Stability Analysis of MHD Stagnation Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Porous Medium with the Heat Generation/Absorption

Abstract

This research explores the magnetohydrodynamic (MHD) stagnation-point flow (SPF) over a permeable surface that either stretches or shrinks, incorporated into a permeable surface while also accounting for internal heat generation and absorption effects. Through a similarity transformation, the complex nonlinear partial differential equations (PDEs) describing the flow as well as heat transfer are simplified into a system of nonlinear ordinary differential equations (ODEs). Consequently, these equations are numerically solved with MATLAB’s boundary value problem solver, bvp4c. The obtained outcomes include detailed analyses into velocity as well as temperature profiles, along with evaluations of the skin friction coefficient (SFC), as well as the local dimensionless heat transfer rate, which quantify surface drag and the rate of heat transfer, respectively. Notably, for the shrinking sheet, the model results to dual solutions, whereas for the stretched sheet, only a single solution is obtained.The findings indicate that an improve in the permeability coefficient R leads to enhancements in both SFC and the heat transfer rate at the surface. Conversely, a rise in the heat generation or absorption parameter  results in a decline in the surface heat transfer rate. Furthermore, a temporal stability analysis confirms that the primary (first) solution remains stable over time, while the secondary solution is found to be unstable.