Precise prediction of thermal processes is one of the major concerns in the field of heat transfer and within energy research communities. It has been proven that using LTE (local thermal equilibrium) conditions within a porous medium may give researchers erroneous data. From another point of view, the entropy generation which is directly related to the loss of available work within a system, is in the core of energy associated analyses. This work investigates temperature distribution, Nusselt number, and local and total entropy generation rates within a channel partially filled with porous medium using LTNE (local thermal non-equilibrium) conditions. The lower wall of the channel is exposed to a constant heat flux and the upper wall is assumed in the adiabatic condition. Viscous dissipation effects are incorporated into the energy equations. Rigorous analytical solutions are obtained for the velocity and temperature fields. Incorporating the achieved formulas into certain formulations, Nusselt number, and local and total entropy generation rates are obtained and plotted. Similar to previous publications [Int. J. Heat Mass Transf 2011;54:5286-97. Transp. Porous Media 2012;96:169-72. J. Heat Trans. 2011;133:052602], some bifurcation phenomena for temperature field and Nusselt number are reported. Moreover, for the first time, a bifurcation phenomenon regarding the entropy generation rate is reported. Comprehensive discussion regarding effects of some thermophysical parameters such as porous thickness, Blot number, Brinkman number, Peclet number and some other parameters on the velocity, temperature, Nusselt number and entropy generation rates is provided. Due to the broad applications of the fundamental studied geometry in this work and, more importantly, the importance of LINE model in a porous medium, these findings are useful for both industries and scientific researches. (C) 2015 Elsevier Ltd. All rights reserved.