In this work, the entropy generation due to the flow of a gravity-driven laminar viscous incompressible fluid through an inclined channel is investigated. Fully developed flow field is solved for a Newtonian fluid. Then, temperature field is represented in a purely analytical expression and subject to isothermal boundary conditions on the walls and constant rectangular temperature profile at the inlet. This analytical solution is not similar to the already existing ones in the open literature. Also, the temperature field is numerically resolved by using the method of lines with the same inlet and boundary conditions. These two solutions overlap, which indicates the correctness of both solutions. In obtaining both analytical and numerical solutions, no assumption is made on the initial transition and entrance region. It is shown that the effect of this region, which has been omitted in previous studies, is highly dominant on the overall entropy generation. Therefore, the detailed thermal analysis of the entrance section is outlined.