Need Help w/ Transient Conduction Problem

[julchak]

Hi everyone,
I'm a newly registered member here but have been onlooking for awhile now. Stuck on what I feel like should be an easy problem...but can't waste any more time trying different methods and need some guidance.

I am currently designing an electronics enclosure which I am trying to have maintain a near room level temperature for as long as possible in a freezer. My ambient air is moving, so I have forced convection. I will have a sturdy outer panel for the enclosure along with foam insulation on the inside.

I've been working on the calculations to determine the time it will take for the inside surface of the outer panel's wall to reach ambient temperature, and then to determine how long it will take for the insulation layer to conduct and have IT's inside surface equal the ambient temperature.

I used Lumped Capacitance for the first calc - found the convection coefficient for the problem by solving for Re and then Nu - my Bi let me use Lumped Capacitance for an aluminum panel. When I ran the calc's for a Delrin panel my Bi was > .1 so I used the approximation method, getting the coefficients from a table, solving for Fo and then solving for my time.

I believe that was correct, and the results seem realistic.

When it comes to the conduction through the insulation I am running into issues. I do not have any convection going on at this point, it is simply a constant temperature boundary condition on the outside of the insulation. Ts=Tamb (surface=ambient). I can't remember a way to use anything with an h value in it for this calculation (don't think you do/can), so I've been looking at transient conduction with an infinite solid.

I've tried the following:
1) Transient conduction through infinite solid (like soil)
2) Transient conduction through infinite solid of a cuboidal shape w/ constant surface temp
3) Transient conduction through infinite solid of a plane wall w/ constant surface temp


I figured #3 would be easiest and give me an approximate answer, but the answer does not seem realistic.
I realized that the cuboidal shape was probably not the correct choice and instead tried a plane wall.

When I try #2 and #3 I seem to get stuck and can't get answers that make sense. Here's the process I've been trying for that calc:
1) use the approximate solution for q* (dimensionless conduction heat rate) for when Fo >=0.2 with the interior case of a plane wall(since it should be enough time to satisfy this): 2exp(-Z^2*Fo), where Z=PI/2
2) I figured I wanted to solve for the time in Fo, where Fo= alpha*t/Lc^2
3) Saw that q* can also equal: Qs"*Lc/k*(Ts-Ti), where Qs" is the surface heat flux, and tried to solve for Qs" with it equaling k(Ts-Ti)/sqrt(pi*alpha*t) - this led to bad numbers. Then I thought, maybeI want to find when q* equals the steady state qss*

Should I set my equation for q* equal to zero since it approaches 0? Do I use something else?

I could keep going on with what else I've tried but there's no sense as none of it has worked. I'm kind of lost at what to do....any help?

 

[julchak]

Realized how long that was...the short version...

I am insulating a box which is in forced convection at -100 F. It has a Delrin panel on the outside and foam insulation on the inside.

I'm trying to find out how long it will take for the initially room temp (68 F) inside wall of the insulation to reach -100 F.

I've been working with transient conduction and lumped capacitance/approximation method to determine the time for the inner wall of the Delrin panel to reach -100 F but am stuck at choosing the correct method to determine the time it will take to go through the insulation.

I believe it would be some sort of transient conduction through a plane wall of thickness 2L with a constant temperature boundary condition on the outer wall of the insulation.

How would you do this?

 

[EnergyMix]

julchak

Transient conditions are almost always difficult to solve. The "easiest" way often is through direct observation: hooking up some instrumentation and measuring the length of time and adjusting as needed. Also "unreasonable results" sometimes, unfortunately, are what would actually occur -- we just might not like the answers we're getting. My workload is such though that I don't have time to go through calculations and you haven't supplied enough specifics for the normally helpful folks to jump on it.

However, realizing that might not suit your needs, you might want to read through this older thread: thread391-268322.

I seem to remember another thread also involving insulation of a square box, but I have limited search time. You can try searching yourself, using the search tool found next to the green forum button right above the "READ NEW POSTS." I tried searching on the word "transient."

Good luck