The Thermal Contact feature node has correlations to evaluate the joint conductance at two contacting surfaces.

The heat fluxes at the upside and downside boundaries depend on the temperature difference according to the relations:

At a microscopic level, contact is made at a finite number of spots as in Figure 4-21.

The joint conductance h has three contributions: the constriction conductance, hc, from the contact spots, the gap conductance, hg, due to the fluid at the interstitial space, and the radiative conductance, hr:

The microscopic surface asperities are characterized by the average height σu, asp and σd, asp and the average slope mu, asp and md, asp. The RMS values σasp and masp are (4.16 in Ref. 1):

The Cooper-Mikic-Yovanovich (CMY) correlation is valid for isotropic rough surfaces and has been formulated using a model assuming plastic deformation of the surface asperities. However, this model does not compute nor store the plastic deformations of the asperities. It means that, despite that a plastic deformation of the asperities is assumed, this contact model has no memory. For example, if a load is applied twice the thermal contact is identical in both cases. The Cooper-Mikic-Yovanovich (CMY) correlation relates hc to the asperities and pressure load at the contact interface:

Here, Hc is the microhardness of the softer material, p is the contact pressure, and kcontact is the harmonic mean of the contacting surface conductivities:

The relative pressure p ⁄ Hc can be evaluated by specifying Hc directly or using the following relation (4.16.1 in Ref. 1) for the relative pressure using c1 and c2, the Vickers correlation coefficient and size index:

The coefficients c1 and c2 are the Vickers correlation coefficient and size index, respectively, and σ0 is equal to 1 µm. For materials with Brinell hardness between 1.30 and 7.60 GPa, c1 and c2 are given by the correlation below (4.16.1 in Ref. 1):

The Brinell hardness is denoted by HB, and H0 is equal to 3.178 GPa.

The Mikic correlation is valid for isotropic rough surfaces and assumes elastic deformations of surface asperities. It gives hc by the following relation:

Here, Econtact is an effective Young’s modulus for the contact interface, satisfying (4.16.3 in Ref. 1):

where Eu and Ed are the Young’s moduli of the two contacting surfaces and νu and νd are the Poisson’s ratios.

The gap conductance due to interstitial fluid cannot be neglected for high fluid thermal conductivity or high contact pressure. The parallel-plate gap gas correlation assumes that the interstitial fluid is a gas and defines hg by:

Here kg is the gas conductivity, Y denotes the mean separation thickness (see Figure 4-21), and Mg is the gas parameter equal to:

In these relations, α is the contact thermal accommodation parameter, β is a gas property parameter (equal to 1.7 for air), Λ is the gas mean free path, kB is the Boltzmann constant, D is the average gas particle diameter, pg is the gas pressure (often the atmospheric pressure), and Tg is the gap temperature equal to:

The mean separation thickness, Y, is a function of the contact pressure, p. For low values of p near 0 Pa, Y goes to infinity since no contact occur. For high values of p — greater than Hc ⁄2 in the Cooper-Mikic-Yovanovich model and greater than Hc ⁄4 in the Mikic elastic model — Y reduces to 0 meaning that the contact is considered as perfect.

At high temperatures, above 600 °C, radiative conductance needs to be considered. The gray-diffuse parallel plate model provides the following formula for hr:

The friction heat, Qb, is partitioned into rQb and (1 − r)Qb at the contact interface. If the two bodies are identical, r and (1 − r) would be 0.5 so that half of the friction heat goes to each surface. However, in the general case where the two bodies are made of different materials, the partition rate might not be 0.5. The Charron’s relation (Ref. 2) defines r as:

and symmetrically, (1 − r) is:

For anisotropic conductivities, nTkdn (resp. nTkun) replaces kd (resp. ku).