This research paper focused on investigating the influence of various factors on steady Couette flow beneath a permeable bed. Factors studied included aligned magnetic field, thermal radiation, temperature gradient heat source, viscous dissipation, and Joules dissipation. The momentum and energy equations governing flow and heat transmission were analytically solved to predict the generation of entropy. The findings were visually presented through graphical representations, which effectively demonstrated the effect of these factors on the fluid's velocity, temperature, entropy production, and Bejan number. In addition, the shear stress and rate of heat transfer coefficient at the channel walls were computed and their behavior was documented in tables to provide further insights.