Bejan's heatlines and numerical visualization of convective heat flow in differentially heated enclosures with concave/convex side walls

Abstract

Numerical simulation for natural convection flow in fluid filled enclosures with curved side walls is carried out for various fluids with several Prandtl numbers (Pr = 0.015, 0.7 and 1000) in the range of Rayleigh numbers (Ra = 103–106) for various cases based on convexity/concavity of the curved side walls using the Galerkin finite element method. Results show that patterns of streamlines and heatlines are largely influenced by wall curvature in concave cases. At low Ra, the enclosure with highest wall concavity offers largest heat transfer rate. On the other hand, at high Ra, heatline cells are segregated and thus heat transfer rate was observed to be least for highest concavity case. In convex cases, no significant variations in heat and flow distributions are observed with increase in convexity of side walls. At high Ra and Pr, heat transfer rate is observed to be enhanced greatly with increase in wall convexity. Results indicate that enhanced thermal mixing is observed in convex cases compared to concave cases. Comparative study of average Nusselt number of a standard square enclosure with concave and convex cases is also carried out. In conduction dominant regime (low Ra), concave cases exhibit higher heat transfer rates compared to square enclosure. At high Ra, low Pr, concave cases with P1P1′=0.4 is advantageous based on flow separation and enhanced local heat transfer rates.