Application of the laplace transform to one-dimensional non-linear transient heat conduction in hollow cylinders

Non-linear transient heat conduction in a hollow cylinder with temperature-dependent thermal conductivity is investigated numerically by using the hybrid application of the Laplace transform technique and the finite-element method (FEM) or the finite-difference method (FDM). The governing equation is discritized in the space domain using the FEM or the FDM, and then the non-linear terms are linearized by using the Taylor series expansion. The time-dependent terms in the linearized equations are removed by the Laplace transform technique. The numerical inversion of the Laplace transform is used to invert the transformed temperature to the result in the physical quantity. Since the present method is not a time-stepping procedure, the results at a specific time can be calculated in the time domain without step-by-step computations. The computational results at a specific time are convergent over the entire space domain at about the fourth or fifth iteration. To show the accuracy of the present method, a comparison of the present results and those using the FDM in conjunction with the Crank-Nicolson algorithm is made.