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?
At the microscopic level, the contact surface only makes point contacts (true contact points) due to surface roughness. The actual contact area is about 1% of the apparent area, with the rest being an air gap. This contact imperfection causes the temperature jump.
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
The Cooper-Mikic-Yovanovich (CMY) model (1969) predicts the contact heat transfer coefficient hc from contact pressure p and surface roughness σ. For metal-to-metal contact, doubling the pressure often increases hc by about 1.5 times. This model is referenced in ISO/TS 22007 and serves as the theoretical basis for mount pressure design in CPU heat sinks.
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?
Caution is needed. Datasheets often measure under ideal conditions (high pressure, perfect wetting). Values under actual implementation conditions (pressure, surface roughness, application amount) can be 1.5 to 3 times worse. For initial design, it's safe to estimate using 50% of the datasheet value.
Thermal Design of Bolted Joints
As a practical example, consider the bolted joint of a heat sink plate. For 4 M4 bolts, tightening torque 1.5 Nm:
- Bolt axial force: ~2600N per bolt
- Contact surface pressure: ~52 MPa at the seat surface (φ8mm)
- From the CMY model: $h_c \approx 8000$ W/(m2K) (Aluminum·Polished surface)
So you can estimate $h_c$ from the contact pressure.
Yes. However, pressure decreases between bolts, so a precise approach is to obtain the pressure distribution via structural analysis first, then map $h_c$ accordingly.
TIM Thermal Conductivity and Effective TCR
Intel's Core i9-13900K (2022) uses InFusion liquid metal TIM between the CPU die and IHS, reducing contact thermal resistance by about 50% compared to solid grease. Liquid metal (GaInSn-based) has a thermal conductivity of about 40 W/m·K, significantly exceeding that of high-end silicone grease (~12 W/m·K). However, it corrodes aluminum IHS, so it was changed to copper.
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators