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Question: 7 30pts a pipe in a district heating network is...

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7. (30pts) A pipe in a district heating network is transporting over-pressurized hot water (10 atm) at a mass flow of 0.5 kg/s. The pipe is 5 m long, has an inner radius of 50 cm and pipe wall thickness of 50 mm. The pipe has a thermal conductivity of 20 W/m-K, and the inner pipe surface is ata uniform temperature of 110 C. The convection heat transfer coefficient of the air surrounding the pipe is 100W/m2-K. The temperature of the water at inlet of pipe is 130 °C and the constant pressure specific heat of hot water is 4000 J/kg- C. If the temperature of the air surrounding the pipe is 20 °C, determine the exit temperature of the water at the end of the pipe. You have to show all your work! Your solution must clearly include the expression for the governing heat conduction equation in
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