Thermal Joint Resistances of Conforming Rough Surfaces with Gas Filled Caps

Abstract

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, that is, 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 other models and with more than 510 experimental data points in the open literature. Good agreement is shown over the entire range of the comparison. Nomenclature A = area, m 2 a = radius of contact, m bL = specimens radius, m c1 =V ickers microhardness coefficient, Pa c2 =V ickers microhardness coefficient d = distance between two parallel plates, m F =e xternal force, N Hmic = microhardness, Pa H � = c1(1.62σ � /m) c2 ,P a H ∗ = c1(σ � /m) c2 ,P a Kn = Knudsen number k = thermal conductivity, W/mK l = depth, m M =g as parameter, m Mg = molecular weight of gas, kg/kmol Ms = molecular weight of solid, kg/kmol m = mean absolute surface slope ns = number of microcontacts P = pressure, Pa Pr = Prandtl number Q = heat flow rate, W q = heat flux, W/m 2 R = thermal resistance, K/W r, z =c ylindrical coordinates T = temperature, K t = dummy variable Y = mean surface plane separation, m z = surface height, m αT = thermal accommodation coefficient γ = ratio of gas specific heats � = mean free path, m λ = nondimensional separation ≡ Y √ 2σ