Solving Steady-State Temperature Distribution

[thermalguy]

Hi, question for some experienced thermal guys out there. I'm modeling a spacecraft and would like to know the steady-state temperature distribution with say 9 nodes (i.e. a hexagonal prism with one node on each of the 8 faces and one in the very middle).

So, my [9] equations are e*sigma*area*T^4 = Qsun + Qearth + Qconduction(linear in temperature) + ... (there are 8 of those equations, one for each face of the hexagonal prism). The 9th equation would be Qconduction1(linear in temperature) + Qconduction2(same) + ... + Qinternal = 0 for the inner 9th node (ignoring internal radiation for the moment).

Since this system of equations is nonlinear, what would be the best way to go about solving for the steady-state temperatures? I've tried using Excel's solver add-in with a least-squares analysis, but it doesn't seem very accurate. Any ideas? Thanks for any input.

-thermalguy

 

[vitorpy]

Well, what a nice topic.

Try finite differences. i would recommend using Matlab for development, if you have the skills. If you haven't, fell free to reply, I'd love to help. I spent some time studying this at a summer course.

Excel is not really for scientific applications. Leave it alone at the finances department, where it is intended to be =)

 

[thermalguy]

Mmm Excel

Hey, thanks for replying. I ended up using fsolve in Matlab...not sure why Excel was bugging out. I believe the Solver Add-In uses a least-squares fit, so you have to start with initial conditions close to the steady-state temperatures. I've used it this way before but with fewer equations...with radiation, too. Anyway, I happen to think Excel is a wonderful science tool. NASA guys use it all the time ;) But you're right, there are better programs out there. Thanks again.

-thermalguy