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contributor authorPal, Gopalendu
contributor authorModest, Michael F.
date accessioned2017-05-09T01:19:47Z
date available2017-05-09T01:19:47Z
date issued2015
identifier issn0022-1481
identifier otherht_137_07_072701.pdf
identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/158509
description abstractThe spherical harmonics (PN) method, especially its lowest order, i.e., the P1 or differential approximation, enjoys great popularity because of its relative simplicity and compatibility with standard models for the solution of the (overall) energy equation. Loworder PN approximations perform poorly in the presence of strongly nonisotropic intensity distributions, especially in optically thin situations within nonisothermal enclosures (due to variation in surface radiosities across the enclosure surface, causing rapid change of irradiation over incoming directions). A previous modification of the PN approximation, i.e., the modified differential approximation (MDA), separates wall emission from medium emission to reduce the nonisotropy of intensity. Although successful, the major drawback of this method is that the intensity at the walls is set to zero into outward directions, while incoming intensity is nonzero, resulting in a discontinuity at grazing angles. To alleviate this problem, a new approach, termed here the “advanced differential approximation (ADA),â€‌ is developed, in which the directional gradient of the intensity at the wall is minimized. This makes the intensity distribution continuous for the P1 method and mostly continuous for higherorder PN methods. The new method is tested for a 1D slab and concentric spheres and for a 2D medium. Results are compared with the exact analytical solutions for the 1D slab as well as the Monte Carlobased simulations for 2D media.
publisherThe American Society of Mechanical Engineers (ASME)
titleAdvanced Differential Approximation Formulation of the PN Method for Radiative Transfer
typeJournal Paper
journal volume137
journal issue7
journal titleJournal of Heat Transfer
identifier doi10.1115/1.4029814
journal fristpage72701
journal lastpage72701
identifier eissn1528-8943
treeJournal of Heat Transfer:;2015:;volume( 137 ):;issue: 007
contenttypeFulltext


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