Dual solutions for MHD hybrid nanofluid stagnation point flow due to a radially shrinking disk with convective boundary condition

Purpose This paper aims to study the stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid over a radially shrinking disk with the imposition of the magnetic field, viscous-Ohmic dissipation and convective boundary condition. Design/methodology/approach Similarity variables are introduced and used in reducing the governing partial differential equations into a system of ordinary differential equations. A built-in bvp4c solver in MATLAB is then used in the computation of the numerical solutions for equations (7) and (8) subject to the boundary conditions (9). Then, the behavior of the flow and thermal fields of the hybrid nanofluid, with various values of controlling parameters, are analyzed. Findings The steady flow problem resulted in multiple (dual) solutions. A stability analysis performed to identify the stable solution applicable in practice revealed that the first solution is stable while the second solution is unstable. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than the Al2O3-H2O nanofluid. Thus, the hybrid nanofluid has a better heat transfer performance than the nanofluid. Besides that, the presence of the magnetic field, suction, convective boundary condition and the enhancement of nanoparticle volume fraction of Cu augments the skin friction coefficient and Nusselt number of the hybrid nanofluid. Meanwhile, the presence of viscous-Ohmic dissipation reduces the heat transfer performance of the fluid. Originality/value To the best of the authors' knowledge, the present results are original and new for the study of the flow and heat transfer of Al2O3-Cu/H2O hybrid nanofluid past a permeable radially shrinking disk. Considerable efforts have been directed toward the study of the boundary layer flow and heat transfer over stretching/shrinking surfaces and disks because of its numerous industrial applications, such as electronic, power, manufacturing, aerospace and transportation industries. Common heat transfer fluids such as water, alumina, cuprum and engine oil have limited heat transfer capabilities due to their low heat transfer properties. In contrast, metals have higher thermal conductivities than these fluids. Therefore, it is desirable to combine the two substances to produce a heat transfer medium that behaves like a fluid but has higher heat transfer properties.