Numerical simulation of the natural convection and entropy generation in an airfilled cubical cavity with active lateral walls is performed in this work. Both the lateral front and right sidewalls are maintained at an isothermal cold temperature. While an isothermal hot temperature is applied for both the lateral back and left sidewalls. The upper and lower walls are kept adiabatic. Entropy generation rates due to the fluid friction and the heat transfer are simulated by using the Second law of thermodynamics. Results are illustrated for Rayleigh numbers varied from (10 3 ≤ Ra ≤ 10 6). It was shown that the increase in the Rayleigh number leads to increase the average Nusselt number and to decrease the Bejan number. Also, it was found that both, S th , and S tot , increase slightly with the increase in Rayleigh number until they reach (Ra = 10 5) and then begin to jump after this value. After (Ra = 10 5), the increase in both, S tot , and S fr , is greater than S th. Moreover, it was observed that iso-surfaces of S tot are similar to S th at (10 3 ≤ Ra ≤ 10 5), while they are similar to S fr at high Rayleigh number.

The steady mixed convection of heat and mass transfer inside and outside a porous vertical wall is numerically studied. The porous wall, placed in a vertical channel, contains a solid phase, a nanofluid phase (Water-Al 2 O 3 or Water-Cu) and gas phase. The effect of several physical quantities such as nanoparticle volume fraction, ambient temperature and initial nanofluid saturation on heat and mass transfer were investigated. Results reveal that the temperature of porous medium is decreased considerably with nanoparticle volume fraction. It has been also found that the heat and mass transfer are dramatically reduced using Water-Alumina nanofluid when compared with pure water.