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by: Antone Mann


Antone Mann
GPA 3.82

Diana Tasciuc

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Diana Tasciuc
Class Notes
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This 13 page Class Notes was uploaded by Antone Mann on Monday October 19, 2015. The Class Notes belongs to MANE 4010 at Rensselaer Polytechnic Institute taught by Diana Tasciuc in Fall. Since its upload, it has received 51 views. For similar materials see /class/224904/mane-4010-rensselaer-polytechnic-institute in Mechanical and Aerospace Engineering at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15
RADIATIVE VIEW FACTORS F V r hr lV oh r Patchto oh 7 Fr w T 39T l V d Ul V Fr wV oh r 4 l w n 4 Sphere to oh 7 Small to very 7 Fnu oh r w um oh r W ml oh r 6 wk hwdr 6 s l w n s s l 7 ere to parallel cyllnder ln mte extent 7 7 7 8 8 8 Fnu an r n V 8 Unequal 10 Equal ll 10 Unequal ll 11 Smpto Mn 11 11 Patch to ll 11 12 12 12 12 Smpto Mn 13 13 Fqul ell m m 13 13 Tu W ul rrm m PM VIEW FACTOR DEFINITION The view factor F12 is the fraction of energy exiting an isothermal opaque and diffuse surface 1 by emission or re ection that directly impinges on surface 2 and is absorbed or re ected Some view factors having an analytical expression are compiled below View factors only depend on geometry and can be computed from the general expression below Consider two in nitesimal surface patches dA1 and dAz Fig 1 in arbitrary position and orientation de ned by their separation distance rm and their respective tilting relative to the line of centres 31 and 32 with Og lgnZ and Ogizg Z ie seeing each other The radiation power intercepted by surface dAz coming directly from a diffuse surface dA1 is the product of its radiance L1M17r times its perpendicular area dA1 1 times the solid angle subtended by M2 1012 ie dzdleL1dAudleL1dAlcos 1dAZcosiZrlzz Thence M 7 dzd7lz leQZdAicos6cos61Aq cos6 ldAzcos z IZTMLdAi MidAi 7 W Z 7t 12 a E ililmd alm 7 A1 A 7 Fig 1 Geometry for viewfactor de nition When nite surfaces are involved computing view factors is just a problem of mathematical integration not a trivial one except in simple cases Recall that the emitting surface exiting in general must be isothermal opaque and Lambertian a perfect diffuser and to apply viewfactor algebra all surfaces must be isothermal opaque and Lambertian View factor algebra When considering all the surfaces under sight from a given one enclosure theory several general relations can be established among the NZ possible view factors what is known as view factor algebra Bounding View factors are bounded to 091151 by de nition the view factor F g is the fraction of energy exiting surface 139 that impinges on surface j Closeness Summing up all view factors from a given surface in an enclosure including the possible se1fview factor for concave surfaces ZFU 1 because the same amount of radiation emitted by a surface must be absorbe J Reciprocity Noticing from the above equation that dA dedAde cos5 cosBf7lrfdA dAj it is deduced that Alli AJFJI Distribution When two target surfaces are considered at once EVM additivity in the de nition Composition Based on reciprocity and distribution when two source areas are considered together If A k AJFJC AJ EJJrEk based on area For an enelosure formed by Nsurfaces there are N2 vlew faetors eaeh surface wrth all the others and rtselo But y N1F12 of thern are rnolepenolent srnee another NltNel ean be oleolueeol from reerproerty relataons and N more by eloseness relatrons For rnstanee for a 3rsurface enelosure p 3 of t n th r 3 ean be obtarned from 4444andtherernarnrng3by 241 1 WITH SPHERES Patch to a sphere Frontal ase Vlew factor Plot From a srnall planar plate faclng a sphere ofradws up p 396 frame DA DJ ngorh2F1f14 U 2 4 m 8 2 Levd Case Vlew factor Plot From a srnall planar plate 1 1 l level to a sphere ofradws Fla amm 03 ata stancerrom F 5 eentres