Example 2.2 Consider a steam pipe of length L = 20 m, inner radius r₁ = 6 cm, outer radius r₂ = 8 cm, and thermal conductivity k = 20 W/mK. The inner and outer surfaces of the pipe are maintained at average temperatures of T₁ = 150°C and T2 = 60°C, respectively. Obtain a general relation for the temperature distribution inside the pipe under steady conditions, and determine the rate of heat loss from the steam through the pipe.