- #1
heritage972
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We solved a simple looking heat diffusion problem because it describes an apparatus used in an NIH sponsored research project. It resembles problems discussed in textbooks and in many papers on the web. A textbook method solves all those problems but a straight forward application of that method fails for our problem. (The textbook approach is to isolate the heat source, if any, and expand the rest in well known eigenfunctions.)
Has anyone seen this problem in print, textbook or other source. Two days of Google searches come up empty and it is not in our library; e.g. Morse and Feshbach.
A homogeneous sphere of radius 1 satisfies the heat diffusion equation with a time independent heat source Q(r). The boundary condition is grad (T)=0 on the boundary. The initial distribution T(r,0)=f(r) is known. What is T(r,t)?
Our first surprise was that blindly applying the textbook method fails and our second surprise was that such a simple, but interesting, problem doesn't seem to appear in print. We are trying to decide on distributing our solution. Thanks
Has anyone seen this problem in print, textbook or other source. Two days of Google searches come up empty and it is not in our library; e.g. Morse and Feshbach.
A homogeneous sphere of radius 1 satisfies the heat diffusion equation with a time independent heat source Q(r). The boundary condition is grad (T)=0 on the boundary. The initial distribution T(r,0)=f(r) is known. What is T(r,t)?
Our first surprise was that blindly applying the textbook method fails and our second surprise was that such a simple, but interesting, problem doesn't seem to appear in print. We are trying to decide on distributing our solution. Thanks