Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall

A penalty finite element analysis with bi-quadratic elements is performed to investigate the influence of uniform and non-uniform heating of bottom wall on mixed convection lid driven flows in a square cavity. In the present investigation, bottom wall is uniformly and non-uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated and moving with uniform velocity. A complete study on the effect of Gr shows that the strength of circulation increases with the increase in the value of Gr irrespective of Re and Pr. As the value of Gr increases, there occurs a transition from conduction to convection dominated flow at Gr = 5 � 103 and Re = 1 for Pr = 0.7. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri (frac(Gr, Re2)) and Pr. As the value of Re increases from 1 to 102, there occurs a transition from natural convection to forced convection depending on the value of Gr irrespective of Pr. Particularly for higher value of Grashof number (Gr = 105), the effect of natural convection is dominant upto Re = 10 and thereafter the forced convection is dominant with further increase in Re. As Pr increases from 0.015 to 10 for a fixed Re and Gr (Gr = 103), the inertial force gradually becomes stronger and the intensity of secondary circulation gradually weakens. The local Nusselt number (Nub) plot shows that the heat transfer rate is very high at the edges of the bottom wall and then decreases at the center of the bottom wall for the uniform heating and that contrasts lower heat transfer rate at the edges for the non-uniform heating of the bottom wall. It is also observed that Nul shows non-monotonic behavior with both uniform and non-uniform heating cases for Re = 10 at higher value of Pr. The average Nusselt number plot for the left or right wall shows a kink or inflexion at Gr = 104 for highest value of Pr. Thus the overall power law correlation for average Nusselt number may not be obtained for mixed convection effects at higher Pr. � 2008 Elsevier Masson SAS. All rights reserved.