Hybrid Nanofluid flow induced by an exponentially shrinking sheet. (English) Zbl 07848616
Summary: The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles is investigated in this paper. The alumina (\(\mathrm{Al_2O}_3\)) and copper (Cu) nanoparticles are suspended in water to form \(\mathrm{Al_2O}_3\)-Cu/water hybrid nanofluid. In addition, the effects of magnetohydrodynamic (MHD) and radiation are also taken into account. The similarity equations are gained from the governing equations using similarity transformation, and their solutions are obtained by the aid of the bvp4c solver available in Matlab software. Results elucidate that dual solutions exist for suction strength \(S > S_c\) and shrinking strength \(\lambda > \lambda_c\). The critical values \(S_c\) and \(\lambda_c\) for the existence of the dual solutions decrease with the rising of the solid volume fractions of Cu, \(\varphi_2\) and the magnetic parameter, \(M\). Besides, the skin friction and the heat transfer rate increase with the increasing of \(\varphi_2\) and \(M\) for the upper branch solutions. The increasing of radiation, \(R\) leads to reduce the surface temperature gradient which implies to the reduction of the heat transfer rate for both branches when \(\lambda < 0\) (shrinking sheet). The stability of the dual solutions is determined by the temporal stability analysis, and it is discovered that only one of them is stable and physically applicable.
MSC:
| 76Dxx | Incompressible viscous fluids |
| 80Axx | Thermodynamics and heat transfer |
| 76Rxx | Diffusion and convection |
Keywords:
dual solutions; exponentially shrinking sheet; hybrid nanofluid; MHD; radiation; stability analysisReferences:
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