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Finite Difference Method + Radiating Boundary = Screwed?
Akilae729
Registered User regular
Registered User regular
I'm working on a small MATLAB heat transfer code that is going to use the finite difference method to solve for the temperature distribution in a solid part made of multiple materials.
For everything that only "sees" conduction, this is super easy. Set up the nodes, set up a GIANT matrix with the algebraic equations, keep track of local material properties, and solve. Done. Easy.
The problem here is that there is a radiation boundary condition on the outer surface. Since this is a function of T^4, I can't solve this with linear algebra.
Is there a clever way to handle a radiation boundary condition????
I could always randomly assign temperatures to the outer nodes and let MATLAB's solver (fminsearch probably) mess with them until I get an appropriate energy balance. But I'm not terribly confident in MATLAB's ability to do this with a large number of nodes.
For everything that only "sees" conduction, this is super easy. Set up the nodes, set up a GIANT matrix with the algebraic equations, keep track of local material properties, and solve. Done. Easy.
The problem here is that there is a radiation boundary condition on the outer surface. Since this is a function of T^4, I can't solve this with linear algebra.
Is there a clever way to handle a radiation boundary condition????
I could always randomly assign temperatures to the outer nodes and let MATLAB's solver (fminsearch probably) mess with them until I get an appropriate energy balance. But I'm not terribly confident in MATLAB's ability to do this with a large number of nodes.
Akilae729 on
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The MATLAB forums would probably help a bit more - they are pretty good guys over there.
After talking to some professors, it looks like there isn't a clever way to fix the boundary condition issue.
I've had a mixed bag with the MATLAB forums. And there are a few engineers floating around here that typically have good ideas.