A new mathematical model for the magnetohydrodynamic couple stress Casson fluid flow in a channel with stretching wall

This research investigates the three-dimensional magnetohydrodynamic flow of a Casson fluid between parallel plates, considering the influence of couple-stress and a magnetic field, along with the heat transfer influenced by a heat source. The fluid flow, driven by the stretching of the lower plate while keeping the upper plate stationary, has applications in various industries. The model involves nonlinear coupled partial differential equations with appropriate boundary conditions. The authors employed the Spectral Quasi Linearization Method (SQLM) to solve the transformed equations, examining the impact of different parameters on fluid temperature and velocities. Increasing the magnetic field strength, Casson parameter, and unsteadiness decreases velocities near the lower sheet but increases them near the upper sheet. Fluid temperature rises with higher Casson parameter and magnetic field strength but decreases with increased Prandtl number, couple stress parameter, unsteadiness, and stretching parameter. Nusselt number and skin-friction coefficients are analyzed numerically and statistically for engineering insights.