Simulation of heat transfer in a square cavity with two fins attached to the hot wall

In this work a numerical study of unsteady laminar natural convection in a differentially heated square cavity filled with air has been carried out. Rectangular thin fins made with a material of high conductivity were placed on the hot wall of the cavity. The governing equations were discretized by the finite volume method. The resolution of the coupling (pressure-velocity) was done with the projection method. A uniform grid in X and Y direction were used for all computations. Grid convergence of vertical bar Psi max vertical bar was studied for the case of the dimensionless length (L-f =0.5) and the dimensionless position (H-f=0.5) with grid sizes from 20x20 to 160x160 at Ra=10(5). Grid independence was achieved with grid size of 120x120. The code (a program with FORTRAN 6.6) was validated by comparing our results with those of other authors for the case of one thin fin where we have found a good agreement with them. Streamlines, temperature fields and the rate of heat transfer with/without fins (average Nusselt number Nu on the hot and cold walls of the cavity) are obtained. A parametric study has been carried out by considering the following parameters: the Rayleigh number Ra=10(5), the dimensionless length (L-f) and the dimensionless position (Hf) of fins. We have found that is always an optimum fins length (Lf >= 0.4) and an optimum fins position (H-f = 0.25 and 0.75). (C) 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of The TerraGreen Society.