Thermal Interface Conductance

Thermal Interface Conductance

Calculates the thermal joint conductance $h_j$ and temperature drop $\Delta T$ across the interface formed by two conforming, rough surfaces with a gap-filling liquid substance (thermal grease, oil, etc.).

Material Properties

Harmonic mean conductivity of the two solids:

$$k_s=\frac{2k_1{k}_2}{k_1+k_2}$$

Combined effective RMS roughness (${\sigma }_1,{\sigma }_2$ in µm):

$$\sigma =\sqrt{{\sigma }_1^2+{\sigma }_2^2}$$

Effective mean absolute asperity slope (empirical fit, $\sigma$ in µm):

$$m=0.125{\sigma }^{0.406}$$

Valid for $0.216\le \sigma \le 9.6$ µm.

Contact Conductance

$$h_c=1.25k_s\frac{m}{{\sigma }^{\prime }}{\left(\frac{P}{H_c}\right)}^{0.95}$$

where ${\sigma }^{\prime }$ is in metres, $P$ and $H_c$ are in the same units (MPa).

Gap Conductance (liquid/grease, M = 0)

Effective gap thickness:

$$Y=1.53\sigma {\left(\frac{P}{H_c}\right)}^{-0.097}[\mu \text{m}]$$

Gap conductance:

$$h_g=\frac{k_g}{Y}$$

Joint Conductance and Temperature Drop

$$h_j=h_c+h_g$$ $$r_j=\frac{1}{LW{h}_j},\Delta T=Q{r}_j$$

Validity

• Contact pressure $P$: 0.035 – 0.35 MPa
• Surface roughness $\sigma$: 0.216 – 9.6 µm
• Gas parameter $M$ is set to zero — model applies to liquid/grease gap fill only.

Reference

Yovanovich, M., Culham, J. R., Teertstra, P., Calculating Interface Resistance, Microelectronics Heat Transfer Laboratory, University of Waterloo.