Assume that the temperature is spherically symmetric, u = u(r, t), where r is the distance from a fixed point (r2 = x2 + y2 + z2). Consider the heat flow (without sources) between any two concentric spheres of radii a and b.
(a) Show that the total heat energy is
(b) Show that the flow of heat energy per unit time out of the spherical shell at
A similar result holds at r = a.
(c) Use parts (a) and (b) to derive the spherically symmetric heat equation
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