Thermodynamic irreversibility in the flow system provides information on the energy and power losses in the system. Minimization of entropy generation in the flow system enables for the parametric optimization of the system operation. In the present study, parallel plates, in between, filled with the fluid are considered. The fluid motion resulted from the bi-vertical compression of the top plate of the parallel plates is examined. The entropy generation rate in the flow system is formulated after considering the constant movement of the top plate, constant applied load, and the combination of the constant velocity and applied load to the top plate. The optimum operating conditions related to the fluid motion in between the parallel plates is determined through the entropy analysis. It is found that the combination of the constant velocity and the constant applied load resulted in the low entropy generation rate.