In the present era of research, entropy generation is one of the most important topics, which is used to control the irreversibility phenomena during heat transfer. Due to the important application in engineering, atomic reactors and cooling process in different fields, this work aims to study the second law analysis of Casson fluid. Vertical plate geometry was considered, where the plate at the boundary exhibits arbitrary wall shear stress and the fluid lies above the plate. Exponential type heating was produced at the bounding plate whereas natural convection is caused because of buoyancy force. Magnetohydrodynamic (MHD) analysis was also considered perpendicular to the plate. The usual Darcy’s law of Newtonian fluid was modified to Darcy’s law for Casson fluid. The exact analysis was performed using the Laplace transform technique to establish exact solutions for the velocity field and temperature distribution. Results are interpreted physically using various plots and discussed in detail.