Thermal design: my C/W of my heat sink needs to be negative #?

[strantor]

Ok, So I'm calculating what size heat sink I will need. I got the formula here.
**broken link removed**
Where

Tj = Maximum semiconductor junction temperature
θjc = Thermal resistance, junction to case.
Tc = Case temperature
θcs = Thermal resistance, case to heatsink (see Hot Tips)
Ts = Heatsink temperature
θsa = Thermal resistance, heatsink to ambient.
Ta = Ambient temperature

values:
Tj = 120C
Ta = 50C
Q = 216W
θjc = .402
θcs = .25 (conservative estimate, based on seeing 1C/W when no thermal paste used, and seeing .09 when good thermal paste used)

I get
-0.328C/W

Does that mean I did something wrong, or that I need to pump liquid nitrogen through my heat sink (or would water suffice?), or that what I want is impossible?

 

[alec_t]

I always thought thermal resistances were additive. Are you sure the - sign in the formula is correct? IMHO it should be a + sign.

 

[JimB]

Your mathematics seem to be correct.
Which means that you seem to be trying to do the impossible.
A negative thermal resistance seems to bust a few of the laws of thermodynamics, at least for a passive device like a heatsink.

Trying to dissipate 216watts in one device seems a bit extreame, what are you trying to do?

JimB

 

[JimB]

I always thought thermal resistances were additive.

They are.

Are you sure the - sign in the formula is correct? IMHO it should be a + sign.

That was one of my first thoughts, but when the equation is manipulated to give θsa, the negative sign comes in and is quite correct.

JimB

 

[strantor]

Your mathematics seem to be correct.
Which means that you seem to be trying to do the impossible.
A negative thermal resistance seems to bust a few of the laws of thermodynamics, at least for a passive device like a heatsink.

Trying to dissipate 216watts in one device seems a bit extreame, what are you trying to do?

JimB

first off, my math resulting in 216W was wrong. it's 113W, but 113W still have me a negative number. I've been pushing numbers around for the past 3 hrs and decided to double my #of FET (from 3 dissipating 113W each to 6 dissipating 56W each) which gives me .768C/w needed for a heat sink. I found a suitable heat sink which, if I put 600CFM through it will get me down to .44C/W (with buffer room).
I'm trying to design a 17KW brushed motor controller

 

[alec_t]

when the equation is manipulated to give θsa, the negative sign comes in and is quite correct.

Doh! Brain not in gear (situation normal then!)

 

[strantor]

Holy Schnikeys! a 600CFM fan is huge! much too huge. back to the drawing board...

 

[audioguru]

113W is huge.
A 2N3055 transistor chip dissipating 115W is close at its absolute max temperature of 200 degrees C when its case is cooled to 25 degrees C somehow.
A huge heatsink and a fan are not enough. A huge heatsink with circulating cooled fluid might work.

 

[strantor]

Thanks; I'm leaning towards increasing my # of FETs to get the dissipation down, but then I encounter other problems, like getting them to switch at the same time.

 

[Mr RB]

6 FETs dissipating 56W each?

A cheap garden variety 60volt 50amp TO220 FET will have Rdson of about 20 milliohms, and at a sensible 20A operating current will dissipate I2R = 20*20*0.020 = 8 watts per FET!

6 of those FETs will allow 120A load current at maybe 48v PSU voltage, so that's close to 6kW motor power. And 6kW is PLENTY to run your electric go cart unless of course you decided to enter it in the land speed records.

How did you work out 56W per FET?

 

[strantor]

6 FETs dissipating 56W each?

A cheap garden variety 60volt 50amp TO220 FET will have Rdson of about 20 milliohms, and at a sensible 20A operating current will dissipate I2R = 20*20*0.020 = 8 watts per FET!

6 of those FETs will allow 120A load current at maybe 48v PSU voltage, so that's close to 6kW motor power. And 6kW is PLENTY to run your electric go cart unless of course you decided to enter it in the land speed records.

How did you work out 56W per FET?

OK, I had made an error in my math:
I originally figured that for 3 MOSFETs in parallel, I would dissipate 113W each, and that was too much, so I did proportions from there to find the wattage dissipation for 4 FETs (84W), 5 FETs(67W), 6 FETS (56W). But it doesn't work proportionally like that. You need to do all the calculations for each combination of FETs, which comes out to 4FETs (63W), 5 FETs (40W), and 6 FETs (28W).

6KW may seem like a lot, but I've been looking at what other guys are using, and how much KW it actually takes to get any decent performance, and 6KW is not very much. I think it would be a lumbering pig at 6KW. My motor is rated 48V @ 100A continuous, and 300A for 10 minutes. That's 6hp/ 18hp peak. And I want my controller to be able to put out the full 14KW. for reference, these are 27KW go carts (I talked to the guy who built them) https://www.youtube.com/watch?v=YazSVi36_X8
and they are a lot lighter than mine is going to be.

EDIT: from the horse's mouth, regarding the go carts in the video:

Electric karts are fun. Or at least semi-fun, as the ones we built a few months ago only have been used a handful of times since building them. lol

For a point of reference, we used Perm132 motors, 60v batteries, and 450amp controllers. It made for a mild, but pleasing powertrain for the karts.