Consider a spherical shell of inner radius r1 and outer radius r2 whose thermal conductivity varies linearly in a specified temperature range as k(T) = k0(1 + ßT) where k0 and b are two specified constants. The inner surface of the shell is maintained at a constant temperature of T1 while the outer surface is maintained at T2. Assuming steady one-dimensional heat transfer, obtain a relation for
(a) the heat transfer rate through the shell and
(b) the temperature distribution T(r) in the shell.
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