Thermal Contact Resistance
Thermal Contact Resistance: Theoretical Foundations
What is Thermal Contact Resistance?
Why does the temperature jump at the interface even when two solids are pressed together?
Microscopic surface roughness concentrates contact in many small regions. The real contact area depends on material, roughness, flatness and contact pressure; it is not universally 1%. Heat transfer through gas or interface material in the gaps can also matter. NASA: Thermal Control
Fundamental Equation
The defining equation for thermal contact resistance is as follows.
The contact conductance is $h_c = 1/R_c$ [W/(m2K)].
What are typical values?
They vary by orders of magnitude depending on conditions.
| Contact Condition | $h_c$ [W/(m2K)] |
|---|---|
| Aluminum to Aluminum·Polished Surface·High Pressure | 10000~25000 |
| Steel to Steel·Machined Surface·Medium Pressure | 2000~5000 |
| With Thermal Grease | 5000~50000 |
| Air Gap (0.1mm) | 250 |
| In Vacuum·Low Pressure | 100~500 |
Cooper-Mikic-Yovanovich Model
A representative theoretical model is the Cooper-Mikic-Yovanovich (CMY) correlation.
Here, $k_s = 2k_1k_2/(k_1+k_2)$ is the harmonic mean thermal conductivity, $m$ is the surface slope, $\sigma$ is the composite roughness, $P$ is the contact pressure, and $H_c$ is the microhardness.
So increasing the pressure reduces the thermal contact resistance.
Exactly. In bolted joint design, the tightening torque determines the performance of the thermal path. Insufficient torque becomes a critical risk in thermal design.
The Discovery of Thermal Contact Resistance Came from NASA
Thermal Contact Resistance (TCR) gained engineering attention in the 1950s during the space race. In a vacuum, where there is no convection, TCR at bolted joints becomes the dominant thermal resistance. NASA's Glenn Research Center built the first systematic experimental database in 1959. Even today, that data is used as a reference value in early-stage design.
Computational Methods for Thermal Contact Resistance
Modeling Thermal Contact Resistance in FEM
How do you represent thermal contact resistance in FEM?
There are three main methods.
| Method | Overview | Accuracy |
|---|---|---|
| Gap Conductance | Set $h_c$ between surfaces | Practical |
| Thin Layer Element | Model TIM with equivalent k, t | Requires thickness |
| Pressure-Dependent Conductance | Calculate $h_c(P)$ via structural coupling | High Accuracy |
In Ansys Mechanical, it's set via TCC (Thermal Contact Conductance) for contact elements. In Abaqus, you can define a pressure-dependent table using the *GAP CONDUCTANCE keyword.
If making it pressure-dependent, coupling with structural analysis is necessary, right?
Yes. In Ansys Workbench, you can link "Static Structural → Steady-State Thermal" to transfer contact pressure and reference the $h_c(P)$ table from the CMY model. This is an essential workflow for thermal path design in bolted joints.
TIM Modeling
Thermal Interface Material (TIM) is represented by the combination of bulk k and contact resistance.
It's the sum of the bulk resistance and the contact resistance on both sides. For thermal grease, even with bulk k=3 W/(mK) and thickness 50um, the bulk resistance is often small, and the contact resistance on both sides tends to dominate.
That's why the application method and pressure are so important.
Exactly. Even with the same grease, the effective $R_{TIM}$ can vary by 2 to 5 times depending on the implementation conditions.
Experimental Correlation Between Applied Pressure and TCR
In the CMY equation above, if roughness, surface slope, hardness and conductivity remain fixed, doubling pressure gives a solid-contact conductance ratio of 20.95 ≈ 1.93. In actual joints, deformation, pressure distribution and heat transfer through gaps also matter. See COMSOL: theory for thermal contact and the CMY correlation.
Thermal Contact Resistance in Practice
Measurement Methods
How do you obtain values for thermal contact resistance?
The most reliable method is actual measurement. Measure using the steady-state method conforming to ASTM D5470.
1. Sandwich the TIM sample between two copper blocks
2. Heat one block and cool the other
3. Extrapolate the interface temperature difference from the temperature gradient within each block
4. $R_{TIM} = \Delta T_{interface} / q''$
Can I use the values from commercial TIM datasheets as-is?
Compare the datasheet test conditions with the installed pressure, surfaces, thickness and temperature. Resistance and conductance change in opposite directions. A fixed multiplier or 50% factor is not a universal safety margin; measure under relevant conditions and assess sensitivity.
Thermal Design of Bolted Joints
For a bolted heat-sink joint, assess bolt preload and interface pressure separately. The following is an illustrative calculation, not a prediction for a real joint:
- Assume 2000 N uniformly distributed over 1000 mm²: the mean interface pressure is 2 MPa.
- Assume contact conductance 1000 W/(m²·K) and heat flux 10000 W/m²: the interface temperature difference is 10 K.
- Preload depends on friction and other factors; local pressure is nonuniform. A CMY estimate also needs roughness, hardness and thermal conductivity.
So you can estimate $h_c$ from the contact pressure.
Pressure distribution can be analyzed structurally, then combined with a model for the surfaces and materials and checked against measurements. Pressure alone does not uniquely determine conductance.
TIM Thermal Conductivity and Effective TCR
Intel states that 13th-generation desktop processors use solder thermal interface material (STIM) between the die and the IHS. The TIM between the IHS and cooler is a separate interface; its material, thickness and contact pressure also affect thermal resistance. Intel: Solder Thermal Interface Material
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