Two dimensional numerical analysis of entropy generation during transient convective heat transfer for laminar flow between two parallel plates has been investigated. The fluid is incompressible and Newtonian and the flow is the hydrodynamically and thermally developing. The plates are held at constant equal temperatures higher than that of the fluid. The bottom plate moves in either parallel or in inverse direction to the flow. The governing equations of the transient convective heat transfer are written in two-dimensional Cartesian coordinates and solved by the finite volume method with SIMPLE algorithm. The solutions are carried for Reynolds numbers of 102, 5×102 and 103 and Prandtl number of 1. After the flow field and the temperature distributions are obtained, the entropy values and the sites initiating the entropy generation are investigated. The results have indicated that the number of the entropy generation has its highest value at the highest Reynolds and Br/Ω values, which is obtained at counter motion of the lower plate. The lowest average number of the entropy generation on the bottom plate is obtained in parallel motion. The corners of the channel plates at the entrance play the role of active sites where the generation of entropy is triggered.