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research-article

NON-GRAY RADIATION EXCHANGE: THE INTERNAL FRACTIONAL FUNCTION RECONSIDERED

[+] Author and Article Information
John H. Lienhard V

Rohsenow Kendall Heat Transfer Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 USA
lienhard@mit.edu

1Corresponding author.

ASME doi:10.1115/1.4042158 History: Received July 04, 2018; Revised November 20, 2018

Abstract

The radiation fractional function is the fraction of black body radiation below a given value of λ-T. Edwards and others have distinguished between the traditional, or "external", radiation fractional function and an "internal" radiation fractional function. The latter is used for simplified calculation of net radiation from a non-gray surface when the temperature of an effectively black source 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 can be useful for certain simplified calculations.

Copyright (c) 2018 by ASME
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