Puzzling Heat Transfer Problem

[Tunalover]

I have an electronics box coated with a thick layer of a poorly-conductive substance. An external heater applies a flux Q'' to the box. I need to obtain the temperature rise as a function of time knowing the specific heats of the substance and box, the thermal conductivities of the substance and box, and the densities of the substance and box. The electronics box has an internal heat generation of Q. There is no way of cooling the box. Once it reaches a certain time it has accomplished its mission and is sacrificial. It is safe to assume the box is of uniform temperature because it has a lot of aluminum in it. I need to determine the temperature at a given time t. Any takers want to tackle this one? The heat flux is not trivial. It's 11,500W/m2.



Bruce aka Tunalover

 

[IRstuff]

Depends on how accurate you want the solution to be. At the minimum, you can bound the solution, somewhat, by assuming a gross lumped mass where the specific heat of the box innards is located away from the external source by the thermal conductivity. Note, however, your description allows for a sizable heat loss to the ambient. A lumpier mass solution might to the trick, i.e., something with a few layers of specific heats and thermal conductivities.

TTFN

FAQ731-376

 

[zekeman]

This sounds like an academic problem, since heat "flux" to a container can't be uniform and you don't state the nature of the the internal heat source nor the target temperature you are seeking.

A little more information including the insulation layer material would be needed to steer you.

 

[Tunalover]

zekeman-
This is not an academic problem. A lumped mass solution would be fine but I'm not sure how to take into account the insulating layer. I'm doing a transient FEA but the solution reaches levels that were not predicted by an earlier FEA solution. I'm trying to do a sanity check calculation. As for the insulating layer, it is by design a very poor conductor and coats the entire box. The heat flux comes from one direction normal to one surface so I can assume that 100% of the normal surface see the flux while the side surfaces see 50%. I know all the properties and the thickness of the insulation.
It sounds like IRStuff is onto something. How about some details IRStuff? I haven't been able to find someone at work who can set up a simple nodal analysis. It's probably almost trivially simple but I just can't put my finger on it.
Thanks for the feedback guys!



Bruce aka Tunalover

 

[electricpete]

IRstuff I'm sure can do much better than me.

It sounds like the problem described in original post allowed some pretty good simplification (one thermal mass at uniform temperature). With the internal heat source specified as energy per time rather than temperature, I'm not sure what would be the role of thermal resistance mentioned by IRStuff. To my thinking the internal heat source plays identical role to external heat flux integrated over area and we can simply add them.
Qin(watts/sec) = InternalHeatGeneration(watts/sec) + ExternalHeatFlux(watts/m^2/sec)*Area(m^2)


d/dt(T) = (1/Cth) * (Qin - Qout)

The only tricky part seems to be Qout. If you can formulate an expression for Qout in terms of box temperature, it is a very simple calculation to solve numerically using any ODE solver (it is basically an integration of d/dt(T) starting from initial condition T0).

That's my take fwiw. Maybe I'm missing something... and still requires some work to define Qout

=====================================
(2B)+(2B)' ?

 

[IRstuff]

Dynamic problems are almost never trivial. Some particulars might be useful. If you have a heat source surrounded by a good insulator, then you would expect a massively high internal temperatures. One might wonder why an external heater is even needed.

I don't have any particularly good examples, since we (our MEs) do most of our transient analyses in CINDA. And CINDA's pretty crude as models go, since it's typical to use just lumped thermal resistances and capacities in a network.

TTFN

FAQ731-376

 

[zekeman]

"d/dt(T) = (1/Cth) * (Qin - Qout)"

The problem with this solution may be at least 2 fold
!) a single thermal mass is assumed
2) according to the OP assumption there is no Qout

I would guess at a minimum you need 2 masses, the outside walls and the inside mass that is heated internally. But that is still a "guess".

So you see when a poster presents a problem he/she must not give any of his/her "simplifications" or simplifying assumptions since they almost always lead to a wrong analysis.
When asked about the insulator thermal properties he answers that it a good insulator.When he says flux to one side and starts with 100% and 50% distributions, what about the other surfaces that may be rejecting heat to ambient.Where are the boundaries?
Further, he wants a temperature time solution but where?
On the internal mass(es) that has a heat generator,on an adjacent mass, in the internal air, on the container wall? Moreover he does not say what accuracy he needs for the times to reach the critical temperature.
Are we mind readers?

