Performance of Pin Fin Cast Aluminum Coldwalls, Part 2: Colburn j-Factor Correlations

An experimental program was conducted over a wide range of geometric cone gurations and Reynolds number with 44 cast, staggered, pin e n test sections producing heat transfer data for streamwise spacing ratios S/d from 1.83 to 3.21, transverse spacing ratios T/d from 2.00 to 6.41, and pin lengths L/d from 1.88 to 7.25. Empirical correlations are presented for the Colburn j factor as a function of the spacing ratios, pin length, and Reynolds number. Analysis of the experimental heat transfer results, as in the case of the isothermal tests for friction factor, indicates that the e ow transitions from laminar to turbulent e ow at Red » 10 3 with unique correlations in each regime. For laminar e ow, the Colburn j factor depends on the three-dimensional cone guration and Reynolds number Red. In the turbulent regime, the Colburn j factor depends primarily on T/d, L/d, and Reynolds number Red. Nomenclature Abase = test section bottom wall area, lw i NpinApin;b, m 2 AHT = Abase C Atop C Apin D 2(lw)C Npin o.davL id 2 =2), m 2 Amin = test section e ow area, wL i Nt Aproe le, m 2 Apin = total pin surface area, Npin odavL, m 2 Apin;b = base area of each pin, m 2 Aproe le = (d Cdtip)L=2DdavL, m 2 Atop = test section top wall area, lw i NpinApin;b, m 2 cp = specie c heat, kJ/ (kg¢K) D = hydraulic diameter, 4 Aminl=AHT, m d = pin base diameter, m dav = average pin diameter, 0.5 (d Cdtip/, m dtip = pin tip diameter, m h = heat transfer coefe cient, q=AHT.Tw;av iTb;av/, W/(m 2 K) j = Colburn j factor, St Pr 2=3 , Nu=Re Pr 1=3 k = thermal conductivity, W/m K L = pin length (see Fig. 1), m L=d = dimensionless pin length l = test section e ow length, m Npin = total number of test section pins Nt = pin count in the maximum transverse row Nu = Nusselt number based on pin diameter, hd=k NuD = Nusselt number based on hydraulic diameter, hD=k Pr = Prandtl number, cpπ=k Q = volumetric e ow rate, m 3 /s q = heat transfer rate, W