Flow dynamics of MHD hybrid nanofluid past a moving thin needle with a temporal stability test: A Galerkin method approach

Heat transmission processes have numerous industrial applications. A novel form of nanofluid known as the hybrid nanofluid that has a higher thermal exponent helps in improving the ability of regular fluids to transfer heat. This article aims to analyze the impact of hybrid nanofluid with effects like magnetohydrodynamics (MHD), Brownian motion and thermophoresis, heat generation/absorption, and chemical reaction past a permeable moving thin needle. Two assorted nanomaterials (MoS2 and Fe3O4) are added in a base fluid such as ethylene glycol (EG) to access the performance of the hybrid nanofluid. Using suitable similarity variables, the governing equations of the problem are turned into customary ordinary differential equations. The resulting equations are solved analytically using the Galerkin method (GM) and dual solutions are obtained in a certain range of moving parameter lambda. Due to this, a stability test is implemented to find a stable solution. With the help of a bvp4c function in Matlab software, the smallest eigenvalues are computed, where positive eigenvalues are linked with the stable solution while negative eigenvalues are linked with the unstable solution. It is concluded that only the first solution is stable while the second solution is not. The skin friction factor and heat transfer rate are reduced by growing the needle size. The magnetic field has an inverse relation with the flow field and direct relation with the temperature field. The improvement in heat generation parameter causes the fluid temperature to rise. The fluid concentration is enhanced with the increment of the chemical reaction parameter.