CKEMtCAl. E~tNE.ElUNO FUNDAMENTJJ.S Vol. '2.fl'IIo. 2 ISSN ro.-3-0966 23 .----'----'-----------------~._---

•

1be Effect of Partial Baffles on Natural Convection in an Inclined Rectangular Enclosure PART I. Experimental Observations

Abstract

Complete partitioning wilb boneyoomb-Iike struetuIes bas previously been proposed to reduce heat transfer by natural con­vection. at the expense of direct oonduction through the Struet\I.fe. in Ihe thin rectangular enclosures used for solar colleclors. 11tis paper presents the results of a sludy of the use of partial ballles for this purpose. 1be heat transfer rate was measured in glycerol using heal !Iw< meters in both the heated and cooled surfaces. and three-<lUnensional sueaklines were photogyaphed using tracer particles for a Rayleigh number 012 x 104, six ballle-ronfigurations and a series of angles of inclinarion aboul!be sboner dimension of a 2 x 1 x 1 enclosure, heated and cooled on the opposing 2 x 1 surfaces. AU 01 the ba!fle-ronfigura­lions pa-oduced oblique strea.klines and decreased the rate of heat transfer. but no single size or configwalion wa.i besl for all iDclinarions. 1be two heal flux meters provided a measure 01 the nel heal OW< to the fluid from the Plexiglas sidewalls. A finite­difference solution lor Ihe same behavior is oompared wilh these result< in Pan D of this paper.

Synopsis� ness 016.35 mm. The tes' ceU was surrounded Ialerally by a vacuum chamber. Copper plates with dimen>ions of 254 x

lbis paper apparently presents the first results for the eflect 177.8 x 19.05 mm served as the lap and bonom 01 the en­of a partial baffle DOnna! to the heated and cooled surfaces closwe and also of the vacuum chamber. Waler jackets ofan iDclined rectangularenclosure. Streak.Jineswere photo­ were attached to these plates to maintain thc:m at differ.enl. graphed and heal transler rales were measured lor six bat­ near-unilonn temperarures. The periphery of both oopper Oe-r0n6gurations at a series of inclinations of the enclosure plales was milled our to provide space for a silver-roated. abow the shorter horizontal dimension. front-swface mirror. The purpose of tbe-:;c mirrors was to

minimize radiative beat transfer betweeD the vertical sur­The internal dimensions 01 !be test enclosure ....re 63.50 x fa<= of !he test end","", and the portion of the copper31.75� x 31.75 mrn, the latter being the height, giving plates comprising the top and bonom surf.... of the ..peel ratios of 2/1 (width!heighl) and 1/1 (depthlheighl). vacuum chamber. Tbe wrtial sides of !be tesl ceO ....re Plexiglas with a thick-

Introduction and radiant inlerchange between the partitions and the en­closing surfaces were taken inlO aa:ounL

Tbe wort reported herein is part ala oonrinuing investiga­ Emery [51 found thai a central, wrtical. parJaI baffle in a tion 01 narural oonvecrion in enclosures. with the primary ralI, lW<>-dimensional enclosure, heated and cooled on the objective of reducing heal losses across Ihe air film in solar opposing vertical sides, had a negligible elfeCl on the flow ooUector>.1n reoenl prior wort [1. 21. il was found thaI non­ field and on the rate of heal uansfer. This geometry wn uniformities in the sucf.ace temperatures generally had an chosen to simulate the cooling cbanllel of a nuclear reactor. adverse eflect, i.e., they increased the rare of heal transfer. His results are nol surprising because the baffIe, although The specific objective 01 the currenl work is 10 investigate extending over 90,"0 of the height of the enclosure. was in experimenlally the effect 01 partial baffles in suppressing the stagnanl cenlral .:ore 01 the fluid. convective heat transfer. Prior work on !be effect of battles

