AIAA 2004-0821 Thermal Resistances of Gaseous Gap for Conforming Rough Contacts

An approximate analytical model is developed for predicting the heat transfer of interstitial gases in the gap between conforming rough contacts. A simple relationship for the gap thermal resistance is derived by assuming that the contacting surfaces are of uniform temperature and that the gap heat transfer area and the apparent contact area are identical. The model covers the four regimes of gas heat conduction modes, i.e., continuum, temperature-jump or slip, transition, and free molecular. Effects of main input parameters on the gap and joint thermal resistances are investigated. The model is compared with the existing model of Yovanovich et al. and with more than 510 experimental data points collected by Hegazy and Song. Good agreement is shown over entire range of the comparison. Nomenclature A = area, m 2 a = radius of contact, m b L = specimens radius, m c 1 = Vickers microhardness coefficient, P a c 2 = Vickers microhardness coefficient d = mean contacting bodies distance, m F = external force, N h = contact conductance, W/m 2 K H mic = microhardness, P a H 0 = c 1 (1.62σ 0 /m) c 2 , P a Kn = Knudsen number k = thermal conductivity, W/mK m = mean absolute surface slope M = gas parameter, m n s = number of microcontacts P = pressure, P a Pr = Prandtl number Q = heat flow rate, W q = heat flux, W/m 2 R = thermal resistance, K/W r, z = cylindrical coordinates T = temperature, K TAC = thermal accomodation coefficient TCR = thermal contact resistance vac. Λ = mean free path, m λ = non-dimensional separation≡ Y/ √ 2σ σ = RMS surface roughness, m σ 0 = σ/σ 0 , σ 0 = 1 µm Subscripts 0 = reference value 1, 2 = solid 1, 2 a = apparent g = gas j = joint r = real s = solid, micro