Fourier Transform

[atedionyahoo]

How should I solve a heat transfer equation in elliptic region by Fourier Transform method?

 

[zekeman]

If this is not a school problem, then what is the application?

 

[hacksaw]

transforms to be sure, related to Fourier but only in a generalized sense

 

[IRstuff]

Perhaps you are referring to Fourier's Law, which is not to be confused with Fourier Transforms:

http://en.wikipedia.org/wiki/Conduction_(heat)#Fourier.27s_law

TTFN

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[rmw]

Does Fourier's law have an elliptic region?

rmw

 

[hacksaw]

my understanding is that the op is wants to use fourier methods (i.e. orthogonal functions) to develop a solution for an elliptical (presumed 2d) region.

Carslaw and Yeager might be a good start. the expansions are not limited to trig expansions and are more generally classified as integral methods.

 

[Jmoore1]

Gradient^2*T - 1/alpha (dt/dx -partial)= -(1/k)qgen

you have x and y positions for the ellipse based off of a starting point (Xs,Ys), size factors (a,b), and angles (alpha and beta)

assuming you have initial values and boundaries, use your formula for the x and y positions for the ellipse and the above formula for heat transfer and using cos/sin series you can come up with the formula for both (T(x) and T) and solve using ure Initial values and boundary equations (after some fun and a ridiculous amount of math) to solve for the unknown constants.....