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8/18/2019 Efficient Evaluation of Diffuse View Factors For
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Efcient Evaluat
o Diuse ViewFactors or
Radiation
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ABSTRACT
•
This paper presents a numerical method of evaluating view factoplanar surfaces.
• The method, which is based on Gaussian quadrature to perform integration is etended to surfaces with curved boundaries.
•As an application, the shape factor between two elliptic surfaceevaluated.
• The following discussion will consider onl! the case of radiant between di"usel! re#ecting and absorbing surfaces with no absorintervening air.
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BAC$GR%&'(
• Thermal radiation is t!picall! as importconvection or conduction in the overall heat babuildings.
• )henever we tal* about net radiation energ! ebetween surfaces, +t starts with the calculationfactors.
• The problem with view factors is not that t
inherentl! dicult to compute, but that the ca
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•Radiation heat transfer betweensurfaces depends on theorientation of the surfaces relativeto each other as well as theirradiation properties and
temperatures, as illustrated in -ig.
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+/) -ACT%R0S1A2/-ACT%R0C%'-+G&RAT+%' -ACT
3 The fraction of the radiationleaving surface i that stri*es surface 4 directl!.
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(+--&S/ ASS&52T+%'
•
The view factor based on theassumption that the surfaces aredi"use emitters and di"use re#ectorsis called the di"use view factor.
• And the view factor based on theassumption that the surfaces aredi"use emitters but specularre#ectors is called the specular viewfactor.
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• Consider a situation involving ' surfaces. Since each supotentiall! interact with ever! other surface, there interactions, or view factors.
• /ven simpli8cations, such as the reciprocit! relation and tha #at surface cannot view itself, reduce the number of vionl! to '9':; or =occlude>< the views between surface pairs, it is to chec* ':7 surfaces as possible obstructing surfaces for factor. This gives '9':;
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+'TR%(&CT+%'
• Since anal!tical solution is not possible for man!geometries of practical interest, accurate determof view factors b! numerical means has been a t
research.
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'%5/'C@AT&R/
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•
Three methods which are considered in this papevaluate the integrals in the equation developedare
• Trapeoidal,
• Simpson and
• Gaussian uadrature
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TRA2/D%+(A@ 5/T1%( 9 TD5
•
simplest of all the quadrature formulas• needs two points on each contour element.
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S+52S%'ES 5/T1%( 9S+5<
• The function to beF integrated is approimated bquadratic function through three points within thof integration
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GA&SS+A' &A(RAT&R/
•
Gaussian quadrature is the most accurate methgiven number of points on the elements.
• An n point quadrature formula approimafunction b! 97n: ;
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•
A two point formula 9GA&SS7< approimafunction with a pol!nomial of degree three and point formula 9GA&SS?< with degree 8ve.
• To get the same accurac!, the S+5 needs four
points, respectivel!. +n general, for a desired aS+5 needs four times more computation time coto the Gaussian method.
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GA&SS+A' &A(RAT&R/ )+T'%'@+'/AR TRA'S-%R5AT+%
The Gaussian quadrature needs the integration limits to bebetween : ; and ; and hence demands a transformation ofglobal coordinates to local ones.
Referring to -ig. ;, the global coordinates of the points on the twocontours are transformed using the following F
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R/S&@TS A'( (+SC&SS+%'
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C%'C@&S+%'S
•
The present method, is capable of computing viefactors for plane surfaces which are located arbistraight or curved and share common edges prawith an! desired accurac!. The method iscomputationall! ver! ecient.
• &se of higher order quadrature is recommendwhen the surfaces share a common edge or if thsurfaces are touching an!where.
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• &se of higher order transformation is recommenwhen the surfaces have curved contours.
• +t is found that the computational e"ort will be l
when the number of elements is increased b! qutransformation than when the order of transformincreased.
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R/-/RR/'C/S
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