This study investigates the unsteady Magnetohydrodynamic (MHD) flow and heat transfer characteristics of a nonlinear third-grade non-Newtonian fluid with temperature-dependent viscosity and nonlinear thermal radiation, which are commonly encountered in advanced engineering systems such as polymer processing, metallurgical operations, liquid-metal cooling technologies, and energy conversion devices. Owing to its viscoelastic nature, which deviates from classical Newtonian assumptions, the fluid behavior is described by coupled nonlinear momentum and energy equations incorporating magnetic field effects, viscous dissipation, nonlinear shear contributions, variable thermal conductivity, and wall suction. The governing equations are non-dimensionalised to identify the key controlling physical parameters and solved numerically using an explicit finite difference scheme, enabling a detailed parametric analysis of the effects of magnetic strength, nonlinear material parameters, radiation intensity, and viscosity variation on velocity and temperature distributions within the boundary layer. The results indicate that increasing magnetic field strength suppresses fluid motion through Lorentz force effects, thereby thinning the momentum boundary layer and providing an effective mechanism for electromagnetic flow control. Additionally, nonlinear rheological parameters significantly alter momentum transport, while radiative heat transfer and viscous dissipation elevate the thermal energy within the fluid, and variations in thermal conductivity strongly influence heat diffusion and temperature gradients. These findings offer valuable design insights for enhancing flow regulation and thermal performance in industrial systems involving electrically conducting non-Newtonian fluids operating under magnetic fields and high-temperature conditions.
Amadi et al. (Thu,) studied this question.