Efficient numerical evaluation of exact solution for 1D and 2D infinite cylindrical heat conduction problem

[+] Author and Article Information
Te Pi

University of Nebraska Lincoln Mechanical & Materials Engineering Department W342C NH, Lincoln, NE 68588-0526

Kevin Cole

University of Nebraska Lincoln, Mechanical & Materials Engineering Department W342C NH, Lincoln, NE 68588-0526

James Beck

Michigan State University College of Engineering Engineering Building 428 S. Shaw Lane East Lansing, MI 48824-1226

1Corresponding author.

ASME doi:10.1115/1.4037081 History: Received September 14, 2016; Revised May 09, 2017


Estimation of thermal properties or diffusion properties from transient data requires that a model is available that is physically meaningful and suitably precise. The model must also produce numerical values rapidly enough to accommodate iterative regression, inverse methods, or other estimation procedures during which the model is evaluated again and again. Bodies of infinite extent are a particular challenge from this perspective. Even for exact analytical solutions, because the solution often has the form of an improper integral that must be evaluated numerically, lengthy computer-evaluation time is a challenge. The subject of this paper is improving the computer evaluation time for exact solutions for infinite and semi-infinite bodies in the cylindrical coordinate system. The motivating applications for the present work include the line-source method for obtaining thermal properties, the estimation of thermal properties by the laser-flash method, and the estimation of aquifer properties or petroleum-field properties from well-test measurements. In this paper the computer evaluation time is improved by replacing the integral-containing solution by a suitable finite-body series solution. Although the series solution is approximate, the precision of the series solution may be controlled to a high level and the required computer time may be minimized, by a suitable choice of the extent of the finite body. An easy-to-use relationship is developed for the finite-body size needed as a function of desired precision and as a function of time.

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