AIAA 2004-0822 Thermal Resistances of Gaseous Gap for Non-Conforming Rough Contacts

An approximate analytical model is developed for predicting the thermal contact resistance of spherical rough solids with the presence of interstitial gases. The joint resistance includes four thermal resistances, i.e., macrogap, microgap, macrocontact, and microcontacts. Simple relationships are derived for each component of the joint resistance assuming contacting surfaces are of uniform temperature and that the microgap heat transfer area and the macrocontact area are identical. Effects of main input contact parameters on the joint resistance are studied. It is demonstrated that a surface curvature exists that minimizes the joint resistance for a fixed contact. The model covers all regimes of gas heat conduction modes from continuum to free molecular. The present model is compared with 110 experimental data points collected by Kitscha and 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 E = Young's modulus, P a E 0 = equivalent elastic modulus, P a F = external force, N 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 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 = vacuum Y = mean surface plane separation, m Greek α = non-dimensional parameter, ≡ σρ/a 2 H γ = exponent of the general pressure distribution γ g = ratio of gas specific heats Λ = mean free path, m δ = maximum surface out-of-flatness, m λ = non-dimensional separation≡ Y/ √ 2σ ν = Poisson's ratio ξ = non-dimensional radial position, ≡ r/a L ρ = radius of curvature, m σ = RMS surface roughness, m σ 0 = σ/σ 0 , σ 0 = 1 µm τ = non-dimensional parameter, ≡ ρ/a H ω = bulk normal deformation, m Subscripts 0 = reference value 1, 2 = solid 1, 2 a = apparent g = gas, microgap G = macrogap H = Hertz L = macrocontact j …