Probert and Ward [6J and Janikowski cl al [7) in'estigated on natural oonvection in encloswes has generally been for the effect of short baffles extending ~rti<ally from the in­other applicalions and amditions. Complete partitions (h0­sulated lap and bonom waUs of !he same type of encl",ure.neycombs) of poorly conducting material, perpendicular 10 The baflIes ....re oonslruCled oflhin Perspex sheel or oopper and extending aU !he way between !he high and low tempe­gauze. The solid ba!fles were found to be more effective than ralUre surfaces, have been proposed and utilized for solar the por0U:5 ones, particularly when the upper baffle wascolleClor>. Cane el a1. [3) and Aroold el al. [41 found ,hat placed near the cold wall and Ihe lower baffle near the hot existing correlations for single enclosures were applicable wall.for the individual cells if conduction along the partitions_ Several, recent inves.ligalions (e.g.. 18) and [9) are concer­ned wilh (he effect of partial room-Jividers on nalural con­

• Mobil Research. and nc...elopment CorporatiCin. P'aulsboro. vection; but the boundar~.... condiliuns are not relc ... ant 10 NJ. CSA Ihis im,·cstigation. HO\l,e ..er. !he: following Iwo more: d()~ly

•• Dep3r1m~n( of IndU5lrial and Mechanica.l Engin~ering. rdall:d P3~PII have arr~~red ,inee (hi" inn: ..lig;l!inn u:;.1'>

Ola..a.ma L'ni1o'entlv. Oka1/.1m~. Japan complctl·t.i. Ch.mg 1.:1 at 1111\ 1.1.>i,.:d 1\l'\i~c:-Jilf..:r~nt:C: cakula­••• 1bc ·Cm\..~rsiIY of ·PennsYh'ama. Phiiaddphia. fA. 191(~. lions 10 JCIl:rminc the lamin~r tll)\\," palh:rn.. am.l ratl: ofUSA

24

Fig. I Close-up or the tcst c:a..ity with top plate rcmo..·cd

Fig, 2 Scbematic dra"'io& of the lest cavity. rn Copper plate. mwateT ja<lce~ rn front-smface ltIirro<.1!l beat-Ott< metel, ~ vacuum chamber. lID le$t cell, and rn boffIe

heal transfer in square ebannels, heated and rooled on lbe opposing vetticaf <ideo, with centrally located partitions of one-tenth width and one-quarter height auacbed to both the t""tom and top insulated surfaces. Tbeir calculations were lor a Rayleigh number 01 6.55 x 10" and a Prandtl number of 0,686, OIId include incrementally tbe effeC15 of surfaa! and gaseous radiation, Winter.; [11) canied out <i­milar two-dimensional calculations for an enclosure with a width-lo-heighl ratio of 8/5 and central, brass panitions in either the insulated top o. bottom surface with heights of 1/4, 1/2 :and 3/4, and a width of 1/16 lhe height of the en­dosure. These c:alculalions were for a Rayleigh number of 3.75 x 10" and a Prandtl number 01 0.7. His compUled

streamlines are in lair agreement with those pbotographed� by Dubury (12) al a slightly diffmnt Rayleigh number,�

. using smolee injection. His photograplu 01 the circulation� patterns revealed some zones of recircWation in addition to '!be pre<ficted ones. and also dissymmetry lor the upper and lower locations of the partitions. 1bis dissymmetry is prob­ably due to ....t losses, ..hieh were about 4O'Y. 01 that transferred. Calculations were also canied out for other aspect ratios and lor partitions 01 different condueti>ities. Insofar as the Nussell number is concerned, the panitions were found to bcl1avc as an infinite conductor, even for a conductivity as low as that 01 air.

Tbe effect of panial baffles has apparenlly nol been '..'esri­gJlted lor enclosures ....ted from belo.. or inclined. or [or three..ffimensional convection under any conditions.

Herein, experimenl3l tales of heal transfer and photo­zraphs of streal<lines are presented roc threc-dimen<ionaJ natural convection in an inclined 2 )( 1 )( 1 enclosure wim a single baffle of various sizes and locations. Theoretical results lor this problem are presented in a companion paper [13J and compared with the experimental result>.

