Variable Property Nusselt Numbers in a Channel with Pin Fins

Abstract

Nusselt numbers and friction factors are presented that show the effects of temperature ratio and variable properties in a rectangular channel with pin ns and an aspect ratio of 8. The ratio of air inlet stagnationtemperature to local surface temperature T 0i /T w varies from 0.68 to 0.93, and Reynolds numbers based on channel height range from 1:8 £ £ 10 4 to 3:38 £ £ 10 4 . The pins are placed in 12 rows, with pin diameter and spacing between adjacent pins in both directions all equal to the channel height. Ratios of globally averaged Nusselt numbers to baseline, constant-property Nusselt numbers, Nu/Nu 0;cp , increase by about 35% as the temperature ratio T 0i /T w decreases, provided that Reynolds number Re H is approximately constant and that the base areas beneath the pins are not considered. When heat transfer from the pin ns is also included, this increase is about the same. Friction factor ratios f /f 0;cp decrease as T 0i /T w decreases over this same range of values. Such global Nusselt number changes are a result of local Nusselt number ratio increases with decreasing temperature ratio, which are especially pronounced beneath the wake and shear layers that are present downstream of each pin and beneath the horseshoe vortex that forms just upstream of each pin n. NomenclatureD h = channel hydraulic diameter d = pin n diameter f = friction factor f 0 = baseline friction factor in a smooth channel with no pin ns H = channel height k = thermal conductivity N u = local Nusselt number, P q 00 0 D h =k.T w ¡ T mx / N u 0 = baseline Nusselt number in a smooth channel with no pin ns Pr = molecular Prandtl number p = streamwise spacing of pin n centers p 0 = streamwise spacing between adjacent pin ns P q 00 0 = surface heat ux Re Dh = Reynolds number based on hydraulic diameter and mean velocity at test section inlet Re d = Reynolds number based on pin n diameter and mean velocity at minimum ow area Re H = Reynolds number based on channel height and mean velocity at test section inlet s = spanwise spacing of pin n centers s 0 = spanwise spacing between adjacent pin ns T = local static temperature W = channel width X = streamwise coordinate measured from the test section inlet Z = spanwise coordinate measured from the test surface centerline Subscripts cp = constant property value mx = local mixed-mean value 0 = baseline value 0i = total or stagnation value at the test section inlet w = local wall value Superscripts -= value spatially averaged along a line either in the streamwise or spanwise direction = = globally averaged value

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