This paper provides a comprehensive study on the heat transfer and entropy generation rates in a channel partially filled with a porous medium and under constant wall heat flux. The porous inserts are attached to the walls of the channel and the system features internal heat sources due to exothermic or endothermic physical or physicochemical processes. Darcy-Brinkman model is used for modelling the transport of momentum and an analytical study on the basis of LINE (local thermal non-equilibrium) condition is conducted. Further analysis through considering the simplifying, LTE (local thermal equilibrium) model is also presented. Analytical solutions are, first, developed for the velocity and temperature fields. These are subsequently incorporated into the fundamental equations of entropy generation and both local and total entropy generation rates are investigated for a number of cases. It is argued that, comparing with LTE, the LINE approach yields more accurate results on the temperature distribution within the system and therefore reveals more realistic Nusselt number and entropy generation rates. In keeping with the previous investigations, bifurcation phenomena are observed in the temperature field and rates of entropy generation. It is, further, demonstrated that partial filling of the channel leads to a substantial reduction of the total entropy generation. The results also show that the exothermicity or endothermicity characteristics of the system have significant impacts on the temperature fields, Nusselt number and entropy generation rates. (C) 2015 Elsevier Ltd. All rights reserved.