Laminar natural convection between vertical isothermal heated plates with different temperatures

Numerical investigation of laminar free convection heat transfer in the vertical parallel plate channel with asymmetric heating is presented. Both inlet and exit effects are included into the analysis. A numerical solution is obtained for a Prandtl number of 0.71 and for modified Rayleigh number `(Ra)]\overline {Ra} = 10⁻¹ ÷ 10⁵, and varying heating ratio T_R = 0 ÷ 1 and aspect ratio A = 10. Fully elliptic Navier-Stokes and energy equations are solved using the finite volume techniques with staggered grid arrangements. The obtained results show a strong influence of the temperature ratio on local and average heat transfer coefficient on the hot and cold plates. With reduction of T_R the heat transfer parameter on the hot wall grows, and on the cold one, on the contrary, it decreases. As a result, the total heat exchange from two plates depends poorly on the parameter T_R.