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^-iso from three vertical fins mounted on a vertical plate and fin efficiency η_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^-iso compare with those obtained from the correlations recommended by current textbooks and other previous results. The present estimates of h^-iso can be applied to obtain a modified correlation of the Nusselt number and Raleigh number.