Radiation Exchange Between Surfaces:Enclosures with Nonparticipating MediaChapter 13Sections 13.1 through 13.4 Basic ConceptsBasic ConceptsEnclosures consist of two or !ore surfaces that en"elop a region of space #t$picall$ gas%filled& and 'etween which there is radiation transfer.( nonparticipating !ediu! within the enclosure neither e!its) a'sor's)nor scatters radiation and hence has no effect on radiation exchange'etween the surfaces. Each surface of the enclosure is assu!ed to 'e isother!al) opa*ue) diffuseand gra$) and to 'e characteri+ed '$ unifor! radiosit$ and irradiation. ,irtual)as well as real) surfaces !a$ 'e introduced to for! an enclosure. ,iew -actor .ntegral/he ,iew -actor #also Configuration or Shape -actor&/he "iew factor)is a geo!etrical *uantit$ correspondingto the fraction of the radiation lea"ing surface i that is intercepted '$ surface j.,ijFi jiji iqFAJ/he "iew factor integral pro"ides a general expression for.ijF Consider exchange'etween differential areas i :jdA and dA01cos cosi ji jij i jA AiF dAdAA R 0cos coscosi ji j i i i j i i i jdq I dAd J dAdAR ,iew -actor Relations,iew -actor RelationsReciprocit$ Relation. 1ith01cos cosj ii jji i jA AjF dAdAA R Su!!ation Rule for Enclosures.11NijjF/wo%2i!ensional 3eo!etries #/a'le 13.1& -or exa!ple)An Infinite Plane and a Row of Cylinders( ) ( )1 01 0 00 0101 1//tanijD D s DFs s D 1 _ + 1 , ]i ij j jiAF A F ,iew -actor Relations #cont&/hree%2i!ensional 3eo!etries #/a'le 13.0&. -or exa!ple)Coaxial Parallel Disks( )1 0000014011/// /ij j ijii i j jF S S r rRSRR r L R r L 1 ' ) ] + + Blac4'od$ EnclosureBlac4'od$ Radiation Exchange-or a 'lac4'od$).i biJ E ij i j j iq q q ij i ij bi j ji bjq AF E A F E ( )4 4ij i ij i jq AF net rate at which radiationlea"es surface i due to itsinteraction with jor net rate at which surfacej gains radiation due to itsinteraction with iNet radiation transfer fro! surface i due to exchange with all #N& surfaces of an enclosure:( )4 41Ni i ij i jjq AF Net radiati"e exchange 'etween two surfaces that can 'e approxi!ated as 'lac4'odies 3eneral Enclosure (nal$sis3eneral Radiation (nal$sis for Exchange 'etween the N5pa*ue) 2iffuse) 3ra$ Surfaces of an Enclosure ( ) 1i i i

(lternati"e expressions for net radiati"e transfer fro! surface i:( )-ig. #'&i i i iq A J ! #1&( )-ig. #c&i i i i iq A E ! #0&( ) -ig. #d&1 /bi iii i iE JqA #3&Suggests a surface radiati"e resistance of the for!: ( ) 1 /i i iA 3eneral Enclosure (nal$sis #cont&( )( )11 1N Ni ji i ij i jj ji ijJ Jq AF J JAF #4&Suggests a space or geo!etrical resistance of the for!:( )1i ijAFE*uating E*s. #3& and #4& corresponds to a radiation 'alance on surface i:( )( )11 1 /Ni jbi iji i ii ijJ JE JAAF #6&which !a$ 'e represented '$ a radiation networ4 of the for! 3eneral Enclosure (nal$sis #cont&Methodolog$ of an Enclosure (nal$sis(ppl$ E*. #4& to each surface for which the net radiation heat rateis 4nown.iq(ppl$ E*. #6& to each of the re!aining surfaces for which the te!perature) and henceis 4nown.i

,biEE"aluate all of the "iew factors appearing in the resulting e*uations.Sol"e the s$ste! of N e*uations for the un4nown radiosities)1 0, ,...., .NJ J J7se E*. #3& to deter!ine for each surface of 4nown for each surface of 4nown.iq and i i iq/reat!ent of the "irtual surface corresponding to an opening #aperture& of area )through which the interior surfaces of an enclosure exchange radiation with largesurroundings at:iAs"r

(pproxi!ate the opening as 'lac4'od$ of area)te!perature) and properties) .,iA ,i s"r1i i /wo%Surface Enclosures/wo%SurfaceEnclosuresSi!plest enclosure for which radiation exchange is exclusi"el$ 'etween twosurfaces and a single expression for the rate of radiation transfer !a$ 'einferred fro! a networ4 representation of the exchange.( )4 41 01 0 101 01 1 1 10 0 01 11 q q qA AF A + + /wo%Surface Enclosures #cont&Special cases are presented in /a'le 13.3. -or exa!ple)8arge #.nfinite& 9arallel 9lates1 0101A A AF ( )4 41 1 0101 01 11Aq + Note result for S#all Con$ex %bje&t in a Lar'e Ca$ity( Radiation ShieldRadiation Shields:igh reflecti"it$ #low& surface#s& inserted 'etween two surfaces for which a reduction in radiation exchange is desired. Consider use of a single shield in a two%surface enclosure) such as that associated withlarge parallel plates:Note that) although rarel$ the case) e!issi"ities !a$ differ for opposite surfacesof the shield. Radiation Shield #cont&Radiation Networ4:( )4 41 010 1 03 1 3 01 01 1 1 13 3 1 3 3 0 3 3 30 0 01 11 11 1 , ,, , q q qA AF A A A F A + + + + +/he foregoing result !a$ 'e readil$ extended to account for !ultiple shieldsand !a$ 'e applied to long) concentric c$linders and concentric spheres)as well as large parallel plates. Reradiating Surfaces/he Reradiating Surface(n ideali+ation for which.R R! J :ence) and; .R R bRq J E (pproxi!ated '$ surfaces that are well insulated on one side and for which con"ection is negligi'le on the opposite #radiating& side./hree%Surface Enclosure with a Reradiating Surface:( )( ) ( )4 41 01 01 011 1 0 01 10 1 1 0 01 111 1 / /R R q qA AAF AF A F + ++ +1 ] Reradiating Surfaces #cont&/e!perature of reradiating surface!a$ 'e deter!ined fro! 4nowledge of its radiosit$ .R

RJ 1ith ) a radiation 'alance on the surface $ields ;Rq ( ) ( )1 01 1 0 01 1 / /R RR RJ J J JAF A F 1 4 /RRJ

_ , Multi!ode EffectsMulti!ode Effects.n an enclosure with conduction and con"ection heat transfer to or fro! one or !ore surfaces) the foregoing treat!ents of radiation exchange !a$ 'e co!'ined with surface energ$ 'alances to deter!ine ther!al conditions.Consider a general surface condition for which there is external heat addition #e.g.) electricall$&) as well as conduction) con"ection and radiation., , , , i ext i rad i &on$ i radq q q q + +(ppropriate anal$sis for%surface) two%surface) etc.) enclosure., i radq N 9ro'le!:-urnace in Spacecraft En"iron!ent9ro'le! 13.