# Correct approach for thermal finite element simulation of layered assembly

I would like to optimise the heat transfer on a PCB. Several dies are on the top and cooling air is going through the fins in heat sink on the bottom. The assembly consists of several layers like shown in the simplified figure below.

I would like to investigate the influence of for instance several thermal greases on the maximum temperature of the chips: I want to vary the thermal coefficient and the thickness of the thermal grease layer.

The “problem”/”issue” is that the dimensions in the Z direction (micrometer) are much smaller than X and Y directions (~10 mm). This makes the meshing process complicated using “naive” finite element simulations.

Is there a better approach to analyse this type of layered assembly using finite element simulation?

• Interesting problem. The issue you mention might be a concern. A big consideration in this model is how accurately you want to model the convection behavior at the cooling fins along the bottom. Were you thinking of modeling each individual fin? If so, were you thinking of doing some kind of fluid analysis to calculate the convection at the fins? Or do you happen to have a reasonable estimate for a convection coefficient for the fins? Jan 23, 2020 at 12:55
• To keep things as simple as possible I am not using CFD, only setting a boundary condition on each fin with a heat transfer coefficient that I computed using Bejan's book "Convection heat trasfer" Jan 23, 2020 at 14:04
• Now I realize that the unit in the dimension of PCB is wrong, it should be 1.55 mm but it's not important for the topic at hand Jan 23, 2020 at 14:05
• Would you expect this analysis to show anything other than the "best" grease layer is the thinnest one with the highest thermal conductivity? My inclination, at least as a first cut, would be to use a 1D, through-the-thickness model. I think you can also find a convection coefficient for an array of fins. A 1D model, of course, eliminates the problem of element aspect ratio. Jan 23, 2020 at 14:39
• Yes, that is to be expected, the tendency is clear but I need to know if a given grease will satisfy some spec: since different greases are more expensive/have different temp ranges and so on, so I want to see if grease "A" with a layer of "X" thickness manages to keep the maximum chip temperature below 125 °C and so no. Jan 23, 2020 at 15:35