Estimation of heat-transfer characteristics from fins mounted on a horizontal plate in natural convection

The finite difference method in conjunction with the least-squares scheme and experimental measured temperatures is proposed to solve a two-dimensional steady-state inverse heat conduction problem in order to predict the natural-convection heat transfer coefficient under the isothermal situation h̄^iso from a three fin array mounted on a horizontal plate and fin efficiency η^f for various values of the fin spacing and fin height. The measured fin temperatures and ambient temperature are obtained from the present experimental apparatus conducted in a small wind tunnel. The heat transfer coefficient on a fin is non-uniform for the present problem, and its functional form can be difficult to be obtained. Thus the whole fin is divided into several sub-fin regions in order to predict the h̄^iso and η^f values. These two estimated values for various values of the fin spacing and fin height can be obtained using the present inverse scheme in conjunction with experimental measured temperatures. The present estimates of h̄^iso can be applied to obtain two different modified correlations of the Nusselt number and Raleigh number and compare with those obtained from the correlations recommended by current textbooks and other references. The results show that the present estimates of h̄^iso are in good agreement with those obtained from the correlations recommended by the present study, current textbooks and other references.