Calculating optimal heat dissipation

[cubusmedusa]

Hi,

during playing around with my setup and trying to find a good cooling solution for my VRMs I was going through the vast amount of different designs and materials available for cooling blocks.
My plan was instead of going for standard coolers that fit to the Mosfets and chokes I wanted to use the available area around the VRM modules to maximize the surface area for best possible heat dissipation. So I knew the base area of the cooling block and I knew that its pretty unlikely to find a single piece of block with the required dimenstions and shape for that spot. So I have to buy a block and cut it into shape.
The question was, which design will give me the largest surface area for my given base area that I can cover on my motherboard.
For a certain block u usually get the dimensions (mainly base area) and the thermal resistance for that specific block which is determined by the material, coating and its dimensions.
Ok. what if I have a 6x4cm with R(th) of 2 and a 15x10 with R(th) of 0.7 and and and. Which one has the largest overall surface area per unit base-area?

I made an excel sheet, entered the length and width (to calculate base area A) and R(th) of all the different products and calculated: 1/[R(th)*A] for each.

Of course it is not a 100% accurate result because the very limited amount of parameters required simplifications but it still works very nicely.
For example it sheds a new light on certain copper heat sink designs and their price compared to other materials and designs.
If you are interested in the rational behind the calculation just ask. Else, just use it and see the difference.

Chris

Edit: i apologize, my english is más o menos - instead of cooling block please read heat sink.

 

[peanutbudder]

Well it's not just the base you have to take into consideration but rather the total surface area of a heatsink in order to dissipate the maximum amount of heat. This is why you see heatsinks with fins because it allows for a greater surface area to dissipate the heat. The base has no direct affect on cooling because it is usually a solid piece. I have seen people take silver dollars and lap them to a mirror finish then braze copper fins to it. The results were amazing when compared to a solid piece of copper.

 

[cubusmedusa]

Hi,
I never claimed that base only determines the dissipation capabilities. I mentioned above that it is indeed the surface area (and of course the material itself) but when you are looking for a heat sink in the internet, what you get is length, width, height and R(th). From that is either impossible or very very tedious to calculate the surface area. So my question was whether it is possible to get a reliable measure for heat dissipation capabilities by knowing only the base and R(t). And this is the mentioned formula.

 

[cubusmedusa]

The idea behind:
We have length and width for the base area and R(th).
The unknown surface area (S) can be seen as the base area (A) multiplied by a factor (b) that is determined by the features of the heat sink. --> total surface area S=A*b
this factor b increases the surface. If its 1 then its a featureless plate and if its 10, the surface is ten times larger then the base.

Thermal resistance and surface area are reciprocal to each other. meaning that if surface is larger, resistance is small. Simplified: R=1/S=1/A*b --> b=1/(R*A)
By calculating b I know how much larger the surface area is than my base area (this is a simplified view but sufficient for our purposes). This equals to the ratio of S/A which is perfect because we normalize the surface area to a unit base area thus making it fully comparable to other heat sinks with different sizes, features and materials.

One more thing to explain: if you calculate for aluminum and copper sinks you will see huge differences which cannot be explained by surface area only. The reason is the simplification that migrated lambda (material constant) into b. (see the formula for thermal resistance) So b is actually the product of the mentioned multiplier and lambda. In that sense a "b" of 1000 is not gonna tell you that surface area is 1000 times larger than base area for that given sink but it is the product of x-times larger surface than base multiplied by the material constant (for copper, aluminum, silver,...) thus creating an "artifical surface area" that is comparable to other heat sinks even with other materials and features.
If a certain aluminum sink gives you 100 per unit base and a copper sink gives you 1000 per unit base, then you know that the combination of better surface features AND lower thermal resistance of copper will result in 10 times better heat dissipation or in other words: the copper sink can be also seen as an "artificial" aluminum heat sink with 10 times larger surface area.

 

[cubusmedusa]

coming back to the cooling issue; if I want to cover an area of say 4x6cm on my mobo which combination of material and surface features will give me the best possible heat dissipation (per unit area). This is what you should get out of this. No surprise that copper is better than aluminum. But you might want to know how much better it is (for a given product you can buy) and whether its worth the price or better go for a cheaper aluminum sink that might have better surface features and thus giving similar/sufficient dissipation capabilities...

Edit:
I forgot to mention that I would be glad if somebody could double check if the approach is consistent. You never know...

 

[bob4933]

edit: the scope of this is limited to the OP's desire for mosfet cooling, with air or ambient cooling only.

Sorry, but your logic is pretty flawed here.

For starters, if you made an completely solid copper heatsink with no external cooling, you will destroy your motherboard. Why? Specific heat capacity of copper is pretty poor. This means it heats up fast, and although the heat transfer coefficient of copper is extremely high, air does not. If you are using copper only, you will get a phenomenon known as "heat soaking". This is where your heat input exceeds your heat output. With just copper and no water cooling solution or other material to draw the heat off of it, you will keep your mosfet cool for a little while, but as it stays hot, your copper piece will get hotter and hotter.