wrth hEHR wrth x If 71 m l 2J3 02 Fu m aari Jhel D 2 eg for FlFU 029 Case Plot Vlew factor elf Mlt7127arcslnlh r e Mosgt1 F 7 cos5 n r f 1f not l l hEHR the trltrng angle g F 7cos areeosye xsln ellryz 7r 1 y 7r x wth szh rl y FAAA nl Xcot Disc to frontal sphere Case Vlew faetor Plot a else ofradlus R to afrontal sphere of dlustata s H between centres ltmust 7 2 be HgtR mm hEHR F 2392 1 and 1R1 RI eg fothH LFlFU 586 H From a sphere of radius R to a frontal else of in 1 u n F a Fm e u n n 1n 3 g forRFH and R191 F120 14s Cylinder to large sphere Case View factor Plot Coaxial go 1 s arcsln s Fe e If 2 asmall cylinder We 5 2h 1h Ls Perpendicular gm i M 4 1 xExdx F 77 7 u u 7391 n Jlrxz Fl mm elliptic integrals E0 1 Mus m a Tllted cylinder U gas 1 25m5 I lizzdgda 12 14 16Hl8 2 F12 I f 4 7 M be with os5cos sln5sm cos M l quota quot ag2 Cylinder to its hemispherical closing cap Case View factor I Plot a nite cylinder ce 3 be the base and surface 4 the virtual base ofthe hemisphere R R eg for RH Fil038 Fiz031 F21031F 050F3019 M4162 Faz038 F34038 Sphere to sphere Small to Very large Case View factor Plot From a small sphere of to larger sphere ofradius R2 ta dis ance Hbetween 03 centres itrnust be R2 F 1 1 7 Fugi but does not depend on 2 h 039 R with hairy 39U 6 for HR27Fu1Z l 12 14115H13 z i E H Equal spheres Case View factor Plot From a sphere ofradius 1 Rto an equal sphere at a up s ance l Ibetween 1 1 a 0 6 centres it must be F2 7 17 17 7 I3 U4 Hgt2R with thR 2 h 39 n1 f H2R F 0057 n e g m 2 2 22 24 26 22 3 hi R P View factor Plot Between conc 39c m spheres of radii Ri and F 71 a R2gtRi with ERiRzlt1 1 F a HF 21 3 4 Fz s o a eg for r12 521 F214 refs4 U El 132 M 16 LS LU R1 r R2 Hemispheres asc V1 cw factor Plot F ahemlsphere of radius R surface 1 to 11s F211 base circle surface 2 FlfAleAl Z 27111727 12 F From ahemlsphere of 1 32 radius R to alarger M q conccnmc hemisphere of p cad s RagtRw1m no 2 1eR2 gt1Lcnlic F 1 F n4 closmgplanar annulust 3 2Rquot 3 R 39 63 n2 ul39face3 W V R R2 1 1 a a 1 1 5 777 JR 717 R 72 arcsln 7 p 2 7r R j e g focR2 Flaw 93 Fai0 23 Age U7F310 05 sto 95 7230 36F220 41 From a sphere of radius 7 Fl239 ii ip R to alarger conccnmc Fflep zz F 17 M F hemlsphereofradlus 2 R FM 214 R2gtRlwlth1 R2Rlgt1 well 4 2 6 Letthe enclosurebe 339 11 Wl iwizhcsmgj M s u AR J 1 2 3 R 4 5 772 OR eg forR FlflZ Fai14 R1F12 R1 7230 34 41 W TH CYLINDERS Cylinder to large sphere See results under Cases with spheres Cylinder to its hemispherical closing cap See results under Cases with spheres Concentric Veryclong cylinders Case 1 View factor Plot e F Between eoneenme m mte cylinders ofradll R1 and R2gtRl with Fl21 F2lr Farm n 11 m 15 12 Ln 7 eg for12F1F1F2112F2214 1 2 Concentric veryelong cylinder to hemiecylinder Case View factor Plot Between eoneenme m mte cylinder ofradlus F Fm F29 F 3 Si R1 to eoneenme hem F 7H7 7F cylinder ofradlus Rpm f 2 2239 F 395 4 l Wth VERlR2lt1 Let the F J12 I arcsln I L4 v enclosure be 339 7 If A e g forF12FF12F2 OR FlF12F2FU 22 F 1 Wire to parallel cylinder infinite extent View faetor Case From a small minute long cylinder to an m mte long parallel cylinder 0 radius R with a alstanee Hbetween axes with hEHR H 1 aesth Fa 7 e g forquot11Y Ara2 Ln 12 15 F12 n 4 n2 tn ln l2 14 L5 L2 u H Parallel veryelong external cylinders View faetor Case From a cylinder ofradlus l Rte an equal cylinder at M adlstaneeHbetween 2 7 3 centres ltmustbe F 7 h 4 h2quot 5 h F Hgt2R Wlt hJiR 2 39 Zn 2 n eg for H2R 71212717F0 18 2 2 H4 5 I H 1 a F Base to finite cylinder View faetor Plot From base 1 to lateral surface 2 m a cylmder ofradlus R and helght H F 7 p F 7 7 p 112 3 wlth ERH 2r 22 3 3 FM Let 3 b are opposlte m 53 ase 2 4quot 171 U1 vmh p i n 2 39 I l S e g forRH FlFU 62 7210 31 R 0 0 Equal nite concentric cylinders Case V1 ew factor Plot 1 h 1 l 12 Between mte concenm eylmders ofradws R1 and R2gtRl and helg H wlth hHRl and RR2R Letthe enclosure be 339 For me mslde