Basic thermal transfer calculations?

I'd like to understand some of the numbers behind thermal transfer a little better than my present "that epoxy is better" sort of mentality. I don't really expect to fill my head with what I should have studied for several years in college, but if I got to the point of being able to calculate some numbers, such as Arctic Silver epoxy theoretically resulting in an emitter running 3 degrees cooler than it would with Arctic Alumina epoxy (or whatever), I'd feel MUCH better off than I am now.

I see published specs for thermal characteristics of thermal compounds, heatsinks, and the like, but don't know what to do with them. I know some things I've seen are specified in terms of Watts per degree, but what do I do with that? Watts of heat? Is that at all equivalent to watts of electricity flowing through the component, or an entirely different animal? How can these specs be used in an intelligent manner?

I've danced around these things long enough. It's time to learn what it all REALLY means. /ubbthreads/images/graemlins/naughty.gif

Thermal calculations would be using Watts of heat which, for all practical purposes when using LEDs is pretty close to Watts of DC input power. In other words, most of the DC input power is converted to heat. (Fortunately, some does get converted to light, but most turns to heat!)

Heatsinks are typcially rated in degrees C/Watt, which specifies what the temperature rise (above ambient) of the heatsink will be per Watt of power. Thermal transfer compounds are the trickiest part and can be specified several ways. It'd helpful if you could post a link to the manufacturer's data sheet. One way is to specify their thermal resistance in degrees C - in^2/Watt, with a specified thickness. There are other common ways to specify it, too.

Basic? OK, heat (energy) moves from the hotter spot to the cooler spot. /ubbthreads/images/graemlins/wink.gif

Heat can move via conduction, convection, or radiation. Moving heat from a LA (incan or LED) through a heatsink and out to the flashlight body is usually through conduction (the heat moves from one area to another by 'flowing' through the different materials). Convection would occur by air flowing (fan, wind, etc) across the thing and the moving air then transfers the heat. Radiation is by the photons themselves moving energy. IR radiation is felt as 'heat' by us. The warmth of sunlight shining on your body is IR radiation of photons that travelled from the sun. Holding a HOLA horizontal and feeling the heat in the light beam a few inches away is IR photons as well. The heat from a fire (place, pit, bon, house-on, whatever) is also felt as IR radiation at a distance, directly above the flames is convection, and in the flames is conduction (mostly).

Every material has certain thermal characteristics, including resistance to thermal heat conduction (just like a resistor in an electrical circuit). Copper and aluminum both conduct heat pretty well (one reason why they are used for pots and pans /ubbthreads/images/graemlins/smile.gif BTW, copper's heat conductivity is about 50% better than aluminum, 300ish versus 200ish). Plastics usually don't conduct heat as well, that generally includes most adhesives.

But a thermal adhesive or paste conducts heat better than an air gap, so it is used between materials to help the heat flow from A to B via conduction.

See Arctic Silver Thermal Interface Basics for some pictures and discussion about "How and Why". Also see Thermal Measurement for some more discussion and a diagram of heat transfer shown as an electrical circuit.

Using some numbers from Artic Silver 5 thermal compound , they spec it as having a thermal conductance of >350,000W/m2 °C (0.001 inch layer). Which means that a layer of AS5 paste just 0.001 inch thick and one square meter in area would transfer more than 350,000 W of heat per degree C temperature difference between the two 'faces'.

Hello there,


Two different compounds will have two different
thermal resistances and therefore give two
different temperature rises.

After putting the thermal resistance specifications into
the form of formulae for two different compounds we end
up with the following two formulas:

For Artic Silver 5:
T_rise_AS = h*P*0.0045/A {in deg C}

For Artic Alumina:
T_rise_AA = h*P*0.01/A {in deg C}

where
h is thickness in thousandths of an inch
P is power in watts
A is contact area in square inches

Lets say you're running a 3 watt LS with a square heat sink contact
area measuring 3/4 inch on one side and we want to compare the
two materials above. The application thickness will be assumed
to be 0.005 inches thick.

We have:

P=3 watts
A=(3/4)*(3/4)=0.5625 square inches
assume h=0.005 inch thickness

[1]
Plugging these values into the formula for Artic Silver:

T_rise_AS=h*P*0.0045/A
T_rise_AS=5*3*0.0045/0.5625
T_rise_AS=0.12 deg C

[2]
Plugging these values into the formula for Artic Alumina:

T_rise_AA=h*P*0.01/A
T_rise_AA=5*3*0.01/0.5625
T_rise_AA=0.267 deg C

Comparing the two we can see the Artic Silver performs better
than twice as good as Artic Alumina, but at the low power level
of 3 watts it doesnt make much difference which one is used.
Even Artic Alumina doesnt cause much more then a quarter
of one degree C rise.


Take care,
Al

Never will I profess that I even remember much of thermo class. But I have a little bit of real world experience getting a bit of heat away from some LED's.

At work we designed an 1" diameter pcb that was stuffed almost completely full of Nichia surface mount LED's (48!). When this board was first powered up on the bench, after about 30 seconds it had become so hot that the solder holding the LEDs down started flowing. Thermally, not so good, eh? Worse yet, this would be enclosed when in actual use, with no chance of convective cooling.

In order to get the heat away from PCB, it took adding a layer of copper to the board design whose only purpose was to conduct heat to the outer edges of the board where the aluminum enclosure could act as a heat sink. Also we jammed the assembly full of this stuff:

http://www.bergquistcompany.com/tm_gap_pad_detail.cfm?
oid=104273

The above stuff, Bergquist Gap-Filler 2000, worked beyond our wildest expectations at helping to conduct the heat away from the pcb. It's non-electrically conducting, pourable, gap-filling and relatively easy to remove for repairs. Once it's cured it isn't messy or greasy at all. It takes on the consistency of an old pink eraser.

