μnf,eff Viscosity of the nanofluid in porous media (Kg

7 Generation of entropy and transfer of heat during forced convection of a nanofluid through a partially-filled 8 porous channel are investigated theoretically. The problem includes a fully developed flow in a channel with a 9 central porous insert and under constant heat flux boundary condition. The system is assumed to be under local 10 thermal non-equilibrium and the solid and nanofluid phases can feature internal heat generations. Darcy11 Brinkman model of momentum transfer along with the two-equation thermal energy transport and two different 12 fundamental porous-fluid interface models are utilised to analyse the heat transfer problem. Analytical 13 expressions are developed for the temperature fields, Nusselt number and, the local and total entropy 14 generations. The subsequent parametric study reveals the strong influences of the pertinent parameters and the 15 utilised porous-nanofluid interface models. In keeping with others, the results show considerable increases in the 16 Nusselt number with increasing the concentration of nanoparticles. Internal heat generations are demonstrated to 17 have major effects on the heat transfer and entropy generation characterises of the system. Further, the existence 18 of internal heat sources signifies the role of nanoparticles concentration in the thermal and entropic behaviours 19 of the system. It is, also, shown that the choice of the porous-nanofluid interface model can significantly alter 20 the predictions of the local and total entropy generations within the system. This appears to be, particularly, the 21 case at low Biot numbers for which the system is significantly away from the local thermal equilibrium 22 condition. 23 24