforced magnetic field. This phenomenon shows a significant impact on the energy transmission process. In view of this, we inspected the stream and energy transport in magnetohydrodynamic dissipative ferro and hybrid ferrofluids by considering an uneven heat rise/fall and radiation effects. We studied the Fe3O4 (magnetic oxide) and CoFe2O4 (cobalt iron oxide) ferrous particles embedded in H2O-EG (ethylene glycol) (50–50%) mixture. The flow model is converted as ODEs with suitable similarities and resolved them using the 4th order Runge-Kutta scheme. The influence of related constraints on transport phenomena examined through graphical illustrations. Simultaneous solutions explored for both ferro and hybrid ferrofluid cases. It is found that the magnetic oxide and cobalt iron oxide suspended in H2O-EG (ethylene glycol) (50–50%) mixture effectively reduces the heat transfer rate under specific conditions.

colloid is well-known as a ferrofluid. A ferrofluid is a colloidal interruption of single-domain ferromagnetic elements in a base liquid. It has several medicinal and biological solicitations like amplifiers, revolving shaft seals, vacuum chambers, computer drives, dissipation of radiation, medicine delivery, cell parting, etc. A nanofluid consists of a single nanomaterial, whereas the hybrid nanofluid consists of more than one unlike nanoparticles with ordinary fluid. The determination behind the invention of a mixture of ferrofluids is to knob the transport phenomena. Madhesh and Kalaiselvam 11 discussed the rheological appearances and temperature transmission of hybrid nanofluids. The magnetohydrodynamic time-dependent liquid film flow of grapheme nanoparticles embedded nanofluid under various thermal transport aspects can be viewed in ref. 12 The influence of drag force on the flow over an expanding surface was discussed by Sheikholeslami et al. 13 Later on, the researchers 14,15 investigated the transport phenomena of Newtonian and non-Newtonian hybrid nanoliquids under various physical effects. Kumar et al. 16 discussed the effect of Brownian moment on bio convective stagnated motion of nanoliquid and presented dual solutions. It was clinched that the measure of thermal transport is high in the case of hybrid nanofluid when matched with another liquid. Sandeep 17 deliberated the influence of drag force and variable viscosity on the hybrid nanofluid drive of liquid film over a fraught sheet.
The inspiration for radiating heat on convective movements shows a massive role in many engineering and scientific procedures like space technology, paper bowls production, freezing of metal bits, satellites, design of electronic chips, and fuel wells. The radiation is either or nonlinear depends on temperature ratio parameter values. The mechanism of asymmetrical heat rise or fall has well-known uses in drug industries and numerous manufacturing happenings like freezing of metal strips and crude oil recovery, etc. Devi and Devi 18 considered a problem to investigate a numerical explanation for MHD flow of nanoliquid across a penetrable sheet with heat rise/fall. Kandelousi and Ellahi 19 scrutinized a time-independent, two-dimensional ferrohydrodynamic flow through a square cavity in the occurrence of drag force. The well-known Lattice Boltzmann technique is utilized to resolve the equations of motion. Afrand et al. 20 contemplated a problem to examine the Power-law fluid. The stimulus of radiation on the hydrodynamic drive of shear thickening over a stretched surface was scrutinized by Ramzan et al. 21 Ghadikolaei 22 deliberated the magnetohydrodynamic free convective motion of two different hybrid nanofluids across an overextended surface. The impact of thermic heat on MHD flow of micropolar shear-thickening nanoliquid thru a nonlinear stretched sheet was examined by Lu et al. 23 numerically with the help of the Matlab package. Kumar et al. 24 discussed the inspiration of asymmetrical heat generation or absorption and nonlinear thermic heat on slanting stagnated motion of shear thickening fluid across a vertical sheet in conducting field. The impact of non-linear thermal radiation and resistive heating on MHD shear-thickening nanoliquid flow over an inclined penetrable stretched sheet was reported by Ghadikolaei et al. 25 Discrete heating effect on free convection flow past a vertical annulus was studied by the researchers [26][27][28][29] . Sankar et al. 30 performed a numerical investigation to analyze the heat and mass transfer rates in the presence of discrete heat source.
In all the afford studies, scientists scrutinized the transport phenomena of nanoliquids past a solid geometry with numerous physical aspects. The main motto of this exploration is to provide a numerical examination of the stream and energy transport in magnetohydrodynamic dissipative ferro and hybrid ferrofluids by considering an uneven heat rise/fall and radiation effects. We studied the Fe 3 O 4 (magnetic oxide) and CoFe 2 O 4 (cobalt iron oxide) ferrous particles embedded in H 2 O-EG (ethylene glycol) (50-50%) mixture. The flow model is converted as ODEs with suitable similarities and resolved them using the 4th order Runge-Kutta scheme. The influence of related constraints on transport phenomena examined through graphical illustrations. Simultaneous solutions are explored for both ferrous and hybrid ferrofluid cases.

Modelling
Consider a time dependent flow of EG-H 2 O based magnetic and cobalt iron oxide mixture hybrid ferrofluid past an extending sheet as depicted in Fig. 1. Here, the surface is placed lengthways x-axis with the temperature and momentum respectively taken as is measured normal to the drive. Thermal radiation, asymmetrical heat rise/fall and viscous dissipation possessions are engaged. The slip between the particles is neglected. With the above conventions, the leading transport equalities are as follows: Frontier limitations:  The ferrofluid restrictions are taken as hnf Using Eqs. (5) to (7), the Eqs. (2) to (4) can be distorted as  Transformed boundaries:  The reduced Nusselt number Nu x is specified as x

Results and Discussion
The Eqs. (8) and (9) Table 1 predicts the physical properties, and Table 2 discusses the authentication of the outputs.   Fig. 2(a). The reason for these trends is the drag force developed against the flow due to the imposing of external magnetic force. As a rise in the resultant temperature, we noticed a fall in the Nusselt number, as shown in Fig. 2(c). Notably, it is less in H 2 O-EG-Fe 3 O 4 /CoFe 2 O 4 hybrid ferrofluid when compared to other two ferrofluids. Figure 3 explicate the influence of R and uneven heat rise/fall on θ η Nu ( ) and x . As per the general nature of and , a rise in the heat input primes to upsurge in the heat field. A similar drift was followed by Fig. 4. However, we observed a significant hike in the thermal field of H 2 O-EG-Fe 3 O 4 /CoFe 2 O 4 hybrid ferrofluid when compared to the other two ferrofluids. These may be due to the enhanced heat conduction between the Fe 3 O 4 -CoFe 2 O 4 solid particles. As a result, we found decay in Nu x in all cases for growing numbers of and (see Figs. 3(b) and 4(b)). Figure 5 expounds the result of λ on η θ η ′ f N u ( ) , ( ) and x . We perceived a depreciation in momentum and thermal arenas for boosting values of λ. Notably, we noticed that the impact of λ is high on the thermal filed of H 2 O-EG-CoFe 2 O 4 ferrofluid when equated to water-EG-magnetic oxide ferrofluid and water-EG-magnetic/ cobalt iron oxide hybrid ferrofluid. Generally, a rise in the film thickness leads to enlarging the flow filed and hence reduces the heat transfer. Cobalt may be the reason for the additional reduction in the heat transfer of H 2 O-EG-CoFe 2 O 4 ferrofluid. Figure 6 illustrate the control of viscous dissipation on η θ η ′ f N u ( ) , ( ) and x . It is profound that the growing values of Ec effectively escalate the thermal and drive boundary layers. Physically, drive force can be converted as heat energy in viscous fluids. If the viscosity of the fluid is high, then more internal heat energy will generate and hence the heat transfer. Interestingly