Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered
The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of ne...
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| Format: | Article |
| Language: | en_US |
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ASME International
2020
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| Online Access: | https://hdl.handle.net/1721.1/124144 |
| _version_ | 1811070079159238656 |
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| author | Lienhard, John H |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Lienhard, John H |
| author_sort | Lienhard, John H |
| collection | MIT |
| description | The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of net radiation from a nongray surface when the temperature of an effectively black environment is not far from the surface's temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function should be used for evaluating radiation thermal resistances, in particular. Keywords: Approximatino, Emissivity; Errors; Radiation (Physics); Temperature; Wavelength |
| first_indexed | 2024-09-23T08:23:21Z |
| format | Article |
| id | mit-1721.1/124144 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:23:21Z |
| publishDate | 2020 |
| publisher | ASME International |
| record_format | dspace |
| spelling | mit-1721.1/1241442020-03-14T03:30:40Z Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered Lienhard, John H Massachusetts Institute of Technology. Department of Mechanical Engineering The radiation fractional function is the fraction of black body radiation below a given value of λT. Edwards and others have distinguished between the traditional, or “external,” radiation fractional function and an “internal” radiation fractional function. The latter is used for linearization of net radiation from a nongray surface when the temperature of an effectively black environment is not far from the surface's temperature, without calculating a separate total absorptivity. This paper examines the analytical approximation involved in the internal fractional function, with results given in terms of the incomplete zeta function. A rigorous upper bound on the difference between the external and internal emissivity is obtained. Calculations using the internal emissivity are compared to exact calculations for several models and materials. A new approach to calculating the internal emissivity is developed, yielding vastly improved accuracy over a wide range of temperature differences. The internal fractional function should be used for evaluating radiation thermal resistances, in particular. Keywords: Approximatino, Emissivity; Errors; Radiation (Physics); Temperature; Wavelength 2020-03-13T15:12:59Z 2020-03-13T15:12:59Z 2019-03 Article http://purl.org/eprint/type/JournalArticle 0022-1481 1528-8943 https://hdl.handle.net/1721.1/124144 Lienhard V, John H. “Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered.” Journal of Heat Transfer 141, no. 5 (March 27, 2019): 052701. © 2019 ASME en_US https://doi.org/10.1115/1.4042158 Journal of Heat Transfer Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf ASME International ASME |
| spellingShingle | Lienhard, John H Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title | Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title_full | Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title_fullStr | Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title_full_unstemmed | Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title_short | Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered |
| title_sort | linearization of nongray radiation exchange the internal fractional function reconsidered |
| url | https://hdl.handle.net/1721.1/124144 |
| work_keys_str_mv | AT lienhardjohnh linearizationofnongrayradiationexchangetheinternalfractionalfunctionreconsidered |