Numerical Simulation of Nonlinear Convective Magnetohydrodynamic Casson-Williamson Fluid Flow over a Wedge with Radiation and Exponential Heat Generation

Abstract

This study examines the nonlinear convective magnetohydrodynamic (MHD) flow and heat transfer characteristics of a Casson-Williamson fluid over a wedge in the presence of nonlinear thermal buoyancy, thermal radiation, a uniform heat source, and exponential internal heat generation. The novelty of the present work lies in the simultaneous integration of the Casson-Williamson non-Newtonian fluid model with nonlinear mixed convection and exponential heat generation over a Falkner-Skan wedge, which has not been comprehensively investigated in previous studies. The nonlinear governing partial differential equations are transformed into a system of coupled ordinary differential equations through appropriate similarity transformations. The resulting boundary value problem is solved numerically using the shooting method in conjunction with the adaptive Runge-Kutta fourth-fifth order (RK45) scheme. The effects of the governing parameters on the velocity and temperature distributions, as well as the skin-friction coefficient and local Nusselt number, are investigated. The numerical results reveal that increasing the Casson and Williamson parameters suppresses the fluid velocity while enhancing the temperature distribution due to reduced convective heat transport. The mixed convection and nonlinear convection parameters accelerate the flow, whereas thermal radiation, uniform heat generation, and exponential heat generation significantly increase the thermal boundary-layer thickness. Moreover, the magnetic field enhances the wall shear stress but reduces the heat transfer rate, while stronger thermal radiation decreases the local Nusselt number. The findings of this investigation provide useful insight into the thermal management of non-Newtonian fluid systems encountered in polymer processing, coating technologies, thermal manufacturing, energy conversion, and related engineering applications.