om39 see premous ease H 2 R f 39 R 1 R h MR 74 R 2 1 7r fsarcsm arcsm lrFJJris 71 UV R11 F 16 2 1 14 e g 1erer and H2Rr FIFO 64 2 1 1720 34 Age 337311 43 Fife 23 39n n 1 2 2H4 5 fr W TH PLATES AND DISCS Parallel con gurations Case Vlew factor Plot Between two identical rte p a11e1 squat platesof M side L and separation H F v W m w nz W arctaniiarctanw H X n 2 2 m w E e H F10 1998 H Case View factor Plot Fz 1n szwttn 7M q 2 2 7 From asquareplate of W1 W2 side W to a eoaenal q E x2 2y2 2 square plate ofsxde W at separation H with W2 th av W2 Wt wWHandwa WyH x v 521A xarctaniiyarctani n n W W 2 t metanieyaetanz H v v Case Viewfactor Between all faces m the S E a and the extemal sxde of a From an externalrbox face eoneentne cubic box F 039 F x FE y F n faces 77879710711712 0 1131 F71 VF 14W me face 7 to the others Frlez4FV lrz4FHUF 0 in Q Fm 0 n39 v F7 with z gven by A genene outenbon face 1 audits correspondAng face 7 tn the lunar box have been chosen 17 2 zE 21n5sz q 47m 2 2 p2 2372 1 11 1812a18a2 q 272 0 2 w 5211 Zarctaniiwarctani u u 2 w 2are1anrrware1an7 v v and eg for a 5 F1 6 17131110 17114116 F15 16 F170 20 17154101 F1F0 FLIDZU 01 711 01 F1120 01 and 17711179 Ffo 05 F F714 05 Ffo 05 man 05 cho 7750 730 F71F0F7110F71r 70 Nouns that a s1mp1e mterpolauon 15 proposed a foryEFn because no analy cal 501mm has been found pm Case V1ew factor P10 1 2 2 7W 1 Between parallel equal W X m rectangularplates of 5123 n3 1 W1 W2 53 arateda x x 2 1 77 1 V dutance H W11 FWlH X y a any a aquot X F 396 z andFWzH v4 1 2yxare1anlearecany 1 U 5 x D yu 1 n 1 2 4 5 W2 mm 5211 and MEJHM X 1 H 1 I F r r 7 0 V Equal discs Case V1ew factor P101 Between two idenueal and se H 1442 H F 17z 2 R R e g forF1F120 382 H Unequal discs Case View factor From a else ofradlns Ri to a coaxial parallel else of radius R at separation H with RiHan FIX martinwag and e g ferriPF1F120 382 Strip tn strip Case View factor Plot Between two idenaeal parallel stnps ofwidth W and separation H with HW F 1hzrh e g forh1 Fi20 414 n in 12 n4 up n8 in H Case View factor Plot From a finite planar plate atadlstancthoan 505 In nite plane tilted an Front Side Fla 7 angle 8 i Baek side F 2 r e g for 3714 45 5 Flzfmfo 854F12hxk0 146 l Patch in disc Case View factor Plot From a patch to a parallel and concenm else of D8 radlus R at dlstance H 1 F 16 wlth hHR FIX 71 h 12 m 02 R eg forh1F120 5 1 15 2 H Perpendicular con gurations 1mm Case Vlew factor Plot From a square plate of 1 1 1 112 1mm Wto an adjacent Wang m mng fln n rectangles at 90 of 1 D39 helght H wlth hHW W11 hi th and 1a F12 4 M2 039 0 H eg forhwFlfgtl4 395 i H vS 1 fork 1F1F0 20004 kw W F r 0 M Re 0000 uaee ase Vlew factor Plot Between adjacent equal 1 1 rectangles at 90 of F12 2 Wm g quotEwan helght H and wldth L 18 1mm hHL L1n F 05 411 4 1 04 1 111 02 0 H mm h 21hzand517 0 l 2 2H4 5 h 1 H I F r 1 0 0001 Re 0000 mate Case Vlew factor Plot From a honzomal L wth hHL and wWL H F e i h aeelan 1 warctan i 7rw h w e Jh w araan W1 01 lh luf h2w2 V h lh w 1 wth a l b w lh w I F r w 0 0001 From nonradjacent reetangles tlne solutaon ean be found wrtln Viewr AM A1 faetor algebra as shown 111 Him 411 A FmorXFr a nere Am 1 A mew Strip tn strip Case View factor Plot Adjacentlong stnps at 2 D8 90 tlne rst 1 ofwroltln F 1 h 6 Wandtne seeonol 2 of 2 F12 4 dLhH wrtln n2 n H eg FH HW e 0293 U1234S W 39 2 E W quot lled con gurations View factor Plot Adjacent equal long F lrslng 3 stn s at an angle a 2 F no N n4 W n2 n W u an on 9 12U15U18U e W Triangular prism ase Vl ew factor Plot Between two sldes1and 2 of an infinite long man 1 nsrn fsldes 4441713 L zn F 7 it Ll LaandLsWltln H 2 M We hLaLr anol agtberng tlne 2 F12 4 We anglebetween sldesl 1h 1h 2hcos 2 m and 2 H Um n LS in 15 2n L E e g forh1 anol gem Fife 293 L References Howell JR A eatalog of radiation con gurauon factorsquotMcGraerlll 1982 Baekto Spacecraft Thermal Control


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