Experimental Apparatus

Tbe e.perimentalapparatus, as sho"'ll in the photograph of Figure 1 and the .leeteb o[ Figuze 2, consisled of a test etl­

closure inside a vacuum chamber. This apparatus was ana· ched to a rotalable disle and an inclinable platfonn. The test ceO could thus be eslablished al any inclinalion up 10 ttl2 rad and at any rolation. For inclinations from 1112 to rr rad the cell was invened. fn the work reported herem, the tesl enclosure was inclined only about its shorter dimension. The eqlJipment was operated in a oonstant-temperature room to minimlze the effect of ambient changes..

The internal dimensions of the IC$t enclosure mJ were 63.50 X 31.75 x 31.75 nun, the latter being the heigh~ giving aspect ratios of 2/1 (widthlheighl) and 1/1 (deplhlbeight). The vertical <ides o[ the tesl cell and vacuum chamber ~

were of PIe.iglas with a thickness of 6.35 mrn :and 9.52 mm, respectively.

CHEMICAl. ENGOl..RING FUNDAMENTAL< Vol. liNo. 2 ISSN 0723-0966

Copper plates rn with dimensions 01 254 x 177.S X 19.05 mm setVed as the lOp and bottom for both the CD­

dosure and the cbarnber. Water jackets rn were attached to lhese plates to maintain them at differen[. ncar-unifonn temperatures. Two bafIIes were inslalled in eacb jackel 10

belp minimize !be tempel1lture variarion over !be plales. The periphery of the copper plates was milled out, as shown in FIgUre 2, 10 provide space for a 3.175 mm-thick, silver­coated, fronl-surface mirror (J]. The pwj>05e of these mir­ron was 10 minimize I1ldiative beal achange between the .erticaI surfaces of !be tesl enclO5llre and !be portion of !be copper plates <XlIIlprisios the lOp and bottom surfaces of the vacuum cbarnber.

The plates were also milled out centrally, as shown. 10 pr0­

vide for beat Oux meten I!I covering the cutise borizootal surface of !be lesl eoclo5ure. The beat Oux meten were Model AB transducen made by the IDlematicnal Thermal Iostruweol Co. Tbeir output was 213,"V/(W/m') and therefore did DOC ~uire amplificaticlL The heal Oux meten were glued to !be respective copper plales. The tem­perature of the Ouickootacting surface of each beal Oux meIer was measwed with a copper-cooslaDtan thermo­couple. The four lead wires from !be heat Oux meIer and thermocouple passed UDder !be inner and through !be outer raised rings of the copper plales.

The outpul of the Ihenoocouple from each meter, their dif­ference. and the OUtpul of !be two beal Oux melen them­selves,...,e periodically displayed 00 a Keilhly 160B digital multiIneter and recorded CD a Keithly 750 prinler, using a manual !bennocouple switch.

O-rings, as sboW1l in FlgUl"e 2, ""re used 10 seal !be vacuum chamber from the test enclosure and the surroundings. A pressure of 1-2 Pa was mainlained in this cIIamber by cooti­DUOUS ope;.alion of !be ncuum pump. and was mentioned with a Piraoi gauge. Al Ibis pressure, beat transler by ther­mal conduction in air is less thaD I 'Yo al thaI of atmospberic pressure.

AD infinite number of <XlIIlbinations of baffle widtID, heights, thkl<nesses, Jncarions and materials are possible. The bafIles used in these aperiments were cuI from the transparenl plastic sheets used with overhead projectOR. They had a lhickness of I.S mm and were attached with .....u Slrips of two-sided ScolCb-brand adhesive tape. Seven ronJigul1ltions were used as sboo-n in !be insel of Figure 5.

