Thermal Contact Resistance

It's true. Actual solid surfaces are full of microscopic asperities, and the true contact area is only about 1-5% of the apparent area. The remaining gaps are filled with air or grease. This imperfect contact causes a temperature discontinuity. This is thermal contact resistance.

Yes. Therefore, the thermal contact resistance $R_c$ is defined as the ratio of the interface temperature jump $\Delta T$ to the heat flux $q''$.

Its unit is [m$^2$ K/W]. Its reciprocal is the contact conductance $h_c = 1/R_c$ [W/(m$^2$ K)].

There are four main factors.

The Cooper-Mikic-Yovanovich model is widely used.

Here, $k_s$ is the harmonic mean thermal conductivity $k_s = 2k_1 k_2/(k_1+k_2)$, $m$ is the surface slope, $\sigma$ is the composite roughness $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}$, and $H$ is the microhardness.

Exactly. In heat sink mounting for electronics, bolt torque management directly affects temperature. In some cases, doubling the tightening torque can roughly double the contact conductance.

Either by creating a thin virtual layer at the interface or by directly specifying the conductance value to contact elements. The basic discretization is expressed by a thermal conductance matrix between interface nodes.

Assembling this at the element level yields the interface heat transfer matrix.

Good observation. Implementation-wise, it can be handled the same as the Robin condition. However, pairing of contact surfaces (matching master/slave surfaces) is additionally required.

In practice, variable conductance depending on the contact state is often used.

Exactly. The standard practice is to perform a sensitivity analysis, checking the temperature difference with $h_c$ halved and doubled. If the results strongly depend on $h_c$, obtaining measured values should be considered.

Pressure-dependent or temperature-dependent thermal contact resistance becomes a nonlinear problem. It involves coupling with structural analysis to determine contact pressure, calculating $h_c$ from that pressure using the CMY model, and feeding it back to the thermal analysis. This iteration is repeated until convergence.

Ansys Mechanical and Abaqus automate this coupling. In Ansys, you just need to set TCC (Thermal Contact Conductance) for contact elements CONTA174/TARGE170.

The standard flow is as follows.

1. Identify Contact Surfaces: Clearly define surface pairs that contact each other in CAD.

2. Determine Conductance Value: From measured values, literature values, or calculated using the CMY model.

3. Set Contact Pairs: Define master/slave surfaces and assign $h_c$.

4. Mesh Conformity: Adjust the mesh so that nodes are aligned on opposing contact surfaces.

5. Solve & Verification: Verify that the temperature jump at the interface is physically reasonable.

It can be solved with non-conforming meshes (Mortar method or GGI connection), but conforming meshes tend to yield higher accuracy for contact surfaces. Especially when the temperature jump is small, artifacts from mesh non-conformity can become visible.

That's because grease fills the gaps instead of air (k=0.026 W/(m K)). However, grease degradation over time (pump-out, drying) should also be considered; values after degradation should be used for long-term reliability evaluation.

Here are the verification points for thermal contact resistance analysis.

• Confirm Temperature Jump: Plot node temperatures on both sides of the contact surface and check if $\Delta T = q'' \cdot R_c$ holds.
• Energy Conservation: Check if the heat flow passing through the contact surface matches upstream and downstream.
• Sensitivity Analysis: Quantify the impact on results by varying $h_c$ by $\pm$50%.