AN EIGENVALUE METHOD FOR SOLVING TRANSIENT HEAT CONDUCTION PROBLEMS

Publisher Website
Google Scholar
Abstract
The eigenvalue method, which has been used by researchers in structure mechanics, is applied to problems in heat conduction. Its formulation is described in terms of an examination of transient heat conduction in a square slab. Taking advantage of the availability of the exact solution, we compare the accuracy and other numerical properties of the eigenvalue method with those of existing numerical schemes. The comparison shows that, overall, the eigenvalue method appears to be fairly attractive. Furthermore, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed and retained to yield reasonably high accuracy. Great savings are attained in the computation time for a transient problem with long time duration and a large computational domain.