APPLICATION OF THE LAPLACE TRANSFORM TO NONLINEAR TRANSIENT PROBLEMS

The hybrid application of the Laplace transform technique and the finite difference method to one-dimensional nonlinear transient heat conduction problems is studied. The equation is discretized in the space domain by the finite difference method. The nodal temperatures are then transformed by using the Laplace transform technique. The transformed temperatures are inverted numerically to obtain the results in the physical quantities. This statement shows that the present method does not need to perform a time-stepping procedure. Thus the results at any time can be calculated in the time domain without any step-by-step computations. The present results are compared in tables with those obtained by the direct variational method and other methods. It is found that their results are in good agreement with each other. It can be concluded that the present hybrid method is reliable. In addition, two different linearization schemes for the nonlinear boundary condition are investigated.