Consider a steam pipe of length L, inner radius r₁, outer radius r₂, and constant thermal conductivity k. Steam flows inside the pipe at an average temperature of T_i with a convection heat transfer coefficient of hi. The outer surface of the pipe is exposed to convection to the surrounding air at a temperature of T₀ with a heat transfer coefficient of h_o. Assuming steady one-dimensional heat conduction through the pipe,

(a) Express the differential equation and the boundary conditions for heat conduction through the pipe material,
(b) Obtain a relation for the variation of temperature in the pipe material by solving the differential equation, and
(c) Obtain a relation for the temperature of the outer surface of the pipe.

Transcribed Image Text:

hi T₁ 12 To ho