I think giving an "answer" or direction to such reticent posters is an exercise in futility.

My advice to posters who want meaningful answers is to give us ALL of the information you have with NO assumptions on their part. Otherwise, some well meaning people will give less than useful help.

 

[davefitz]

The input heat flux Q'', if provided by a temperature source radiating to the box at a much higher temperature, would be considered to be a known , fixed heat flux. If the heat input device is any other type of source, then it would not be known fixed value and its net heat flux to the box would vary in time based on the intantaneous temp of the box's surface temp.

The box with its outside insulating surface coating , could be modeled with a finite element program, the geomentry and physical paramters suitably input. The issue with such models is stability of the solution, which is a function of the integration schem selected , the size fo teh mesh , and the time step selected. As I recall, one method of confirming convergence of solution is to integrate it twice, the second integration with a time step 1/2 the size of teh first solution. If the answer did not change appreciably, then the corect time step was selected.

 

[Tunalover]

Folks-
The electronics box is mounted to a rocket. Before mounting, the entire box is molded into an RTV-like material to protect it from the thermal plume from the rocket engine. There is no conduction path between the rocket and the box and natural convection is a trivial help when it does exist (once it leaves the atmosphere there is no air for any kind of forced or natural convection cooling). The only cooling is by radiation but I want to simplify the problem so that I can get a handcalculation solution. Note that the dT through the insulation is not the same as the dT the box experiences over time.


Bruce aka Tunalover

 

[Twoballcane]

Hmmm...I think your working to hard. Try delta t = Q/C where delta t is degF/hour, Q is btu/hr due to radiation, and C=WCp where W is the weight of the unit and Cp is the specific heat of the unit (which you said most of it is aluminum). This will give you the temp rise of the unit per hour.

Tobalcane
"If you avoid failure, you also avoid success."

 

[zekeman]

"Hmmm...I think your working to hard. Try delta t = Q/C where delta t is degF/hour, Q is btu/hr due to radiation, and C=WCp where W is the weight of the unit and Cp is the specific heat of the unit (which you said most of it is aluminum). This will give you the temp rise of the unit per hour."

So you are telling him that insulating the thing is a waste of time! I don't think so, but you are technically right in view of the OP assumptions.

 

[Twoballcane]

Nope, I meant that trying to go from a simple problem to a more complicated ideology. This is not an adiabatic problem. We have the mass of the box, should be able to find the specific heat of the material used, thus you should be able to find the thermal capacitance. Divide Q by the thermal capacitance and you will get degF/hour. Once you know degF/hour, we can figure out at what time interval you will hit your max temp.

Tobalcane
"If you avoid failure, you also avoid success."

 

[zekeman]

Then explain where all his effort on insulating it shows up in your equation.

 

[IRstuff]

Just a general observation about the insulation; insulation works both ways, while keeping the external heat out, it also keeps the internal heat in. And since insulation, by definition, means letting less heat out than what is being generated, the electronics within the box will get pretty toasty lickety split.

One possible option is to have a layer of phase change material (PCM) to absorb some of the electronics heat. That's sometimes done in missile electronics. Alternately, some systems have a coolant resevoir to draw on.

TTFN

FAQ731-376

 

[zekeman]

Yes, but for this problem with overwhelming external heat, more insulation is better, and in fact, why not ablation type on the outside.

 

[davefitz]

In radiation dominated heat transfer( espescially in spacecraft applications), one common solution is to use an engineered coating on the surface facing the heat source.

If you want to minimize the heat absorbed or minimize the temperature of the composite body, you can select a surface coating that has very low absorptivity for the wavelengths that dominate the source body, yet also provide high emissivity for the weavelengths that dominate the selected max permitted temperature of the composite body.

 

[Twoballcane]

If there is enough insulation where you can assume adiabatic, then Q is simply the power used in the box.

Tobalcane
"If you avoid failure, you also avoid success."