Why is the Heat equation solved with separation of variables but not with Fourier transformations?

[yaman]

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Why in heat transfer books Fourier's partial differtial unsteady state heat transfer equation is solved with seperation of variables but not with Fourier transformations?

 

[fresh_42]

Hello and !

Have fun and stay curious!

Moderator's Note: I moved this into a technical forum. The "New member introduction" forum is only meant to say 'hello'.

 

[pasmith]

Why in heat transfer books Fourier's partial differtial unsteady state heat transfer equation is solved with seperation of variables but not with Fourier transformations?

Have you tried solving it on a finite interval subject to initial and boundary conditions (the typical geometry appropriate for separation of variables) using a transform method? Is that easier or harder than separation of variables?

 

[Orodruin]

Why in heat transfer books Fourier's partial differtial unsteady state heat transfer equation is solved with seperation of variables but not with Fourier transformations?

This is simply incorrect. The method applied will generally depend on the domain. An infinite domain will be suited for transforms such as the Fourier transform, whereas a finite domain will be more suited for series expansions. Both methods are effectively the same and amount to separation of variables.

I know at least one textbook that uses Fourier transforms to solve the heat equation (and series expansion on finite domains). I know this because I wrote it.

 

[mathwonk]

Is this of interest?
https://math.mit.edu/~luccul/after-klein/SummerCourseThetaProbs.pdf