- McMurray, J. T. and Shaughnessy, E. J., SPECTRAL METHODS FOR TRANSIENT HEAT CONDUCTION PROBLEMS IN SIMPLE GEOMETRIES.,
American Society of Mechanical Engineers (Paper) no. 79-HT-62
pp. 6 - .
(last updated on 2007/04/06)
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.
MATHEMATICAL TECHNIQUES - Chebyshev Approximation;