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Originally Posted by Cathar
If I'm understanding correctly what you're showing there, what you're seeing there is not the influence of the heat capacity of the base-plate, but the influence of the spreading resistance due to the thickness of the base-plate.
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Yep thickness it was.
I'll get back on the heat capacity now. For that I'll use some more geochemistry oriented examples (since that's my background) and compare heat to a conservative compound (no degradation) that's produced locally (at the die) and has to be transported through a medium (the solid phase = heat spreader + TIM + cooling block) to a cooling medium (water/vapor). We now can translate the heat capacity/heat conductivity of the solid phase to a difference in diffusion speed (also called retardation).
You’re right that under the assumption of steady state the amount of heat removed within a time unit has to be the same for all cooling solutions. But if the solid phase is more restrictive with regard to diffusion, there will be a certain build up of the compound within the solid phase.
Mathematically this looks like:
diffusief transport
fluxi,j = Di,j . Oppi,j . (Ci - Cj) / lengtei,j (2)
with:
fluxi,j mass transport between segment i and segment j (M/t)
Di,j diffusion coefficient between segment i en segment j (O/t)
Ci concentration of compound in segment i (M/V)
Cj concentration of compound in segment j (M/V)
Oppi,j surface area between segment i en j (O)
Lengtei,j distance between center of segment i en j (L)
The diffusion coefficient is normally given in (cm2/s) and is influences by the porosity (read conductivity of the solid phase in case of heat) of the sediment. An increase in the porosity will lead to a higher diffusion speed and therefore a higher flux with the same delta C (or delta T for heat) versus delta X.
So, assuming a linear relation between the heat conductivity and the diffusive flux, silver should have a 10% higher flux. While not completely linear, this should to a decrease in the delta T between the die and cooling medium of roughly 10% to have the same flux. A normal delta T for a water block with a 100 watt load would be around +15 oC (water chiller). Assuming that heat conductivity is the primary limiting factor in transporting heat, using silver would have lowered the delta T with roughly 1.5 oC.