Theres a very specific reason why mosfet coolers are aluminum. replacing them with only copper is a bad idea.

The best solution is to either include an active cooling solution (i.e. a water block), or adding aluminum on top to help dissipate the heat well. More to this game then just "which material conducts heat the best". Also, copper can not be extruded easily, which means copper finned blocks would be far more expensive.


If I had to guess, Id say you are 2nd or 3rd year engineering student?

 

[cubusmedusa]

Hi Bob,

what you say in your edit is not correct. My approach is not limited to mosfet cooling and I never ever mentioned that I aim at ambient cooling nor to suggest somebody to do ambient cooling!
I am well aware of the need to do air cooling irrespective of the sink-material used. But that was not the purpose of my thread anyway.
As I said, seeking for a good heat sink I ran into the "real world" problem that its actually not easy to decide which heat sink design will give the best performance PER base area (which is always the limiting factor, regardless whether we are talking about a CPU, Mosfets, GPU, etc.)
I was brainstorming and came to that formula and thought this could be an easy tool to help finding the right heat sink. How the people are transporting the heat away from the sink was not in the scope of my writing.
Lets call it "A how-to to find the best heat sink for your purposes"
Of course the performance of a heat sink is dependent of the air flow and will improve with higher airflows but these are all extra-parameters not so relevant for this comparative approach.
Actually I wanted to suggest somebody to try the math and have a look whether there is something severly wrong.

But thanks for the compliment. No I am not a student and its not homework.
Actuall I have nothing to do with engineering and was just trying to find a solution for my problem.

 

[EarthDog]

The board didn't come with sinks on the vrm? Otherwise, just buy them, they make kits. Maybe you like the mental exercise, and that is awesome, but, buy em.. no need to make em, orcimprove upon what is there. I use extreme.cooling methods and speeds not achievable on air or water and leave the stock ones on.

 

[bob4933]

I know what you're saying, but you're limiting your entire scope to simply thermal conductivity. While its true that copper has a much higher thermal conductivity then aluminum, it has a much lower specific heat. Without taking specific heat into consideration, performance will be compromised.

Air is a **** poor coolant medium with an incredibly low specific heat. It would not be enough to cool off a copper heatsink alone. All the thermal conductivity in the world means nothing if you can't get rid of said heat. The only way a copper only heatsink becomes viable in this application is if you either attach aluminum fins or you are using water cooling.

edit: while this is a noble mental exercise, there's 0% feasibility in any of this anyway. There is no way you can simply "make" anything like this anyway with out advanced CAD and CNC capabilities (Read: $$$$).

How the people are transporting the heat away from the sink was not in the scope of my writing.


Of course the performance of a heat sink is dependent of the air flow and will improve with higher airflows but these are all extra-parameters not so relevant for this comparative approach.

These "extra-parameters" are ENTIRELY relevant. What you're suggesting simply will not work in any fashion, much less "real world" scenarios. Guess what happens to the block over time? It heats up. If you can't get rid of the heat from the heat sink, guess what? The heat sink stops being a heat sink once they reach an equilibrium point (heat soaking). Once heat soaked, your heat sink is now a shiny piece of copper doing absolutely nothing.

 

[cubusmedusa]

@EarthDog
no sinks on the VRMs on this board. Unfortunately. And no holes to fix a kit. Only way is to use thermal adhesive and glue the block onto the thingis I want to cool. Thats the challenge. I know, buying another mobo is adviced. It would be too easy with a dedicated board. ;-)

@Bob
I understand what you are trying to tell me but I try to convince you that you are misunderstanding something in my aim.
Lets say you want to cool something on your mobo that gives you 6x4cm of space and therefore you are looking for heatsinks. Because however you cool (passive, water, aktive,...) you need something that transports the heat away from the primary heat source and dissipates it to the medium you use. (air stream, water,...) You find lets say 3 shops offering a 100 different heat sinks of different size, shape, surface features, materials and price (this was the situation I had). How the hell are you going to decide which sink will give you the best possible heat transfer away from the heat source to the medium for the given base area you can use on your mobo? You would need to know the total surface area of each sink and relate it to the base area of the sink which is not possible because you are lacking info about the surface area.
What I wanted to provide is an easy calculation to find the right heat sink in the shop. I thought this could help because it helped me a lot.

I know that air has low specific heat which is the reason why a 5400rpm 120mm fan blows 250m³/h onto my heat sinks - just for the fun of it. I know that you need that or water which has a far better specific heat than air. What I wanted to state is that what you are choosing to transport the heat away from the heat sink is a problem thats downstream of what my initial post refers to. I just wanted to help find a heat sink in the shop. And as I said, for me it worked just fine.