Optimum wall thickness ratio based on the minimization of entropy generation in a viscous flow between parallel plates

The influence of the geometrical and physical parameters on entropy generation for a viscous flow between infinite parallel walls of finite thickness is studied by solving the momentum and energy conservation equations. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid–wall interfaces. Analytic solutions for the velocity and temperature fields in the fluid and walls are used to calculate the local and global entropy generation rate. Conditions under which this quantity is minimized are determined for certain suitable combination of geometrical and physical parameters of the system. Special attention has been given to the effect of the wall thickness on the entropy generation rate. It is found that the global entropy generation reaches a minimum for specific values of the wall thickness ratio, when the other parameters are fixed.