Thermal calculations.

[davelectronic]

I know this is a topic all of its own, but was hoping to work out how to calculate thermal cooling for semiconductors. I've always guesstimated it, and not always got it correct. Example is 6 X power transistors carrying current in a power supply. I used a 100mm X 200mm X 20mm aluminium plate, the power supply does have cooling by fans. But I feel such a large mass of aluminium doesn't dissipate heat very well, in other words it holds the heat longer. I was starting to think thinner plate would dissipate heat faster as it's a lower mass of aluminium. So I know it comes down to watts per C° but unsure how you can calculate this. Also I know ambient temperature has to be factored in to any cooling scheme. Any tip on calculating heatsinking for a given project would be great. But there is forced air cooling and just convection cooling, both are going to be a totally different size heatsink, and then there's case ventilation cut outs. How do you work out all those variables. Any help appreciated, and thanks for reading.

[Just_another_Dave]

I know this is a topic all of its own, but was hoping to work out how to calculate thermal cooling for semiconductors. I've always guesstimated it, and not always got it correct. Example is 6 X power transistors carrying current in a power supply. I used a 100mm X 200mm X 20mm aluminium plate, the power supply does have cooling by fans. But I feel such a large mass of aluminium doesn't dissipate heat very well, in other words it holds the heat longer. I was starting to think thinner plate would dissipate heat faster as it's a lower mass of aluminium. So I know it comes down to watts per C° but unsure how you can calculate this. Also I know ambient temperature has to be factored in to any cooling scheme. Any tip on calculating heatsinking for a given project would be great. But there is forced air cooling and just convection cooling, both are going to be a totally different size heatsink, and then there's case ventilation cut outs. How do you work out all those variables. Any help appreciated, and thanks for reading.

Most manufacturers provide the junction to package thermal resistance of their devices. The one of the heatsink is also normally provided by manufacturers, but there are some analytical equations that can be used for estimating it otherwise. Using those values it is possible to assemble the equivalent thermal circuit, representing the power losses by current sources and the temperature with voltage ones (earth corresponds to the ambient temperature)

Edit: For estimating the thermal resistance of the heatsink you might want to check Incropera’s book or the one by Cengel

[Just_another_Dave]

Additionally, if the geometry is too complex to estimate the thermal resistance, you can also use a finite element simulator. Ansys has Icepak for simulating complex PCB cooling systems

[TimFox]

You mention "dissipate heat faster" in your question.  If the actual time dependence of the heat-sink temperature is important, you need to include the "thermal capacity" (in K/J) of the metal mass as well as its thermal resistance (K/W).
A calculator for thermal capacitance can be found at  https://www.omnicalculator.com/physics/specific-heat  .  The material constant required is the "specific heat", which is 897 J/(kg K) for aluminum.

[Benta]

The end-to-end calculation is junction-to-ambient-air temperature difference (unless you use liquid cooling, but we'll leave that out here).

For a heat sink. mass is much less interesting than the surface area where the heat can be transferred to ambient air. This explains the complex finned designs of the commercially avalable heat sinks. They do need a certain cross section to transport heat from the device to the fins, but surface area is the main point.
Vertical fins with free space above and below provide much better heat transfer to ambient air due to natural thermal airflow. Horizontal fins do not work as well. With forced airflow (=fan) this is unimportant.

Colour also plays a role. A black heat sink has better IR radiation than a metallic one and thus contributes a bit extra to heat transfer.

[davelectronic]

Thanks for your replies, this looks quite complicated. I generally use or repurpose heatsinks from other sources, IT computer heatsinks is a typical one that I re use in projects. I have used aluminium plate, but I think I've got a recent heatsink size wrong. Just a brief overview, I am cooling 6 X power transistors, a bridge rectifier, and an L7812 voltage regulator. The case of the PSU is two cases bolted together, in the lower half are the two transformers. And in the top half are all the silicon components and 4x capacitors. Although each half has an 80mm fan at the back the fans are on to often (thermal switch control) I selected a 40° C contacts normally open, closing on temperature rise. I didn't take the heat rising from the transformers when idle. At an ambient temperature of 25°C the internal of the upper half of the PSU reaches the threshold to turn the fans on. I know I can change the thermal switch to a higher temperature, but it would have been useful to know the thermal outcome before I assembled it. My other possible mistake is the heatsink itself.

Being a plate of aluminium 200mm X 100mm X 20mm, I thought the mass would stay cooler for longer. In practice I have a large thick heatsink that holds the heat a bit to well, once it warms up. So the fan air cooling takes ages to get it below 40° C. I now think I would have got better results in terms of cooling efficiency in half the thickness of the 20mm plate I used, and possibly less thick than that. It's difficult to work out cooling with heatsinks that have no thermal data. Although pc heatsinks have a figure quoted in watts it can disipate using the processor used in its original intended computer use. Certainly going to look at the link for the calculator you posted, thanks for that. On reflection of this PSU I mentioned above, with the aluminium plate heatsink above, I failed to factor in other processes of heat I completely overlooked, like the transformers in the bottom half of the PSU and heat rising from them. Picture for idea of explaining the case above.

