Natural Convection at Different Prandtl Numbers in Rectangular Cavities with a Fin on the Cold Wall

The natural convection in differentially heated rectangular cavities with a fin attached to the cold wall was investigated numerically. The top and the bottom horizontal walls of the cavities were insulated while their left and the right vertical walls were maintained at a constant temperature Th and Tc، respectively with Th > Tc. The governing equations written in terms of the primitive variables were solved numerically using the finite volume method while the velocity and pressure fields were coupled using the SIMPLER algorithm. Using the developed code effects of pertinent parameters such as length and location of fin، aspect ratio of the enclosure، Rayleigh number، and Prandtl number on heat transfer and fluid flow in the enclosure were investigated. The results showed that for the cavity filled with water، at high Rayleigh numbers، a longer fin placing at the middle of the right wall has more remarkable effect on the heat transfer inside the cavity. Also، it was observed that at low Rayleigh numbers، the effect of fin on heat transfer enhancement in low Prandtl numbers is more than that in high Prandtl numbers. Moreover، it was found that the fin has more effect for narrow enclosures.