Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach

The present analysis examines the magnetohydrodynamic (MHD) flow of non-Newtonian Casson fluid on an exponentially shrinking surface under constant and exponentially varying wall temperature with suction. The main objective is to investigate multiple solutions of self-similar coupled nonlinear ordinary differential equations derived semi-numerically via the shifted Chebyshev collocation approach. The occurrence of a dual solution is found and variations in the velocity and temperature profiles are analyzed under different physical flow governing factors. The stability analysis is performed and it confirms that the first solution is stable and the second solution is unstable. The obtained results are confirmed by comparing them with earlier published results and show good agreement. The skin friction coefficient and wall temperature gradient increase for the first solution and decline for the second solution with enhancement in Hartmann number and suction parameter in case of exponentially varying surface temperature. Whereas, for constant surface temperature, increasing the Hartmann number and suction parameter results in the intensification of the wall temperature gradient. The velocity and temperature profiles decrease with improving the Casson parameter. As the Prandtl number strengthens, the heat transfer rate in a constant surface temperature situation is comparatively higher than exponentially varying surface temperature situation.