The experiments .... inlended primarily 10 simulate natural convectioo in air. However, prior work bas shown thaI na­tural convection in air is approximately !be same in <limen­sioaI... ternlS as for bigh-Prandti number Ouids. Therefore, 99% glycerol (Sigma O1emical Co. No. G 77-57) was chosen as the working Ouid because of its grealer density, thermal conductivity and visrosity. The grealer thermal conductivity and density minimize the relative effects 01 conduction through and aJong the side wall<. The grealer visrosity and density provide a larger tiIne-conslaDI and re­du<:e the sensitivity 10 external perturbations. The grealer density also impedes the diffusion of the suspended par­ticles used for visualizarion. The properties of glycerol were taken from N....man (14).

The glycerol was introduced into the test enclosure through a hypodermic needle, passing horizontally through com­pression fittings with rubber inserts in the Plexiglas walls as indicaled in Figure 2. The displaced air es<aped Ihrough a second needle. Once the cavity was filled. one needle .....as closed and lhe other left open to allow for thermal expan­sion and contraction of the glycerol.

25

For visualizariOll of the Bow, a suspension of aluminium flakes in glycerol was injected at various deplhs by means of a smaller hypodermic needle passing through the glycerol injection needles. The aluminium flakes align with the shear planes of the Oow, promoting coherent reflection of the in­cident illumination so that dear pictures of the stteaklincs can be obtained.

P!Iolograpbs of !be aluminium flakes ""re taken with ASA 400, black and white film, using a 35 mID Penta>: cameta with an extension tube. A narrow strip of Iigh t from a 35 DUD projector was used 10 ilIuminale selected regions of the fluid

Experimental Procedure

The two heal flux meten were finl calibl1lled in the !WO possible juxlapositions by comparison with the theorelical heal Oux for pure thermal conduction (with the higher-Iem­pel1lture plate A on lOp). The results are shown in Figure 3. &cause of the lower scan.er and the smaner correction ( - 2%), heal Oux meter No.2 on the highcr-Iemperalure swfaa: ,..". used fo' the primary results presenled berein.

The waler baths and jackets were operaled to produce lem­pel1ltures of 27.75 ± 0.05·C and 31.S5 ± 0.05"C on the Ouid-<ontacting surfaces of !be heat Oux meIe". These tempel1ltures correspond 10 the upper and lower surfaces, respectively, in their initial uninclined position. 1his tem· perature difference produces a Rayleigh number of -2 x H)".

Twelve 10 !Wenry-four boun were required 10 eslablish a steady state at each inclination. The flow panem was 0b­served al six inclinations, using fresh glycerol for each run. After the srcady state was attained, alwninium Ilakcs were introduced Forty more minutes ""re required for the Oakes 10 establish good streak!ine pallems. By 90 minUles the aluminium flakes were too disponed 10 reve<d dislinct strealdines.

,...

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'" .; G.l ~ ...... L.,U....tat ..... lrr (. .... 121

a.l'

0----0 .... I _ C..d Or, ...ll:lI:O" 1

"

, '---~--~"---~--20~~~-~-~,

6T/(K}

Fig. J Calibration of the two hear tltU meters in two hori­zontal orientalions

••

Heat Flux Measurements

The Nusselt number is defined as the ratio of heat trans­ferred by thermal conduction alone. For these experiments

(I)

where

q, = theoretical heat OUll due to lhermal conduction, W q = heat OUll from meter, W liq= COITection factor for heal OUll meter, as delermined

from F'8W"e 3, W

Figure 4 is a plot of Nu as determined at the surfaces for no balDe. 'The vahle determined at the lower-temperarure pla­Ie has a much higher muumuu at no indination than at ./3 rad. 'The reason for this anomaly became evident when the streakJine experiments were conducted For the horizontal orientation. the stable circulation pattern consists of two roU-ceUs with their 3lles parallel 10 the shorter horizontal dimensioo. Theoretically, for a ~uid· that conforms to the Boussinesq approximations, the probability is equal for cir­culation in either direction (upward or downward in the central plane and conve""ly at the eDds). In these experi­ments the eircularion was always upward near the eenler of the 2 X 1 plane aod'downward nelr the distant waUs. and iIIdeed could not be iIIduced to circulale steadily ill the 0p­posite direction.1bis preferred m9de of cireuiation, as 0p­

posed 10 ckl'...oward Oow ill the eenter, is presumably cou­"'d by a slightly ~ater heat OUll density near the midplane than at ODe end ""'ing to the presence of the lead wires at that end.

