Hybrid Laplace transform technique for non-linear transient thermal problems

A hybrid numerical method combining the application of the Laplace transform technique and the finite-difference method (FDM) or the finite-element method (FEM) is presented for non-linear transient thermal problems. The space domain in the governing equation is discretized by FDM or FEM and the non-linear terms are linearized by Taylor's series expansion. The time-dependent terms are removed from the linearized equations by Laplace transformation, and so, the results at a specific time can be calculated without step-by-step computation in the time domain. To show the efficiency and accuracy of the present method several one-dimensional non-linear transient thermal problems are studied.