When a long section of a compressed air line passes through the outdoors, it is observed that the moisture in the compressed air freezes in cold weather, disrupting and even completely blocking the air flow in the pipe. To avoid this problem, the outer surface of the pipe is wrapped with electric strip heaters and then insulated. Consider a compressed air pipe of length L = 6 m, inner radius r₁ = 3.7 cm, outer radius r₂ = 4.0 cm, and thermal conductivity k = 14 W/m · K equipped with a 300-W strip heater. Air is flowing through the pipe at an average temperature of 210°C, and the average convection heat transfer coefficient on the inner surface is h = 30 W/m² · K. Assuming 15 percent of the heat generated in the strip heater is lost through the insulation,

(a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe,

(b) Obtain a relation for the variation of temperature in the pipe material by solving the differential equation,

(c) Evaluate the inner and outer surface temperatures of the pipe.

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TA 0 Compressed air Electric heater Insulation -10°C