Estimation of heat-transfer characteristics on a fin under wet conditions

Abstract

The finite difference method in conjunction with the least-squares scheme and experimental temperature data is proposed to solve the one-dimensional (1-D) and two-dimensional (2-D) inverse heat conduction problems in order to predict the average overall heat-transfer coefficient h ¯ on a fin and wet fin efficiency η f for various air speeds under wet conditions. The sensitive and overall heat-transfer coefficients on the fin, the Lewis number and the functional form between the relative humidity and fin temperature are unknown a priori in the present study. In addition, the sensitive and overall heat-transfer coefficients on the fin are also assumed to be non-uniform. Thus the whole fin is divided into several sub-fin regions in order to predict the h ¯ and η f values. Variations of these two predicted values with the relative humidity (RH) for various air speeds can be obtained using the present inverse scheme in conjunction with measured fin temperatures. In order to validate the accuracy and reliability of the present inverse scheme, a comparison between the present estimates obtained from the 1-D and 2-D models and exact values is made using simulated temperature data. The results show that the present estimates of the h ¯ value obtained from the 1-D and 2-D models agree well with the exact values even for the case with the measurement errors. Variations of the h ¯ and η f values obtained from 2-D model with the RH value are similar to those obtained from 1-D model for various air speeds. However, the present estimates of the h ¯ and η f values obtained from the 2-D model an slightly deviate from those obtained from the 1-D model. It is worth mentioning that the deviation between the h ¯ value in the downstream region and that in the upstream region can be observed using the 2-D model. This phenomenon cannot be obtained from the 1-D model.