Since the PleJ<iglas endwaUs bave a higher thermal conduc­tivity than the Ouid, a nel amount of energy enters the Ouid from the vertical waDs and a greater total beat OUll is trans­ferred from the Ouid to the cooled, horizontal plate than eaten from the heated horizont;U plate. If the Ouid eircula­led downward at the center and upward along the endwalls. energy would be transferred from the passing heated Ouid, and the heat DUll from the Ouid to the cooled plate would be less than thaI from the heated plate to the Ouid.

r----.----------------~

,..

,.. Nu

" ,..

• II.., .. JIIlIle

• t...... ....t. "�

"� .. •"_--=-.-""~o-~...-~_"_=., --c'-,.o----.;,.c-~.t.:.,.-.L=-. -".­

"itl Tt, e- ru_d -.J

For inclinations just beyond thai for the minimum in the heal Dux, the fluid moves up along the inclined heated sur­face as a single roll-cell, and the elevated endwaU has a lower temperaNre and the unele\--ated endwaU a higher temperature than the passing fluid. thus minimizing the net rransfer from lhe endwalls to the fluid. As a consequence, the Nussell numbers for the healed and cooled surfaces dif­fer insignificantly for inclinations greater than 11/9 fad. 'The Nusselt number determined from the healed plot< is be­tieved to be more representative of the idealized ca.« of non-<:ondueting sidewalls-than that from the cooled plale or their average, and is considered exclusively hereafter. 'These values from the heated plate are also in beller agree­ment with prior measured and computed values for the lim­iting case of no baffles.

The Nusselt numbers determined from the heat OUll meIer on the higher-temperature plate are plotted in Figure 5 for the indicated configurations of the haffle. A minimum in the rale of heat transfer """"" between 5111180 and 10111180 rad and a maximum between 40111180 and 6Olr/ 180 rad for aU configurations.

Case I, for no baffle, sho.... the highest rate of beat transfer al aU angles of inclination. 'The one-quarter baffle, Case 2, produces a significant reduction in the Nusselt number at aU inclinations, but the least of any of the baffled configura- . lions for inclinations ~ater than 4../9. Comparison of Cases 2, 3, and 6 indicales thaI the extension of the bclfle reduces Nu for aU inclinations beyond 20111180 rad. For lesser inclinations the optimal baffle-width is inclination­dependent.

.. " €Je... ,;. a... • • : . " • •

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Fig. 4 Measured Nussell numbers on heated and cooled Fig. 5 Experimental Nus.«lt numbers at various angles of plates for an unbalOed enclosure inclination and bafOe-configurations

6

27

Locatioa of rbe baffJe near !he oIevared end, as in Ca>e 4, reduces rhe fare of hear transfer, whereas location near !he unelevared CIId, as in Case 5, increases !he me, relative to Ibe cenlIlIi location of Case 3.

Case 7, wilb a baffle of half-heigh!, complcr<ly across !he enclosure. generally reduces the NlW>elt Dumber more than !be other configuratio.... for all inclinatioDS grealer !han 15../180 rad

1r is cooclU<led !hal !he heal Dux can be redua:d by rhe in­slallatioD of a baffle, and rhat !he optimal si2Io and locatioD of !he baftJe deperlI! oa !be angle of inclination.

