Application of hybrid laplace transform/finite-difference method to transient heat conduction problems

A new method involving the combined use of the Laplace transform and the finite-difference method is applicable to two- and three-dimensional linear transient heat conduction problems. The method removes the time dependences from the governing differential equations and boundary conditions by using the Laplace transform and then solves the transformed equations with the finite-difference method. The transformed temperature is inverted by the method of Honig and Hirdes to obtain the result in the physical quantity. The results are compared in tables with exact solutions and other numerical data, and the agreement is found to be good. The method can also be used to calculate the specific nodal temperature at a specific time.