Water-vapor mixture flows through a long pipe at an average temperature of T=100C. The inner and outer radii of the pipe are r1=6cm and r2=6.5cm, respectively. The outer surface of the pipe is wrapped with a thin electric heater that consumes 300W per m length of the pipe. The exposed surface of the heater is heavily insulated so that the entire heat generated in the heater is transferred to the pipe. The temperature of the inner surface and water-vapor mixture is maintained at 100C by evaporation of the liquid. The thermal conductivity of the pipe material is 16 W/mK. Find out temperature distribution T(r) in the pipe wall. Calculate heat flux and heat flow at r = 6 cm and 6.2 cm, respectively. Is heat flux constant? Is heat flow (per unit length of the pipe) constant in the radial direction?

(1) What are the assumptions?

(2) Write the general heat conduction equation for this problem (Cartesian or Cylindrical)

(3) Customize the heat conduction equation in Step 2. Dimension, state, is there heat generation in the volume?

(4) Solve the equation to obtain a general solution containing unknown constants. (5) Provide boundary conditions at r1=6cm and r2=6.5cm. Commonly used boundary conditions: at r = rb, T = Tb, or kdT/dr = q0, or h(Tf-T)=-kdT/dr (5) Provide boundary conditions at r1=6cm and r2=6.5cm. Commonly used boundary conditions: at r = rb, At surface 1 (in contact with vapor mixture) you are given (d) temperature? (e) heat flux (temperature gradient)? (f) the surrounding fluid temperature and heat transfer coefficient if the surface is exposed to convection? Repeat the same to formulate the boundary condition for the other surface in contact with the heater.

(6) Use the boundary conditions to determine the values of unknown constants in your general solution.

I can get to step four but I don't know how to solve for my constants in order to manipulate the equation