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In this work, the effects of the presence of a heat sink and a heat source and their lengths and locations and the entropy generation on MHD mixed convection flow and heat transfer in a porous enclosure filled with a Cu-water nanofluid in the presence of partial slip effect are investigated numerically. Both the lid driven vertical walls of the cavity are thermally insulated and are moving with constant and equal speeds in their own plane and the effect of partial slip is imposed on these walls. A segment of the bottom wall is considered as a heat source meanwhile a heat sink is placed on the upper wall of cavity. There are heated and cold parts placed on the bottom and upper walls, respectively, while the remaining parts are thermally insulated. Entropy generation and local heat transfer according to different values of the governing parameters are presented in detail. It is found that the addition of nanoparticles decreases the convective heat transfer inside the porous cavity at all ranges of the heat sink and source lengths. The results for the effects of the magnetic field show that the average Nusselt number decreases considerably upon the enhancement of the Hartmann number. Also, adding nanoparticles to a pure fluid leads to increasing the entropy generation for all values of D for λl=−λr= 1.

Continuum equations governing thermal non-equilibrium modeling of steady natural convection inside wavy enclosures with the effect of thermal radiation are developed. These equations account for such effects as the inter-phase heat transfer coefficient effect, the thermal radiation effect, the modified conductivity ratio effect and the Rayleigh number effect. Finite difference method is employed to solve these equations and comparisons between previous published works are presented. Numerical results for the flow and heat transfer for the fluid and solid phases are obtained for various combinations of the physical parameters. Graphical and tabular results illustrating interesting features of the physics of the problem are presented and discussed.