In this paper, heat transfer and entropy analysis are carried out for Couette Poiseuille flow between two parallel plates containing porous media, considering the viscous effect and constant heat flux at the walls. The considered flow is with a temperature jump and slip. The momentum and energy equations are solved analytically. The solution was performed at three situations of channel upper plate movement (V-=0, V-=1, V-=-1). Explicit expressions are obtained for velocity and temperature distributions and Nusselt number has been calculated through numerical integration. The results show that, as the Brinkman number increases and Knudsen number decreases the Nusselt number increases. However, the upper plate situation is a determinant factor in establishing the effect of porous media shape parameter on the Nusselt number. It was observed that, as the ratio (Br/W) and the porous media shape parameter increase the entropy generation increases. In addition, decreasing (Br/W) and increasing S results in an increase of Be number. Moreover, with increasing Kn number, the non-dimensional entropy generation number decreases and Be number increases.