Our application also required a thermal transfer material that was electrically benign as there was also a ccd camera module immediately behind the led board. This worked for us.

The thermal conductivity on is listed as 2.0 W/m2-K. That sounds waaaaay off from the 35,000 number quoted on the Artic Silver spec sheet. Something doesn't compute in my old coconut (not much does anyhow!) I wonder what the difference is...

This isn't meant as a slam at the metalized epoxies, rather another alternative.

Ordin

Looks like the cut and paste of that link doesn't quite take you all the way to the product that I was talking about. Do a site search for Gap Filler 2000. That's the stuff.

Ordin

[ QUOTE ]
Ordin_Aryguy said:
Looks like the cut and paste of that link doesn't quite take you all the way to the product that I was talking about. Do a site search for Gap Filler 2000. That's the stuff.

Ordin

[/ QUOTE ]

Dude! The link works, it just got cutoff by the CPF board software. I pieced it together again, and it's over here. /ubbthreads/images/graemlins/grin.gif

All, thanks! This is good stuff. Mr. Al, your example in particular made a LOT of sense to me... somehow that post was the one that finally flipped the light switch in my dark skull, so to speak. /ubbthreads/images/graemlins/wink.gif

Hello again,

Milky:
Thanks

OrdGuy:
In some of the specs for GapFiller they are using
Kelvin, not degrees C. If you look at the graph they
give it makes more sense

The formula for the GapFill material is this:
T_rise_GF=h*P*0.02/A

Which makes it look only half as good as Artic Alumina,
but still not too bad i guess. This would give us
about 0.53 deg C rise with our 3 watt example in the previous
post.

Take care,
Al

I don't see any reference to the temperatures on either side of the filler materials in the formulas posted earlier. Do temps on either side of the junction influence anything? For example, if the heatsink is at a particularly cool temperature, as it might be when using a flashlight outdoors during the winter, will that speed heat transfer off the die? Intuitively, it seems like the greater the temperature differential on either side, the greater the rate of heat transfer. But my intuition very well might be wrong. How does the calculated 0.12 deg C fit into things in this regard?

Also, is there any way to understand where the temperatures might end up settling once reaching a steady state, or are the calculations for that sort of thing too complex? Or maybe the 0.12 deg C is the steady state relationship?

Hi there Milky,

Yes the 0.12 deg C is the 'final value' of the temperature
difference between surface 1 and surface 2.
This is almost always good enough information in heak sink
calculations.

Since 0.12 deg C is the temperature difference, that means
if surface 1 is 40 deg C then surface 2 is 40.12 deg C.
If surface 1 is 50 deg C, then surface 2 is 50.12 deg C.
Surface 2 might be the bottom of an LS, or the bottom
of a CPU chip or something else. Surface 1 might be
the heatsink surface, which is slightly cooler because
it looses heat to the atmosphere.

It makes a much bigger difference with higher power devices.
If we had a 30 watt device running we may see 1.2 deg C
across the layer of compound, and if a 300 watt device
12 deg C across the layer of compound, etc. Since in
this last case (300w) if we were instead using the Gap
Filler material we might see four times that, or 48 deg
C across the layer of material! This is where the
better stuff can really make a difference.

[Edited]

If you increase the heating power then there will be an
increase in temperature difference.


Take care,
Al

The actual temperatures don't matter much. The 0.12 degC is the temp rise across the interface. For example if the cold side is 0C, the hot side will be 0.12C. If the 'cold' side is 45C, the hot side will still be .12C hotter, or 45.12C.

Keep in mind that the 0.12C value is only a (small) part of the whole thermal system. It represents the temp rise from the LED mounting surface to the heatsink surface. The biggest rise will probably be the rise from the heatsink to the ambient air temp. And you have to add these two temp rise values together to get the whole story. You'll probably find tha the temp rise of the heatsink to the ambient will eclipse the rise across the Arctic Alumina or Artic Silver.

MrAl,

Is there anything you don't know!? You seem to be able to piece together a detailed response to every topic!

/ubbthreads/images/graemlins/bowdown.gif

-YC

yclo,
I'm with you... pretty smart egg we're dealing with here!

Mr. Al,
I missed the difference in units. Oops. The numbers make a little more sense this way. Thanks for pulling my head out of my butt. /ubbthreads/images/graemlins/thumbsup.gif

Ordin

yclo & OrdGuy,

Gee thanks

Is there anything i dont know? Well, i'd make a list
but it would take up too much time and space
Im always looking for answers to questions that havent
been asked yet.
Nature is such that the more questions you ask the
more answers you get, and the more answers you get
the more questions you ask...

I like to contribute to CPF by helping other members
with their circuits if possible. I like to see people
getting along with their circuits as much as possible

Take care,
Al

Hello again,

OrdGuy:
I guess a better description about the strange looking
spec they give in the GapFiller 2000 data sheet would
be not to mention Kelvin, but rather simply say that
in order to get thermal resistance the thermal
conductivity is first converted to thermal conductance,
then the reciprocal taken. Then area can be added
to get the same formula i stated previously.
I think that's the best way to look at it

Take care,
Al

Aahhh... Like Ohms and Mhos.

Reciprocals. The completion backwards principal.
/ubbthreads/images/graemlins/grin.gif

The Gap Filler stuff fit our needs as we did have some circuitry that was going to be potted with the stuff and part of the requirements was "do no harm." I'm afraid that metallized fillers probably wouldn't have met that spec.

Ordin