Laminar Free Convection in a Vertical Channel With Asymmetrical Heating

A numerical investigation of laminar free convective heat transfer in a vertical channel with asymmetrical heating has been presented. Uniform wall temperatures are prescribed as thermal boundary conditions. The governing differential equations were solved by a finite volume method. The SIMPLER algorithm for pressure velocity coupling was adopted. A new iterative scheme based on mass balance at inlet and outlet has been used. By solving the flow as an elliptic problem, the effect of vertical diffusion of thermal energy, which was neglected in previous numerical studies, was taken into consideration. Variation of the mean velocity and average Nusselt number for Rayleigh number range of 10 to 10³, channel aspect ratio range of 10 to 10³ and Prandtl numbers of 0.72 and 5 are determined. For uniform wall temperature the average Nusselt number based on wall to ambient temperature difference and heat flux at different points are compared to the experimental results. The results revealed that the average Nusselt number from the thermally active surface in an asymmetric channel to be higher than from a comparable surface in a symmetric configuration, for fixed channel aspect ratio, at low values of Rayleigh number. There was no appreciable change in Nusselt number when Prandtl number was changed from 0.72 to 5. The minimum axial pressure for free convective flow of air is the highest for the symmetric heating condition.