Analysis of mixed convection flows within a square cavity with linearly heated side wall(s)

Finite element simulations have been performed to investigate the influence of linearly heated side wall(s) or cooled right wall on mixed convection lid-driven flows in a square cavity. It is interesting to note that multiple circulation cells appear inside the cavity with the increase of Pr for Re = 10 and Gr = 10 5 in the case of linearly heated side walls. For Pr = 0.015 , only two circulation cells are formed inside the cavity. As Pr increases to 0.7, three circulation cells are formed inside the cavity. Further increase in Pr to 10, leads to the formation of four circulation cells inside the cavity. On the other hand, only two circulation cells are formed inside the cavity for the case of cooled right wall. A detailed analysis of flow pattern shows that as the value of Re increases from 1 to 10 2 , there occurs a transition from natural convection to forced convection depending on the value of Gr irrespective of Pr. It is observed that the secondary vortex at the top left corner disappears for Re = 10 2 and Gr = 10 5 due to enhanced motion of the upper lid in the case of cooled right wall while a small secondary vortex exist at the bottom right corner in the case of linearly heated side walls. The local Nusselt number ( Nu b ) plot shows that heat transfer rate is equal to 1 at the edges for the case of linearly heated side walls case and that is zero at the left edge and thereafter that increases for the case of cooled right wall. It is interesting to observe that Nu b is large within 0.4 ⩽ X ⩽ 0.6 due to compression of isotherms for Pr = 0.7 and 10 in the case of linearly heated side wall. It is also observed that Nu r or Nu l exhibits oscillations especially for Pr = 10 at higher Gr due to the presence of multiple circulations. It is also observed that Nu r ¯ or Nu l ¯ vs Gr plots show oscillation for two case studies. Average Nusselt numbers at the bottom and right walls are strong functions of Grashof number at larger Prandtl numbers whereas average Nusselt number at the left wall at a specific Pr is a weaker function of Gr.