Unrestraining the Biot Number for Systems With Internal Heat Generation.
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| Title: | Unrestraining the Biot Number for Systems With Internal Heat Generation. |
|---|---|
| Authors: | Yoder, Elijah1 epyoder@liberty.edu, Strasser, Wayne1 wstrasser@liberty.edu, Kacinski, Robert1 rpkacinski@liberty.edu, Jones, Braden1 bkjones@tamu.edu |
| Source: | Journal of Solar Energy Engineering. Aug2025, Vol. 147 Issue 4, p1-11. 11p. |
| Subjects: | Energy storage, Number systems, Heating, Heat transfer, Rapid tooling, Thermal conductivity |
| Abstract: | Thermal runaway from hot spots in systems such as solar energy storage poses a safety concern. Tools for rapid analysis of these systems would be exceedingly useful in their development and maintenance. The "lumped capacitance" (LC) assumption is one of these analysis tools and is limited to Biot numbers less than about 0.1. However, for systems like energy storage batteries with internal heat generation, there is no such tool. A numerical solution was, therefore, used to compute the spatiotemporal temperature of cooling spheres with varying thermal conductivity, characteristic length scale, and internal heat generation rate to determine the effects that internal heat generation has on LC accuracy. Increasing the heating time or decreasing the thermal conductivity hinders LC accuracy, while increasing the internal heat generation rate or characteristic length scale improves it. This means that larger volumes improve the accuracy of LC, completely inverting its previous relationship. The Buckingham-Pi theorem was then used to create a new nondimensional group, the Yonkist number, in order to provide an analogous Biot number for systems with heat generation. Ultimately, it was found that LC can be utilized for systems with unlimited Biot numbers, as long as the internal heat generation rate is sufficiently large or the heating time is sufficiently small to make the Yonkist number less than the Biot number. The use of the new Yonkist number removes the upper boundary from the range of Biot numbers to which the LC assumption can be applied and allows expedient heat transfer analyses for thermal runaway problems. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Solar Energy Engineering 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: 188376310 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Unrestraining the Biot Number for Systems With Internal Heat Generation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yoder%2C+Elijah%22">Yoder, Elijah</searchLink><relatesTo>1</relatesTo><i> epyoder@liberty.edu</i><br /><searchLink fieldCode="AR" term="%22Strasser%2C+Wayne%22">Strasser, Wayne</searchLink><relatesTo>1</relatesTo><i> wstrasser@liberty.edu</i><br /><searchLink fieldCode="AR" term="%22Kacinski%2C+Robert%22">Kacinski, Robert</searchLink><relatesTo>1</relatesTo><i> rpkacinski@liberty.edu</i><br /><searchLink fieldCode="AR" term="%22Jones%2C+Braden%22">Jones, Braden</searchLink><relatesTo>1</relatesTo><i> bkjones@tamu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Solar+Energy+Engineering%22">Journal of Solar Energy Engineering</searchLink>. Aug2025, Vol. 147 Issue 4, p1-11. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Energy+storage%22">Energy storage</searchLink><br /><searchLink fieldCode="DE" term="%22Number+systems%22">Number systems</searchLink><br /><searchLink fieldCode="DE" term="%22Heating%22">Heating</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+transfer%22">Heat transfer</searchLink><br /><searchLink fieldCode="DE" term="%22Rapid+tooling%22">Rapid tooling</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+conductivity%22">Thermal conductivity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Thermal runaway from hot spots in systems such as solar energy storage poses a safety concern. Tools for rapid analysis of these systems would be exceedingly useful in their development and maintenance. The "lumped capacitance" (LC) assumption is one of these analysis tools and is limited to Biot numbers less than about 0.1. However, for systems like energy storage batteries with internal heat generation, there is no such tool. A numerical solution was, therefore, used to compute the spatiotemporal temperature of cooling spheres with varying thermal conductivity, characteristic length scale, and internal heat generation rate to determine the effects that internal heat generation has on LC accuracy. Increasing the heating time or decreasing the thermal conductivity hinders LC accuracy, while increasing the internal heat generation rate or characteristic length scale improves it. This means that larger volumes improve the accuracy of LC, completely inverting its previous relationship. The Buckingham-Pi theorem was then used to create a new nondimensional group, the Yonkist number, in order to provide an analogous Biot number for systems with heat generation. Ultimately, it was found that LC can be utilized for systems with unlimited Biot numbers, as long as the internal heat generation rate is sufficiently large or the heating time is sufficiently small to make the Yonkist number less than the Biot number. The use of the new Yonkist number removes the upper boundary from the range of Biot numbers to which the LC assumption can be applied and allows expedient heat transfer analyses for thermal runaway problems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Solar Energy Engineering 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: 10.1115/1.4068113 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 1 Subjects: – SubjectFull: Energy storage Type: general – SubjectFull: Number systems Type: general – SubjectFull: Heating Type: general – SubjectFull: Heat transfer Type: general – SubjectFull: Rapid tooling Type: general – SubjectFull: Thermal conductivity Type: general Titles: – TitleFull: Unrestraining the Biot Number for Systems With Internal Heat Generation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yoder, Elijah – PersonEntity: Name: NameFull: Strasser, Wayne – PersonEntity: Name: NameFull: Kacinski, Robert – PersonEntity: Name: NameFull: Jones, Braden IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 01996231 Numbering: – Type: volume Value: 147 – Type: issue Value: 4 Titles: – TitleFull: Journal of Solar Energy Engineering Type: main |
| ResultId | 1 |
