Question 1 ( 50 points): A pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate 0.3kg/s. The pipe is 10m long, has an inner diameter of 5cm and a pipe wall thickness of 6mm. The pipe has a thermal coductivity of 17W/m.K, and the inner pipe surface is at uniform temperature of 120C. The temperature drop between the inlet and the exit of the pipe is 7C and the constant pressure specific heat of vapor is 2190J/kg.C. a. Starting with an energy balance over a suitable control volume, derive the differential equation and write the boundary conditions for the steady on-dimensional heat conduction through the pipe wall, b. Obtain a relation for the variation of temperature in the container wall by solving the differential equation, c. If the air temperature in the manufacturing plant is 25C determine the heat transfer coefficient as a result of convection between the outer surface and surrouinding air