Photographs of Streaklines

FJgUCes 6-38 are photographs of streaklines for !be .....eD amJigurations listed above. The vi....ing angles are indica­red Bl !be top and !he speciJie fields of iDuminatioa below !be photographs. The apparatus bad to be c:Ieoned OUl afler each run. Heooe, a more limited Dumber of_gles of incH-· natioD were investigated than lor !he heal transfer rare. 1Wenl)'-foUJ' hows .... allowed for !he eslabishmenr of a steady Slate bef"'" injection of !be aluminiwa rraoers. Be­cause of !be copper plates, photographs were possible only from !be four sides. Therefore, a skelCh .... alI15trUCled of !be presumed lOp view of the stIeakIine••

Case 1

FJgUCes 6-8 sbow slIeaklines for DO baffle. F<>r DO inclina­tion, as sbowD in FJgUCe 6, there are two roU-cdIs, symmet­rical about the shorter vertical midplane, each composed of two balf-oells, symmelrical aboul !be longer toerticaI· mid­plane. The axes of these cells are parallel to the shorter borizoIIlaI dimension, wilb upDow in the midplane, as st.elched.

For an inclinalioo of 4./180 rad, as shown in Figure 7,the roD-oeD moving up rhe heated surface iDcrea>es al !be e>;­

pense of !be other. Al an inclinatioD of 8.1180 rad, as <bown in figUre 8, !be weaker ceO has disappeared, and the circulation amsists of a single 2 x 1 roU-<:d moving up along !he inclined heated swfaee and <Iowa along !he cooled 5UIface.

Case 2

"'JgUCe 9 shooo.. !he motion lor the quarll:r-baflk: with DO in­iinatioa. ThelDOtion is very similar to rhal of Figure 6 for 10 bafIle. However, for 4./180 rad of im:Iination, as slKlWTI a FJgUCe 10, !he axis of the roU-c:U al !he incIiDed end has >eaJIIlC quite oblique and !he upper roD-oeU esllends into be lower half of rhe enclosure. Al 8../180 rad of mclina­iolt, as shown in Figure II, both of the rear loa1f-c:lls are ,blique to lhe shoner horizoDtal dimension, and the fronla! laJf-c:lls appear to have roa1e=d. At 2OIr/180, 600/180 nd 900'/180 rad, as shOWTI in Figures 12-14, !he single ronlal roll-eell is .imilar to tMt of CJse I (or large inclina­io.... whereas the rear half-c:lI. have also coalesced to a ingle roU-c:lI ..ith rhe fonn of a rontinuous typewriter ;bbon.

Case 3

1bis configuration was pholographed in Japan with the e>;­

perimenla! setup described by Owe, et al. [15J." should be DOted rhat the elevation in these pholographs is on the lelt instead of on the right, a1so thaI the circulation is downwa<d al rhe cenrer. Strealtlines and .ketches for inclinations of 0, 5../180 and IOrr/I80 rad are .hown in Figure 15 and 20u/ 180,45../180 and 90,,/180 rad in Figure 16. For DO inclina­tiOD the- circulation is seeD 10 be similar to rhat of FJgur< 6. Al 5../180 rad rhe roU-c:U al the elevated end is quite obli­que and !he one al the other end bas rotaled ../2 rod. By IOrr/18O rad the elevated roU-oeU bas wrapped around the baffle. For inclinations of 45./180 and greater the axes of the two roU-c:Us OD rhe baffled side of !he enclosure and the coupled roU-oeU on the unbafOed side have become nearly parallel 10 !he shorrer borizonlal dimension.

Case 4

For the bafOe location near the elevated end, as shown in FJgUCes 17-22, the circulalioo pattern is more complicated. E.'i.en for DO inclination the axis of Ibc rear balf-eeU al the elevated end is roughly paraJlelto the longer horiwntal di­mension, while the associaled Cronla! half-c:U is in front and OD !be downslope side of the baffle, bql wirh its axis nearly parallel to the shoner horizonla! dimension. Al incli­nations of 4./180 and 8./180 rad the axis of the upslope half-c:lls become oblique. At 2Orr/I80 rad!he two upslope -h4lf-<>ells appear to have coalesced 10 a single roIJ-oeU with its'am in the longer horizontal dimension. and the bunlal Mlf-<eU on !he downslope side bas expanded to 2 x I roU­ceU in Croul of the baffle. At 600/180 rad !he roU-c:U OD !be upslope side of the baffle has rolaled .12 rad 50 that all three axes are paralkl to the shorter horizonla! dimension.

