ISSN Online: 2377-424X
ISBN Print: 978-1-56700-421-2
International Heat Transfer Conference 15
Accuracy of the First Eigenvalue of Heat Conduction Problems Calculated Through Tables and Explicit Approximate Expressions
摘要
Many solutions in the form of infinite series of heat conduction problems depend on eigenvalues that are defined by equations that can only be solved numerically. The heat transfer texts present tables of eigenvalues as function of the parameters of the equations. However, while the problems given as examples to illustrate the content of heat transfer textbooks can lead to values of parameters similar to those tabulated, in real problems this hardly occurs. In this case, the accuracy of the eigenvalues obtained through tables depends on the precision of the results of the linear or higher order interpolations. Initially this accuracy for typical tables will be presented. Next, approximate explicit expressions will be analyzed for the first eigenvalues obtained by other authors, and new expressions will be developed having sufficient accuracy and simplicity in the utilization as to
justify them as alternatives to the use of tables.