Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.