First and second law analyses of nanofluid forced convection in a partially-filled porous channel: The effects of local thermal non-equilibrium and internal heat sources

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