OF THERMAL JOINT RESISTANCE MODELS FOR NON-CONFORMING ROUGH SURFACES IN A VACUUM

The thermal contact resistance (TCR) problem is categorized into three different problems: geometrical, mechanical, and thermal. Each problem includes a macro and micro scale subproblem; existing theories and models for each part are reviewed. Empirical correlations for microhardness, and the equivalent (sum) rough surface approximation are discussed. Suggested correlations for estimating the mean absolute surface slope are summarized and compared with experimental data. The classical conforming rough contact models, i.e elastic and plastic, as well as elastoplastic models are reviewed. A set of scale (dimensionless) relationships are derived for the contact parameters, i.e. the mean microcontact size, number of microcontacts, density of microcontacts, and the external load as functions of dimensionless separation, for the above models. These scale relationships are plotted; it is graphically shown that the behavior of these models, in terms of the contact parameters, are similar. The most common assumptions of existing thermal analysis are summarized. As basic elements of thermal analysis, spreading resistance of a circular heat source on a half-space and flux tube are reviewed, also existing flux tube correlations are compared. More than 400 TCR data points collected by different researchers during last forty years are grouped into two limiting cases: conforming rough, and elasto-constriction. Existing TCR models are reviewed and compared with the experimental data at these two limits. It is shown that the existing theoretical models do not cover both of the above-mentioned limiting cases. 1Ph.D. Candidate, Department of Mechanical Engineering. 2Associate Professor, Director, Microelectronics Heat Transfer Laboratory. member ASME . 3Distinguished Professor Emeritus, Department of Mechanical Engineering. Fellow ASME. 4Professor, Department of Mechanical Engineering. NOMENCLATURE A = area, m a = radius of contact, m b = flux tube radius, m c1, c2 = microhardness coefficients, GPa,− d = mean plane separation, GW model dV = Vickers indentation diagonal, μm E = Young’s modulus, GPa E0 = equivalent elastic modulus, GPa F = external force, N H,HB = bulk hardness, GPa Hmic = microhardness, GPa HBGM = geometric mean Brinell hardness, GPa h = thermal contact conductance, W/mK k = thermal conductivity, W/mK ks = harmonic mean thermal conductivity,W/mK L = sampling length, m m = effective mean absolute surface slope, − m0 = effective RMS surface slope, − ns = number of microcontacts P = pressure, Pa Q = heat flow rate, W q = heat flux, W/m R = thermal contact resistance, K/W RMS = root mean square Ra = arithmetic average surface roughness, μm Rq = RMS surface roughness, μm T = temperature, K Y = mean surface plane separation, m 1 Copyright c ° 2003 by ASME Greek β = summits radii of curvature, m γ = plasticity index δ = surface max out-of-flatness, m ε = flux tube relative radius η = microcontact density κ = HB/HBGM λ = dimensonless separation ν = Poisson’s ratio φ = normal probability function ψ = dimensionless spreading resistance ρ = radius of curvature, m σ = RMS surface roughness, μm ω = normal deformation, m ξ = emprical correction factor Subscripts 0 = value at origin 1, 2 = surface 1, 2 a = apparent b = bulk c = conduction, contact e = effective g = gap GW = Greenwood and Williamson Hz = Hertz j = joint L = large (macro scale) m = mean mac = macro mic = micro r = real s = small V = Vickers