The core objective of the present study is to examine entropy generation minimization via Hall current and Ohmic heating. Carreau fluid considerations interpret the unavailability of systems' thermal energy (for mechanical work). The magneto hydrodynamic flow is in the channel, which is not symmetric. We have solved analytically the resulting nonlinear mathematical model. Moreover, physical exploration of important parameters on total entropy generation, temperature, and Bejan number is plotted and discussed. We observed that the generation of entropy takes place throughout the confined flow field y = W1 and y = W2 because of the viscous dissipation effect. In addition, reducing the operating temperature minimizes the entropy.
Keywords: Carreau fluid; entropy; heat transfer; peristalsis; perturbation; pumping and trapping.