SPECTRAL METHODS FOR TRANSIENT HEAT CONDUCTION PROBLEMS IN SIMPLE GEOMETRIES.

Solutions to the unsteady heat conduction problem are obtained using a numerical procedure based on a Chebyshev series representation for the spatial dependence of the temperature field. This series contains time dependent coefficients which are selected so that the spectral series represents a good approximation to the evolving temperature field. The fundamental equations describing the spectral coefficients are derived using the Chebyshev-Tau matrix method. These equations are stepped forward in time using the Crank-Nicolson time differencing scheme. The technique is illustrated by applying it to several classical problems of unsteady conduction in simple geometries.

Duke Scholars

Author Edward J. Shaughnessy Thomas Lord Department of Mechanical Engineering and Materia ...