Heat Source and Slip Impacts on Porous Medium Flow of Williamson Nanofluid: Numerical Approach via Keller-Box Scheme

Abstract

This study presents a mathematical model to analyze the combined effects of prescribed heat sources, velocity slip, and thermal slip on the stagnation point boundary layer flow of a non-Newtonian Williamson nanofluid. The investigation incorporates a time-varying magnetic field and considers two thermal boundary conditions—prescribed surface temperature and prescribed heat flux—within the framework of the Buongiorno nanofluid model. To account for fluid movement through porous media, the Darcy–Forchheimer model is employed. Using similarity transformations, the governing partial differential equations are reduced to a set of nonlinear ordinary differential equations. These equations are then numerically solved using the Keller-box method, an implicit finite difference approach well-suited for handling nonlinear boundary value problems. Numerical results for velocity, temperature, and concentration profiles are illustrated through 2D plots, while 3D visualizations highlight the influence of various parameters on the skin friction coefficient, Nusselt number, and Sherwood number. The findings contribute to a deeper understanding of Williamson nanofluid dynamics in porous environments and hold potential applications in the optimization of nanofluid-based thermal systems.