.,'This pattern persists at 90../180 rod.

Case 5

For the baffle location near !he unelevated end of the eD­doswe the circulatioa is agaiD very complicaled, as jjIUSllated in Figures 2>-28. For no inclination rhe roU-cells are remarkably oblique, as besl indicated by the skelCb of the presumed do.onward v;.w. At 4..1180 rad rhe pattern is further developing. bUI al 81l/180 rad has become similar to the mirror image of FJgur< 20. By 20u/180 rad rhe roU-oeU on the do.....5Iope side oflhe baffle bas rotated ./2 rad, and at an inclination of 9Ors/lBO rad the roU-cells in front of and below !be baffle appear to be coalescing.

Case 6

The circulalion pattern for the tbree-qlWter bame is shown in Figures 2<),,34. For 00 inclination the circulation is .ymmerricaJ abour Ihe baffle bUI the rear half-oells have approximately Ibe length of the baffles. For an inclinarion of 4,,/180 rad the half-oells on the downslope .ide have be­rome stronger and those on the upslope side oblique. This panern persists al 101l/180 rad, but ar 20./180 ",d lhe single frontal cell has the configuration 0' a continuous type""Titcr ribbon, as previously noted in Figures 12-24, and this paucm pe~i~ts at 90711180 rad.

CIII:.~IC"L ENGISLI:-IUNG FL'""DA"4Eo,;TAL5 Vol. 2/NO. :2--------------'===

Case 7

The baffle of full·width but half·height results in a some­what different pattern of circulation on elevation. as might be expected. 1be panem for no indination is similar to that 01 Figure 6 and hence is not shown. The pbotognphs lor 6../180, 1000/180, 40../180 and 9Olr/180 racI 01 inclination

AT"

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Fig. 6 StreakIines for Cas<: 1 (00 bafile) with DO inclina· lion

aA- J>:~ •• ,. 'SIDE

:' ,./WI'" 4r fRc.tIT l b) ,op

(0)

Ie' ....'

are, however. shown in Figures 35-38. At an inclination of 6rr/180 rad both 'oll-<:<:lIs have become highly oblique. At IOrrl180 racI the two rear and Ihe two frontal hall·cell; ap­pear 10 be coalescing, and at 40,,1180 rad and 90,,1180 rad a single continuous type'MoTirer-ribbon pattern is very evi­dent with symmetrical frontal and rear half-<:<:lIs.

Lb/Y:.LX

4- FRONT

101

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,t.v"','"lI!-:JiIl G.ooQ;~

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Fig.7 Streaklines lor Cas<: 1(no baflle) with 4ul 180 racI 01 iocIination

(0) (b) Ttl" vIEw

Cd) REAR t.) SlOE It) SIDE 'flEW

Fig.8 Sncaklines for Cas<: 1 (no bafiIe) with 8..1180 raclol Fig. 9 Slreaklines lor C.ase 2 with no inclination iocIination

29

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F". 10 StreaIdi.... for Case 2 with 4../180 r.uI of in­ Fig. II Slreaklines for Case 2 with 8../180 r.uI of in­clination clination

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(.) SIJe: "'(E""

Fig- 12 Slreaklines for Case 2 with 20rrfl8fl Tad of io­ Fig. J] $rreakJincs for C4.l.'Oe : with 6Orr/180 rad of io­clination dination

. E "GISH klo,;C; . Vol. 2/No. :!.30 CHBtlCU S .. _Ft.:SUA!\.fE!'oTAU _ _ __

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~ 1 f indinarioa Fog. 14 ,,-- 2 with TIn. tad 0Streaklines for ___

1180rad of InclinationIOn SO

IS Streaklines for Case 3 with O. STIllSO aDd 10../1~.of indinatioD

(bl F,..., Vi_ .�

4S",/180rod of Inclination�

....~11td ft'IlfJ(bl S'd. V_I ~(O}F,.... ' Yi_ .

