### Abstract

A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

Original language | English (US) |
---|---|

Pages (from-to) | 81-87 |

Number of pages | 7 |

Journal | Journal of Heat Transfer |

Volume | 85 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1963 |

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*Journal of Heat Transfer*,

*85*(2), 81-87. https://doi.org/10.1115/1.3686058

**A new and simpler formulation for radiative angle factors.** / Sparrow, Ephraim M.

Research output: Contribution to journal › Article

*Journal of Heat Transfer*, vol. 85, no. 2, pp. 81-87. https://doi.org/10.1115/1.3686058

}

TY - JOUR

T1 - A new and simpler formulation for radiative angle factors

AU - Sparrow, Ephraim M

PY - 1963/1/1

Y1 - 1963/1/1

N2 - A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

AB - A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

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U2 - 10.1115/1.3686058

DO - 10.1115/1.3686058

M3 - Article

VL - 85

SP - 81

EP - 87

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

SN - 0022-1481

IS - 2

ER -