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. 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. The key finding of this paper is that the resulting series may be accurately evaluated with a fixed number of terms at any value of time, which removes a long-standing difficulty with series solution in general. The method is demonstrated for the one-dimensional case of a large body with a cylindrical hole and is extended to two-dimensional geometries of practical interest. The computer-evaluation time for the finite-body solutions are shown to be hundreds or thousands of time faster than the infinite-body solutions, depending on the geometry.
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December 2017
This article was originally published in
Journal of Heat Transfer
Research-Article
Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems
Te Pi,
Te Pi
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: alitem0829@gmail.com
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: alitem0829@gmail.com
Search for other works by this author on:
Kevin Cole,
Kevin Cole
Professor
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: kcole1@unl.edu
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: kcole1@unl.edu
Search for other works by this author on:
James Beck
James Beck
Professor Emeritus
College of Engineering,
Michigan State University,
Engineering Building, 428 S. Shaw Lane,
East Lansing, MI 48824-1226
e-mail: jameserebeck@gmail.com
College of Engineering,
Michigan State University,
Engineering Building, 428 S. Shaw Lane,
East Lansing, MI 48824-1226
e-mail: jameserebeck@gmail.com
Search for other works by this author on:
Te Pi
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: alitem0829@gmail.com
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: alitem0829@gmail.com
Kevin Cole
Professor
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: kcole1@unl.edu
Mechanical & Materials Engineering Department,
University of Nebraska Lincoln,
W342C NH,
Lincoln, NE 68588-0526
e-mail: kcole1@unl.edu
James Beck
Professor Emeritus
College of Engineering,
Michigan State University,
Engineering Building, 428 S. Shaw Lane,
East Lansing, MI 48824-1226
e-mail: jameserebeck@gmail.com
College of Engineering,
Michigan State University,
Engineering Building, 428 S. Shaw Lane,
East Lansing, MI 48824-1226
e-mail: jameserebeck@gmail.com
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 14, 2016; final manuscript received May 9, 2017; published online July 25, 2017. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Dec 2017, 139(12): 121301 (10 pages)
Published Online: July 25, 2017
Article history
Received:
September 14, 2016
Revised:
May 9, 2017
Citation
Pi, T., Cole, K., and Beck, J. (July 25, 2017). "Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems." ASME. J. Heat Transfer. December 2017; 139(12): 121301. https://doi.org/10.1115/1.4037081
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