Intrinsic verification and a heat conduction database

Abstract

In this paper several unique concepts in transient heat conduction are discussed, including intrinsic verification, time partitioning, and a database of solutions organized with a numbering system. The database and numbering system have been developed to address the following problem: existing solutions in books and traditional publications are not truly organized, and consequently they are not readily accessible. The database that we have developed contains added material such as algorithms, consistent statements of the number of required terms, and verified computer programs for evaluating eigenvalues and solutions. The purpose of the database, called the Exact Analytical Conduction Toolbox, is to provide improved access to precise numerical values from verified solutions for application to engineering problems of current interest. Heat conduction is an appropriate discipline in which to develop and demonstrate these concepts because it is a mature field with a large number of existing analytical solutions. It is anticipated that these concepts can also be applied to diverse fields in engineering and science. Several examples are given of exact analytical solutions that are available in the database, some not previously published. One application for this type of exact analytical solution is for measurement of thermal properties.