Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems.
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| Title: | Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems. |
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| Authors: | Pi, Te1 alitem0829@gmail.com, Cole, Kevin2 kcole1@unl.edu, Beck, James3 jameserebeck@gmail.com |
| Source: | Journal of Heat Transfer. Dec2017, Vol. 139 Issue 12, p1-10. 10p. |
| Subjects: | Heat conduction, Diffusion, Transient analysis, Mathematical models |
| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Heat Transfer is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 126256354 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Pi%2C+Te%22">Pi, Te</searchLink><relatesTo>1</relatesTo><i> alitem0829@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Cole%2C+Kevin%22">Cole, Kevin</searchLink><relatesTo>2</relatesTo><i> kcole1@unl.edu</i><br /><searchLink fieldCode="AR" term="%22Beck%2C+James%22">Beck, James</searchLink><relatesTo>3</relatesTo><i> jameserebeck@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Heat+Transfer%22">Journal of Heat Transfer</searchLink>. Dec2017, Vol. 139 Issue 12, p1-10. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Heat+conduction%22">Heat conduction</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion%22">Diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Transient+analysis%22">Transient analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Heat Transfer is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1115/1.4037081 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 1 Subjects: – SubjectFull: Heat conduction Type: general – SubjectFull: Diffusion Type: general – SubjectFull: Transient analysis Type: general – SubjectFull: Mathematical models Type: general Titles: – TitleFull: Efficient Numerical Evaluation of Exact Solutions for One-Dimensional and Two-Dimensional Infinite Cylindrical Heat Conduction Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Pi, Te – PersonEntity: Name: NameFull: Cole, Kevin – PersonEntity: Name: NameFull: Beck, James IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 00221481 Numbering: – Type: volume Value: 139 – Type: issue Value: 12 Titles: – TitleFull: Journal of Heat Transfer Type: main |
| ResultId | 1 |
