Convective transport in case of variable properties in porous enclosures with/without two heated ellipsis with rough boundaries

Numerical emulations are conducted to study the physical situation of a variable properties nanofluid inside enclosures with rough boundaries. Two cases are considered based on way of the heating in the enclosures, namely, case1 the enclosure is heated from inside using two heated and cross-section ellipsis at the center of the enclosure and case2 in which differentially heated enclosures are assumed. The numerical procedure which applied to solve the non-homogenous Buongiorno mathematical model is based on the control volume technique with SIMPLE algorithm. Wide ranges for the temperature differences, roughness parameter and Darcy number are considered and the dynamic viscosity of CuO nanofluid is expressed as a mathematical form of the temperature and nanoparticle volume fraction based on experimental results. The main results revealed that the average Nusselt is enhanced by 11% in case 1 and by 30% in case 2 when the temperature differences are increased by 10 °C. Also, the decrease in Darcy number causes that rate of the heat transfer is reduced regardless way of the heating. Moreover the increase in the roughness parameter reduces the maximum values of the stream function in all cases.