Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered

Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered

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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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Main Author: Lienhard, John H
Other Authors: Massachusetts Institute of Technology. Robust Design Group
Format: Article
Published: ASME International 2019
Online Access:https://hdl.handle.net/1721.1/121988
_version_ 1811070433559052288
author Lienhard, John H
author2 Massachusetts Institute of Technology. Robust Design Group
author_facet Massachusetts Institute of Technology. Robust Design Group
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.
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spelling mit-1721.1/1219882022-09-23T13:10:52Z Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered Lienhard, John H Massachusetts Institute of Technology. Robust Design Group 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. 2019-08-15T14:25:10Z 2019-08-15T14:25:10Z 2019-03 2018-11 Article http://purl.org/eprint/type/JournalArticle 0022-1481 https://hdl.handle.net/1721.1/121988 Lienhard, John H., V. "Linearization of Nongray Radiation Exchange: The Internal Fractional Function Reconsidered." Journal of Heat Transfer 141, 5 (March 2019): 052701 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 10.1115/1.4042158 http://dx.doi.org/10.1115/1.4042158 Journal of Heat Transfer Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ 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/1721.1/121988
work_keys_str_mv AT lienhardjohnh linearizationofnongrayradiationexchangetheinternalfractionalfunctionreconsidered

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