Optimization of a magnetohydrodynamic flow based on the entropy generation minimization method

The entropy generation minimization method is applied to the optimization of a magnetohydrodynamic flow between two infinite parallel walls of finite electrical conductivity. The aim is to minimize the total energy loss due to irreversibilities produced by heat conduction, viscosity and Joule dissipation. The analytic solutions for the velocity, temperature and electric current density fields are used to calculate the global entropy generation rate explicitly in terms of the dimensionless parameters of the problem. It is shown that the entropy generation reaches a minimum when the walls that contain the flow are cooled convectively in an asymmetric way. In order to get a deeper insight of the physical process, a detailed analysis of the different dissipation sources is carried out.