[Just_another_Dave]

Thanks for your replies, this looks quite complicated. I generally use or repurpose heatsinks from other sources, IT computer heatsinks is a typical one that I re use in projects. I have used aluminium plate, but I think I've got a recent heatsink size wrong. Just a brief overview, I am cooling 6 X power transistors, a bridge rectifier, and an L7812 voltage regulator. The case of the PSU is two cases bolted together, in the lower half are the two transformers. And in the top half are all the silicon components and 4x capacitors. Although each half has an 80mm fan at the back the fans are on to often (thermal switch control) I selected a 40° C contacts normally open, closing on temperature rise. I didn't take the heat rising from the transformers when idle. At an ambient temperature of 25°C the internal of the upper half of the PSU reaches the threshold to turn the fans on. I know I can change the thermal switch to a higher temperature, but it would have been useful to know the thermal outcome before I assembled it. My other possible mistake is the heatsink itself.

Being a plate of aluminium 200mm X 100mm X 20mm, I thought the mass would stay cooler for longer. In practice I have a large thick heatsink that holds the heat a bit to well, once it warms up. So the fan air cooling takes ages to get it below 40° C. I now think I would have got better results in terms of cooling efficiency in half the thickness of the 20mm plate I used, and possibly less thick than that. It's difficult to work out cooling with heatsinks that have no thermal data. Although pc heatsinks have a figure quoted in watts it can disipate using the processor used in its original intended computer use. Certainly going to look at the link for the calculator you posted, thanks for that. On reflection of this PSU I mentioned above, with the aluminium plate heatsink above, I failed to factor in other processes of heat I completely overlooked, like the transformers in the bottom half of the PSU and heat rising from them. Picture for idea of explaining the case above.

40ºC is a pretty low temperature. Normally semiconductors can stand more than 100ºC

Using a copper heatsink or adding a layer of thermal paste between the heatsink and the mosfet should reduce the risk of damage due to overheating

[davelectronic]

I do use thermal compound on all components that require it. An example of a heatsink that I haven't used yet is below. It's for 6 X transistors again, but I wouldn't know where to start calculating it thermal abilities. Is an aluminium plate 200mm X 100mm X 6mm and 6 X additional approximately 40 mm X 40mm X 40mm heatsinks reclaimed from a few old thin client machines. These additional heatsink are solid aluminium. It's for a possible future project. But I couldn't tell you how hot it's likely to get, under a given power rating in watts from 6 X power transistors.

[Just_another_Dave]

I do use thermal compound on all components that require it. An example of a heatsink that I haven't used yet is below. It's for 6 X transistors again, but I wouldn't know where to start calculating it thermal abilities. Is an aluminium plate 200mm X 100mm X 6mm and 6 X additional approximately 40 mm X 40mm X 40mm heatsinks reclaimed from a few old thin client machines. These additional heatsink are solid aluminium. It's for a possible future project. But I couldn't tell you how hot it's likely to get, under a given power rating in watts from 6 X power transistors.

If you want to estimate it’s thermal resistance analytically, you could ignore the plate that connects all of them as, if the same amount of power losses is produced in all those mosfets (worst case), considering it to have a constant temperature across all the surface of the plate can be a good approximation. All in all, you will be analyzing a worse scenario, so the real temperature will be lower.

I think that the analytical equation for each of the “towers” screwed to the plate can be found in Incropera’s book

[davelectronic]

If I only took the aluminium plate into consideration, I think I'd be under estimating the full cooling ability of this aluminium combination. I can see the aluminium towers getting saturated with heat long before the plate get untouchable. Could be wrong though, I'd have though material weight might help in trying to calculate it thermal abilities, although it's more complicated due to the spacing between the towers. I expect in practice my multimeter thermal couple and some load tests will yield some off the cuff ideas of how much heat it can take in reality. I was hopeful for some equation that could work out thermal properties of heatsinks, but my maths isn't the best. I've never heard of that book, I will have to look it up. That heat sink, with an 80mm fan pulling air over it, I'm hopeful of getting 30 Amps at 12 Volts. But at a 50% duty cycle, not continuosly. That migh be to much expectation.

[Just_another_Dave]

If I only took the aluminium plate into consideration, I think I'd be under estimating the full cooling ability of this aluminium combination. I can see the aluminium towers getting saturated with heat long before the plate get untouchable. Could be wrong though, I'd have though material weight might help in trying to calculate it thermal abilities, although it's more complicated due to the spacing between the towers. I expect in practice my multimeter thermal couple and some load tests will yield some off the cuff ideas of how much heat it can take in reality. I was hopeful for some equation that could work out thermal properties of heatsinks, but my maths isn't the best. I've never heard of that book, I will have to look it up. That heat sink, with an 80mm fan pulling air over it, I'm hopeful of getting 30 Amps at 12 Volts. But at a 50% duty cycle, not continuosly. That migh be to much expectation.

Maybe I understood the photo wrong. Are you attaching the mosfets to the towers or to the plate?

[davelectronic]

I'm attaching the mosfets to each tower heatsink. The tapped for M3 thread.

[Just_another_Dave]

I'm attaching the mosfets to each tower heatsink. The tapped for M3 thread.

Sorry, I was thinking that they were attached to the plate. In any case, you can still simplify the system by ignoring the plate if it doesn’t reach a significant temperature in the worst case operating point (most of the heat will probably be dissipated by the towers as they have a larger surface).

If that’s not the case, you’ll need to find an analytical equation for estimating its thermal resistance (If I remember well, Incropera’s has one). By supposing that the surface that is in contact with the towers has a constant temperature (for an analytical model it is normally an acceptable assumption), you will be able to connect that resistance in series with the ones of the towers.

However, if you don’t want to do all that math, use a FEA simulator. Elmer and calculix are free and open source and both of them are able to solve thermal problems

[davelectronic]

Ok, yes I will look into this calculator. The towers are attached to the plate, should see the little excess thermal compound that I've not removed yet.