COMPARATIVE STUDY ON FREE VERSUS MIXED CONVECTION IN MHD BOUNDARY LAYER FLOW OF VISCOELASTIC MICROPOLAR FLUID OVER A SPHERE

Abstract

This study presents a numerical investigation comparing free and mixed convection in boundary layer flow of viscoelastic micropolar fluid over a sphere under magnetohydrodynamic (MHD) effects. A mathematical framework was formulated that consists of the continuity equation, momentum conservation, energy balance, and micropolar constitutive relations. They are expressed as a coupled system of partial differential equations (PDEs). These equations were simplified into ordinary differential equations (ODEs) through similarity transformations and then solved numerically using the Keller-box method in Fortran. The comparative analysis focuses on the distinct characteristics of free and mixed convection regimes, examining the effects of various parameters on skin friction coefficients and heat transfer. Results reveal that viscoelastic and micropolar parameters significantly dictate skin friction and heat transfer, while the magnetic parameter exhibits contrasting impacts depending on the convection regime. Furthermore, boundary layer separation is found to be sensitive to parameter variations only under mixed convection, where increased magnetic and assisting flow effects provide a stabilizing delay. This comparative framework offers a deeper understanding of the fundamental mechanisms governing these convection regimes and their practical implications in engineering applications.