Mathematical Methods in the Physical Sciences · Problem 9.23

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · miscellaneous-two-spheres-temperature

Problem

Find the steady-state temperature in the region between two spheres r=1r = 1 and r=2r = 2 if the surface of the outer sphere has its upper half held at 100∘100^\circ and its lower half at −100∘-100^\circ and these temperatures are reversed for the inner sphere. HintHint: See Problem 7.14. Here you will need to find two Legendre series (when r=1r = 1 and when r=2r = 2) and solve for ala_l and blb_l.

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