Physics Help Forum Real World Thermodynamics Question

 May 26th 2016, 11:59 AM #1 Junior Member   Join Date: May 2016 Posts: 2 Real World Thermodynamics Question So forgive me if this isn't the typical question fielded here, but I have a practical application question concerning thermodynamics. Say you have 9 electronic devices that have a maximum, constant heat output of 110°F in an enclosed space that's roughly 11'x4' canister with no airflow. Each device is about 3'x1'x1' and they are stacking in a triangle configuration one set of 3 on top of the other, vertically. The ambient air temperature around and inside the canister is 95°F. In that scenario, is it a possibility for the ambient air temperature with all 9 devices outputting at 110° to climb as high as 300°, or will the canister reach an equilibrium temperature near 110°? Again, I don't have much experience in this matter, but I'm hoping from some guidance from some subject matter experts. Thank you!
 May 27th 2016, 06:45 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,324 You need to be more specific about the heat output of the devices. That heat output is measured in watts, not degrees F. Now, it may be that the surface temperature of the device is 110F when operating on its own. But the problem as stated, which says they are a constant 110 degrees, implies that the devices have some sort of temperature regulation system that keeps them at no more than 110. If that was the case then the max temp of the enclosure would also be 110. So I suspect what you meant is this: if the devices have a surface temp of 110 degrees when operating in open air with ambient temp of xxF, can we draw any conclusions about the max temperature inside an enclosure with ambient temp of 95F if nine of these devices are operating simultaneously? The answer is no, because we don't know (a) the manner of construction or insulation of the enclosure, or (b) the heat produced by each of the 9 devices, measured in watts. But we can say this: if the enclosure is well insulated, and if the devices put out a constant amount of heat energy of X watts, then the temp inside the enclosure could rise to virtually any value.
May 27th 2016, 12:12 PM   #3
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Join Date: May 2016
Posts: 2
 Originally Posted by ChipB You need to be more specific about the heat output of the devices. That heat output is measured in watts, not degrees F. Now, it may be that the surface temperature of the device is 110F when operating on its own. But the problem as stated, which says they are a constant 110 degrees, implies that the devices have some sort of temperature regulation system that keeps them at no more than 110. If that was the case then the max temp of the enclosure would also be 110. So I suspect what you meant is this: if the devices have a surface temp of 110 degrees when operating in open air with ambient temp of xxF, can we draw any conclusions about the max temperature inside an enclosure with ambient temp of 95F if nine of these devices are operating simultaneously? The answer is no, because we don't know (a) the manner of construction or insulation of the enclosure, or (b) the heat produced by each of the 9 devices, measured in watts. But we can say this: if the enclosure is well insulated, and if the devices put out a constant amount of heat energy of X watts, then the temp inside the enclosure could rise to virtually any value.
Thanks for the reply, to provide better detail to your two points:

(a) 3/8" galvanized steel enclosure
(b) 100w total power output per device

 May 28th 2016, 08:27 AM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,324 This helps, but we need one more piece of information: what is the surface area of the enclosure? To answer your question we can use Fourier's Law of Conductive Heat Transfer which describes the rate of heat flow through a material that has steady temperatures on either side: Rate of Heat flow = k(A/d) Delta T Where k is the coefficient of conductivity for the material, A is the surface area of the material, d is its thickness, and Delta T is the difference in temperature between the two sides of the material. In this case in the steady state condition we know the rate of heat flow is 900 watts. The value for k for steel is about 40 W/m-K. Given dimensions A and L (in meters) you can calculate Delta T in K (which is the same as degrees C). I suggest you run the calculation and post back with what you get. You will probably find that Delta T is not very large, because this assumes that the surface temp of the enclosure is equal to ambient. This is valid only if there is some method of cooling, like externsl fans, to ensure that heat is efficiently carried away. Otherwise the surface temp of the enclosure will become significantly greater than ambient, and a more complex analysis involving a calculation of convective cooling from the surface of the enclosure is required. Last edited by ChipB; May 28th 2016 at 11:59 AM.

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