Effects of Averaging the Heat Transfer Coefficient on Predicted Material Temperature and Its Gradient

Abstract

The heat transfer coefficient (HTC) is often averaged spatially when designing heat exchangers. Since the HTC could vary appreciably about a heat transfer enhancement feature such as a pin fin or a rib, it is of interest to understand the effects of averaging the HTC on design. This computational study examines those effects via a unit problem—a flat plate of thickness H and length L, where L represents the distance between pin-fins or ribs. This flat plate is heated on one side, and cooled on the other. Variable HTC is imposed on the cooled side—a higher HTC (hH) over LH and a lower HTC (hL) over LL = L − LH. For this unit problem, the following parameters were studied: abrupt versus gradual transition between hH and hL, hH/hL, LH/L, and H/L. Results obtained show that if the averaged HTC is used, then the maximum temperature in the plate and the maximum temperature gradient in the plate can be severely underpredicted. The maximum temperature and the maximum temperature gradient can be underpredicted by as much as 36.3% and 542%, respectively, if the Biot number is less than 0.1 and as much as 13.0% and 570% if the Biot number is between 0.25 and 0.4. A reduced-order model was developed to estimate the underpredicted maximum temperature.