Magnetic Field Impacts on Nanofluid Flow Towards a Stretching Sheet Embedded in a Porous Medium with Considerations of Variable Viscosity and Convective Boundary Conditions

This investigation elucidates the intertwined effects of magnetic fields and porous media on the flow of nanofluids towards a stretching sheet, contemplating variable viscosity and convective boundary conditions. A nanofluid model, incorporating the influences of thermophoresis and Brownian motion, is adopted. Via judicious transformations, the fundamental governing coupled non-linear partial differential equations are condensed, and the consequent transformed equations are numerically resolved employing the Finite Element Method (FEM). Paramount emphasis is accorded to parameters embodying notable physical significance, inclusive of the Prandtl number (Pr), Hartmann number, Lewis number (Le), Brownian motion number (Nb), thermophoresis number (Nt), and permeability parameter. The numerical results acquired, as particular instances of the aforementioned study, are found to be congruent with previously reported findings, substantiating the accuracy and reliability of the proposed methodology. A thorough examination of the collective impact of the selected parameters on flow and heat transfer characteristics has been systematically undertaken, revealing intricate dependencies and fostering a deeper understanding of the complex phenomenon under consideration. This study, hence, paves a pathway towards bolstering the comprehension of flow mechanics in porous media under the influence of magnetic fields, contributing valuable insights to the overarching field of fluid dynamics in nano-engineering applications.