# Calculate Thermal Resitance from Heat Sink Geometry

## Main Question or Discussion Point

Hi all,

I have a heat sink for which I know the exact geometry (have the CAD model). This heat sink was custom designed and machined from a hunk of aluminum, though it is very basic and I have a hunch I can find an extrusion or OTS part that will match its performance. Rather than trying to just match the surface area, I'd like to know what the thermal resistance of it is so that I can try to match it.

How do I calculate the thermal resistance of the heat sink given its geometry and material?

Here's a rough description of the heat sink:

18 square fins spaced evenly in a single row at a pitch of 0.36". Each fin is 2" tall by 2" wide and is 0.08" thick.

Thanks

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berkeman
Mentor
Hi all,

I have a heat sink for which I know the exact geometry (have the CAD model). This heat sink was custom designed and machined from a hunk of aluminum, though it is very basic and I have a hunch I can find an extrusion or OTS part that will match its performance. Rather than trying to just match the surface area, I'd like to know what the thermal resistance of it is so that I can try to match it.

How do I calculate the thermal resistance of the heat sink given its geometry and material?

Here's a rough description of the heat sink:

18 square fins spaced evenly in a single row at a pitch of 0.36". Each fin is 2" tall by 2" wide and is 0.08" thick.

Thanks
The thermal resistance will depend on the orientation (horizontal or vertical), and whether there is forced airflow over it.

Often it is easier to just measure the thermal resistance θ with a thermocouple and power resistors...

I'm sorry, I forgot to mention: this is free convection. So I can make whatever assumptions I need to about ambient temperature, air density, air viscosity, etc.

It's about impossible to calculate, and certainly unreasonable, sorry. Measure it.

The heat exchange depends fundamentally on how much air circulates and how, which is already inaccessible to hand calculation and which computer programmes are bad at.

Add to it that the exchange is limited by the fine layer of air right against the metal that circulates less good... A few formulas are known for very simple shapes and that's all.

Some people specialize in that and, after months and years, are capable of giving an estimate. If you read French: Sacadura, "Initiation aux transferts thermiques". Hard, lengthy, and it won't help so much in a practical case.

Besides measuring, you could compare with existing similar heatsinks. Take a catalogue with data, say like Fischer, find the most resembling profile. By the way, I'm surprised someone machines a heat sink instead of cutting it from a bought profile.

Free convection is the most difficult to predict.

Mech_Engineer
Gold Member
It's about impossible to calculate, and certainly unreasonable, sorry. Measure it.

The heat exchange depends fundamentally on how much air circulates and how, which is already inaccessible to hand calculation and which computer programmes are bad at.
Engineering calculations w.r.t. fins and heatsinks (arrays of fins) are very possible and used often for things like electronics cooling and heat exchanger design. Unfortunately an internet forum isn't really the right place to try an teach someone how to do such calculations; you really need to take a college senior-level heat transfer class to do it.

Short of that, a text book on the subject is a good reference on how such calculations are done, the text book I have, Introduction to Heat Transfer, covers everything you need to do such calculations.

Suffice to say the general calculation procedure would be:
• Conceptualize a thermal-equivalent circuit for the component being cooled, with thermal resistance variables for the heatsink, component, and convection.
• Estimate ambient temperature and required power dissipation.
• Using fin geometic properties calculate fin efficiency and thermal-equivalent resistance as a function of temperature. This would be accomplished using the "fin efficiency" for your particular geometry, out of a table in the book.
• Plug the equation into the thermal-equivalent circuit and solve for the resulting temperature of the component and heatsink.
• Iterate.