Consider a cylinder with an inner radius of r1 and an outer radius of r2, and constant thermal conductivity k. Heat is generated inside the cylinder wall at a constant rate of e_gen. The inner and outer surface temperatures are kepy constant at T1 and T2, respectively.
1. Starting with the general form of conduction equation in three dimensions, find the one dimensional steady differential equation with internal generation. Then find the general solution.
2. Apply the boundary conditions and find the temperature distribution.