Transient Conduction in a Hollow Cylinder With Variable Thermal Conductivity

A closed form approximate solution has been obtained for the transient temperature distribution in a hollow cylinder with a linear variation in thermal conductivity with temperature. The boundary conditions considered are convective heating (Newton's law) at the exposed inner surface and adiabatic outer surface. The solution is obtained using the method of optimal linearization, with the initial solution given by the integral method. The nonlinear analytical solution is shown to compare well with the finite difference solution.