Thermal conductivity with plating

[kmaryan]

This relates to design of a heat spreader. My intuition is failing me and I'm not familiar with this area of thermodynamics/heat flow.

Assume I have a heat source, attached to a large flat surface used as a heat spreader/sink. The size of the source is negligible w.r.t. the surface area (A) of the heat spreader. Consider that the heat spreader is made from a material with thermal conductivity X. Now consider an alternative where the heat spreader has a thin coating (metal plating) with heat conductivity Y on top of the material with conductivity X. How does the effective thermal conductivity from the heat source to the ambient air change in the X and Y vs. the X only case?

I'm probably missing information, but I'm not sure what's relevant here. Let me know if anything else is relevant in coming up with at least a first order approximation of how the heat flow changes.

Thanks,

Chris

 

[Aaron Barnard]

The first order approximation of how the heat flow changes depends on a few factors. First, you need to consider the thickness (t) of the coating and the thermal conductivity ratio (Y/X) of the coating relative to the substrate material. Assuming that the thickness of the coating is much smaller than the thickness of the substrate material, then the effective thermal conductivity (K) can be approximated by: K = X + (Y-X)*(t/A), where A is the area of the heat spreader. This equation assumes that the coating is homogeneous and isothermal. If the coating is not homogeneous or isothermic, then the equation will need to be modified accordingly.