Linear and non-linear transient heat conduction problems by the Lanczos-Chebyshev method

Abstract

Abstract The Lanczos-Chebyshev method is used to reduce the linear and non-linear transient equations for heat conduction in one dimension to a set of ordinary differential equations, which is solved by an implicit backward finite difference formulation. An iterative approach is used if the problem is non-linear. It is shown that the method can be used for multi-region as well as one region problems. Test examples involving constant properties in slab and cylinder quench problems are used to show the accuracy of the method. A heat generating slab with temperature dependent conductivity and a canned fuel rod with spatial and temperature dependent thermal properties under simulated transient operating conditions, both of which have been solved previously by other methods, are used to demonstrate the possible application of the method to complex transient heat conduction problems.