1. Beginning with a differential control volume in the form of a cylindrical shell, derive the heat diffusion equation for a one-dimensional, cylindrical, radial coor- dinate system with internal heat generation. Compare your result with Equation 2.26.
2. Beginning with a differential control volume in the form of a spherical shell, derive the heat diffusion equation for a one-dimensional, spherical, radial coordinate system with internal heat generation. Compare your result with Equation 2.29.
3. A steam pipe is wrapped with insulation of inner and outer radii ri and ro, respectively. At a particular instant the temperature distribution in the insulation is known to be of the form For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express appropriate boundary conditions for the solution of these equations.