Estimation of Natural-Convection Heat-Transfer Characteristics from Vertical Fins Mounted on a Vertical Plate

The inverse scheme of 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 estimate the natural-convection heat transfer coefficient under the isothermal situation (h) over bar (iso) from three vertical fins mounted on a vertical plate and fin efficiency eta(f) for various values of the fin spacing and fin height. The measured fin temperatures and ambient air temperature are measured from the present experimental apparatus conducted in a small wind tunnel. The heat transfer coefficient on the middle fin of three vertical fins 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 before performing the inverse calculation. In order to validate the reliability of the present estimates, the present estimates of (h) over bar (iso) compare with those obtained from the correlations recommended by current textbooks and other previous results. The present estimates of (h) over bar (iso) can be applied to obtain a modified correlation of the Nusselt number and Raleigh number.