TRANSFORMATION OF NONLINEAR PDEs TO LINEAR FORMS FOR MHD BOUNDARY LAYER FLOW OF NON -NEWTONINAN FLUIDS OVER STRETCHING/SHRINKING SURFACES

Abstract

This study focuses on transforming the nonlinear partial differential equations (PDEs) governing the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Casson fluid over stretching and shrinking surfaces into linear ordinary differential equations (ODEs). Similarity transformations reduce the nonlinear PDEs for momentum and energy to a system of nonlinear ODEs, which are then linearized using a novel quasilinearization technique. The resulting linear ODEs are solved analytically via the homotopy analysis method (HAM). The effects of key parameters, such as the Casson parameter, magnetic parameter, and stretching/shrinking parameter, on velocity and temperature profiles are analyzed. Results demonstrate that the linearization enhances computational efficiency while preserving physical accuracy. Validated against numerical solutions and existing literature, the findings offer new insights into non-Newtonian fluid dynamics under MHD effects, with applications in heat exchangers and polymer processing.