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 Authors

Cited Authors

  • McMurray, JT; Shaughnessy, EJ

Published Date

  • 1979

Published In

  • ASME Pap