Consider a spherical shell of inner radius r 1 and outer radius r 2 whose thermal conductivity varies linearly in a specified temperature range as k(T) k 0 (1 T) where k 0 and b are two specified constants The inner surface of the shell is maintained at a constant temperature of T 1 while the outer...

a Heat transfer rate through the shell The heat transfer rate through the shell is given by q kT dTd ...

Consider a spherical shell of inner radius r 1 and outer radius r 2 whose thermal conductivity

Question:

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 + βT) 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

(b) The temperature distribution T(r) in the shell.

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