Solving Circular Thermodynamics: Calculating Heat Flow & Boundary Temperatures

[99.9% Void]

Hey everybody, no idea if this is the right place for me to post this…

This is the first post I've ever written, in any forum, ever. Complete forum newbie with a complex problem, hence my desperate plea for help on this nexus of knowledge forged through experience that I have yet to gain.

The problem is one of Thermodynamics and is as follows, I have a hot gas contained in a chamber and I only want a set about of energy to escape it. Given the very hot temperature of the gas I will need a few layers of insulation of different properties to try and contain the heat. I have built a tool in excel that uses the Materials properties and dimensions to calculate the heat flow through each layer of insulation, and the temperature at each of these boundaries, taking into account the heat flow from conduction, forced convection and radiation to sum the net heat flow through all layers.

It seems to be a circular problem, in that the heat flow and temperature depend upon each other, something that excel doesn't agree with, so I devised a series of tables in order to de-link their relationship and used the solver function to try and converge to an equilibrium but with no joy. I wonder if my method is fundamentally flawed…

The problem I put forward to the floor is this, If you had to calculate the heat flow and boundary temperatures through multiple layers of materials how would you go about doing it? Any help, even if it is to just point me in the right direction would be appreciated.

Looking forward to a reply.

 

[SteamKing]

Without looking at your equations or calculations, it sounds like you have to make some initial assumptions about the temperatures at the various layers and then iterate to find a solution. I would first start off with a simple model, say one layer of insulation, and develop the excel routines until a solution was reached. Then I would add additional complexity (more layers of insulation) to the model and adjust as required. A canned routine like Solver may not be suitable for what you are doing. You might have to play around with adjusting individual layer temps by hand until the physical properties of your model (heat flow from the reservoir) agree with the temps of the insulation.

If you want specific ideas, you'll have to provide more detail about your model and calcs.

 

[99.9% Void]

Thank you for the swift reply. Using approximations as a starting point to determine the flow of heat through each layer is where I began, since then the model has grown in complexity. Starting again, one layer at a time might be the best option for me at this point, especially as a way of sense checking the results. The layers of reflective material sandwiched in-between the insulation to counter the flow of radiation add an extra dimension of confusion.

Even though specific help would be appreciated, there is nothing like solving a problem that's been hanging over your head a while! That said, if I don’t crack it soon I’ll be posting further details…