Blindasabat
Flashlight Enthusiast
So I'm sketching up some new lights and wondering "How big of a heat sink do I need?" I have a given diameter, but how thick will it need to be?
So I do some comparison calculations to see the difference between 5mm thick and 3mm thick heatsinks made from aluminum.
The results were enlightening.
Ideally, the following calculations should be solved simultaneously, but I didn't want to do that if I didn't need to (I've forgotten more math then I ever knew) so I decided to see if the results warranted it first.
I first did the steady state convection equations with the assumption that the body would add some area over the sink area alone to convective heat transfer. My old Heat Transfer book from college said that convection coefficient to air was from 5-30 Watts/square meter-C. Since it used 5 for a coal powder example, I picked 20 for nearly ideal aluminum condition. I also assumed 0.6W total power dissipated into the aluminum sink (divided by two as I calculated it in halves below).
Convection
Temp at surface = T(air) + (W/m^2 energy flow)/h
h = convection coefficient = 12W/m^2 * C
Energy flow for HALF the cylindrical sink = 0.3W power / (10mm x 40mm convectin area on the surface of the body) = 0.3W/(400mm^2) = 0.3W/(.0004m^2) = 750W/m^2
Ts = 20C + (750W/m2) / (12W/m2-C) = 82.5 deg C (181 F)
Conduction inside Sink
Flux for half the sink = 0.3W/(5mm x 15mm) = 0.3W/0.000075m^2 = 4000W/m^2
for Auminum k = 167 W/m-C, Q= heat flux, L = length heat travels to outside surface, A= sink cross section area (estimated for my round sink)
T at center = T outside + (QL/kA) = 82.5C + (0.3W * 0.013m) / (167W/m-C * 0.000075m^2) = 82.8 deg C
The slight temperature rise across the sink means that the sink is doing a spectacular job of conducting the heat. and that I am close enough that I don't need to solve the Convection and Conduction equations simultaneously. The result shows that convection on the outside (this is for a headlight) is extremely important and needs to be minded.
I redid the above calculations for a 3mm sink and the results were 109.3 deg C (229 F)outside surface and 109.8 deg C at center of heat sink. I assumed less casing area for heat dissipation as the sink contacts less case area which made the entire difference as the small temp difference across the sink again shows. But this convection area may not really be the case, and the thinner sink may work just about as well in the same size outer housing.
Some conclusions :
1) A thin sink will do almost as well as a thick sink - especially if it is still as thick at contact to the outside body.
2) A large, good contact from sink to housing is critical for keeping the sink cool.
2) The insignificant temperature drop across the sink (0.1 deg C) shows that Aluminum is as good as Copper, just lighter.
Commentary:
A hot outside housing may mean you have good heat sinking or that your emitter is very hot from small heat transfer area. A cooler housing may mean your heat is trapped inside, or that the sink is well connected to the body and the body is also highly thermally conductive. A small hot area on the outside means the sink is only conducting in a small area and the body is not highly thermally conductive. Some aluminums are better than others for thermal conductivity.
If anyone sees error in my assumptions or calculations, please let me know! I may be way high on the amount of power dissipated.
<edit> asdalton found an error in my sink diameter, which I corrected above. It was 0.0013m (1.3mm!?) now corrected to 0.013m (13mm). The temperature drop from center to outside (in my non-cylindrical approximation) is now 0.52 deg C. Still small, but pointing to larger overall error in approximation. Of course, my approximate power consumption may be a bigger factor. I think it is high, but if anyone has data, let me know!
<edit #2> I updated power to 0.6W total & 0.3W per side as I calculated it in halves.
I also updated the convection coeff to 12 W/sq meter * deg C
So I do some comparison calculations to see the difference between 5mm thick and 3mm thick heatsinks made from aluminum.
The results were enlightening.
Ideally, the following calculations should be solved simultaneously, but I didn't want to do that if I didn't need to (I've forgotten more math then I ever knew) so I decided to see if the results warranted it first.
I first did the steady state convection equations with the assumption that the body would add some area over the sink area alone to convective heat transfer. My old Heat Transfer book from college said that convection coefficient to air was from 5-30 Watts/square meter-C. Since it used 5 for a coal powder example, I picked 20 for nearly ideal aluminum condition. I also assumed 0.6W total power dissipated into the aluminum sink (divided by two as I calculated it in halves below).
Convection
Temp at surface = T(air) + (W/m^2 energy flow)/h
h = convection coefficient = 12W/m^2 * C
Energy flow for HALF the cylindrical sink = 0.3W power / (10mm x 40mm convectin area on the surface of the body) = 0.3W/(400mm^2) = 0.3W/(.0004m^2) = 750W/m^2
Ts = 20C + (750W/m2) / (12W/m2-C) = 82.5 deg C (181 F)
Conduction inside Sink
Flux for half the sink = 0.3W/(5mm x 15mm) = 0.3W/0.000075m^2 = 4000W/m^2
for Auminum k = 167 W/m-C, Q= heat flux, L = length heat travels to outside surface, A= sink cross section area (estimated for my round sink)
T at center = T outside + (QL/kA) = 82.5C + (0.3W * 0.013m) / (167W/m-C * 0.000075m^2) = 82.8 deg C
The slight temperature rise across the sink means that the sink is doing a spectacular job of conducting the heat. and that I am close enough that I don't need to solve the Convection and Conduction equations simultaneously. The result shows that convection on the outside (this is for a headlight) is extremely important and needs to be minded.
I redid the above calculations for a 3mm sink and the results were 109.3 deg C (229 F)outside surface and 109.8 deg C at center of heat sink. I assumed less casing area for heat dissipation as the sink contacts less case area which made the entire difference as the small temp difference across the sink again shows. But this convection area may not really be the case, and the thinner sink may work just about as well in the same size outer housing.
Some conclusions :
1) A thin sink will do almost as well as a thick sink - especially if it is still as thick at contact to the outside body.
2) A large, good contact from sink to housing is critical for keeping the sink cool.
2) The insignificant temperature drop across the sink (0.1 deg C) shows that Aluminum is as good as Copper, just lighter.
Commentary:
A hot outside housing may mean you have good heat sinking or that your emitter is very hot from small heat transfer area. A cooler housing may mean your heat is trapped inside, or that the sink is well connected to the body and the body is also highly thermally conductive. A small hot area on the outside means the sink is only conducting in a small area and the body is not highly thermally conductive. Some aluminums are better than others for thermal conductivity.
If anyone sees error in my assumptions or calculations, please let me know! I may be way high on the amount of power dissipated.
<edit> asdalton found an error in my sink diameter, which I corrected above. It was 0.0013m (1.3mm!?) now corrected to 0.013m (13mm). The temperature drop from center to outside (in my non-cylindrical approximation) is now 0.52 deg C. Still small, but pointing to larger overall error in approximation. Of course, my approximate power consumption may be a bigger factor. I think it is high, but if anyone has data, let me know!
<edit #2> I updated power to 0.6W total & 0.3W per side as I calculated it in halves.
I also updated the convection coeff to 12 W/sq meter * deg C
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