Effects of Averaging the Heat-Transfer Coefficient on the Predicted Material Temperature Distribution

Abstract

The heat-transfer coefficient (HTC) in internal-coolant passages can vary appreciably about a heat-transfer enhancement feature such as a pin fin, a rib, and a concavity because of stagnation regions and wakes about the enhancement feature. However, the computed or measured HTC is often averaged spatially in the spanwise direction or over some region when used in the design of cooling strategies. Since the variation in the HTC could be a factor of eight or more about an enhancement feature, it is of interest to understand the effects of averaging the HTC on the predicted temperature distribution in the solid subjected to the heating and cooling. In this computational study, a flat plate of thickness H (1 mm) and length L = 20H is heated on one side by either a constant heat flux (68 W/cm2) or a constant HTC (1,167.2 W/m2-K) and a constant hot-gas temperature (1,482 °C). On the cooled side, the free stream or bulk temperature is kept constant (400 °C) and the average HTC (1,442.5 W/m2-K) is kept constant as well. This average HTC on the cooled side is the average of a higher HTC (hH) and a lower HTC (hL). Two types of changes from hH to hL are considered — abrupt (or step) and gradual. When the HTC changes abruptly, hH is imposed over LH, and hL is imposed over LL=L–LH. When the HTC changes gradually from hH to hL, hH is imposed from from x = 0 to LH/2, and hL is imposed from x = 3LH/2 to L with a smooth variation in the HTC to connect hH and hL. Results obtained show that when the averaged HTC is used, the maximum temperature in the plate is 900 °C on the heated side of the plate. However, if the variation in the HTC is accounted for, then the maximum temperature in the plate could be as high as 1.363 times the maximum temperature predicted by assuming an averaged HTC. Also, for the range of parameters studied, the difference in the maximum and minimum temperature in the plate can increase by a factor of 16, which strongly affects thermal stress.