# Confusion about Thermal Resistance and Heat Distribution

I'm trying to understand the flow of heat between electrical components and circuit boards, and I'm having some trouble understanding some basic concepts.

Suppose I'm considering a chip with a $\theta_{JC} = 2^\circ C/W$, attached to a heatsink using thermal compound with $\theta_{CS} = 0.2^\circ C/W$. Suppose for the sake of example I chose a very poor heatsink with $\theta_{SA} = 200^\circ C/W$.

According to the analogy of thermal resistances in series, if my chip is dissipating $1W$, then the temperature increase of the system is: $$(1W)(2^\circ C/W + 0.2^\circ C/W + 200^\circ C/W) = 202.2^\circ C + T_{ambient}$$ This makes sense to me. What I am confused about is how the heat is distributed across the components. Surely this doesn't mean that my heatsink would be at $200^\circ C$ (above ambient) while the chip it's connected to remains comfortably at $2^\circ C$ above ambient? Assuming I have the dimensions of the chip, board, and heatsink, how would I integrate this with the heat equation so that I can find spatial temperature distributions over time?

• A definition of $\theta$ and a diagram with the boundary conditions would be helpful, but a quick look suggests that the heatsink touching the compound would be 200°C higher than ambient, the compound touching the chip would be 200.2°C higher, and the part of the chip generating heat would be 202.2°C higher. Does this not apply? – Chemomechanics Apr 11 '18 at 18:37
• I think that you have the stacking upside down. First, you have ambient temperature. Then you have the heatsink about 200 C above ambient, and then your chip at about 2 C above the heatsink, or in other words about 202 C above ambient. – user93237 Apr 11 '18 at 18:40

## 1 Answer

You have 4 components in series: chip, thermal compound, heat sink and environment. The thermal resistance of chip and thermal compound is very low. But heat sink is very high (insulation!). In order to get 1W out, basically, the temperature of the chip temperature and thermal compound is 200 degrees C and the temperature of one side of the heat sink is 200 degrees, and the other side 2 degrees.