Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/emerald-publishing/a-finite-element-eigenvalue-method-for-solving-transient-heat-GixhUHLSqO
- Publisher
- Emerald Publishing
- Copyright
- Copyright © Emerald Group Publishing Limited
- ISSN
- 0961-5539
- DOI
- 10.1108/eb017493
- Publisher site
- See Article on Publisher Site
Abstract
An eigenvalue method is presented for solving the transient heat conduction problem with timedependent or timeindependent boundary conditions. The spatial domain is divided into finite elements and at each finite element node, a closedform expression for the temperature as a function of time can be obtained. Three test problems which have exact solutions were solved in order to examine the merits of the eigenvalue method. It was found that this method yields accurate results even with a coarse mesh. It provides exact solution in the time domain and therefore has none of the timestep restrictions of the conventional numerical techniques. The temperature field at any given time can be obtained directly from the initial condition and no timemarching is necessary. For problems where the steadystate solution is known, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed. These features lead to great savings in computation time, especially for problems with long time duration. Furthermore, the availability of the closed form expressions for the temperature field makes the present method very attractive for coupled problems such as solidfluid and thermalstructure interactions.
Journal
International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing
Published: Mar 1, 1992