9Onlt80rod of Inclination

Slreal<Iines for Case 3 Wl'th 2Orr1lSO, 4S../180 aDd Fig. 16 f iDcIinatioD9OTIIlSO rod 0

JI

r.,: 18 Streaklin.. 101 Case 4 wilb 4,,/180 nd of in­clinatioD

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tlr FROMr

(a)

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r.,. 19 Stteaklines for Case 4 with 8,,/180 rad of in­c1inatioD

Ibl fOP (a)

(c} FRONT

Id)J"POHT

(r) SI:lE

Fig. 20 Streaklines fOI Case 4 with 2O;r1l80 rad of in· Fig.2/ Streakline' lor Case ~ .. ilh 60"/180 rad 01 in­clination clination

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Fig. 22 Strealdines for Case 4 wilb 901rliBO rad of io­ Fig. 23 Streaklines for Case S wilb no ioclin.tion dination

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Frg. 24 Streaklioes for Case S wilb 4..1180 rad of in­ Fig. 25 Streaklines for Case S wilb s..1180 rad of io­clination dination

33 CJmncALENGlHEElUNG FUNDAMENTALS Vol. 2/No. 2 ISSN 0723-0966 '-'--------~

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(d) SIDE.� VIEw = I (11"DE .... ,.,'" "'••,~,- - -~, Fig. 26 Slreaklincs for Case 5 wilb 20,,1180 rad of in, Fig. 27 Strealdincs for Case 5 wilb 6Otr/180 rad of in­c1ination clination

; " .... A ....

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r". 30 Streaklines for Case 6 with 4"/180 rad of in­ Fig. 31 Streaklines for Case 6 with 1<r.r/180 rad of in­clination clination

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Fig. 32 Strealdines for Case 6 with 201r/180 rad of in­ Fig. 33 Streaklines for Case 6 with 6Olr1l80 rod of in­clination clination

3S

A IIDE

(a) (bJ TO" VIEW

(C) SIDE 'tI!W

(d) FADNT YIE........ il....,;ncl:"Oft tINt rronU

Fig. 34 Saeaktincs for Case 6 with 9Olr/ [SO rad of in­clination

... lIE....

p. "9 ~ • .' _ SlDE :..

•' 110,.. ~ .. FJtO~

(a)

(c) FAo.. r

(d) ItEAR

., 1')"00

Fig. 36 Streakliaes for Case 7 with [Or/180 rad of in­clination

t ~ . -' SIDE�

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tJ., FRONT�

-lflQ ~ (a) (b) TOP

~ .'... .­~•. ~':W'. -,.

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(d) "00

Fig. 35 Streaklincs for Case 7 with 6,,1180 rad of in­clination

(e I SIJ€

Fig. 37 Slreaklines for Case 7 with 40,,/180 rad of in­clination

A !.1D!:.,. REAR

.. B'" 'OP FlllClI'lT

(a) IbhOP

(e) FRONT ldl ....

(ehlDE

Fig. 38 SlreaIdines for Case 7 with 9OlJ/lsO rad of in­dinatioa

Interpretation and Conclusions

The pbolOgr.lphs 01 tracer particles ~eal axnplex but highly stnICtw:ed panems of c:irculatioa due 10 DlItUraI am­\'CCtioa ill iDdined, partially baflIed, rcctangular enclosures. The rate of heat transfer across the enclosure is sbown to be related doscIy 10 tbc<e flow panems.

For a 2 x 1 x 1 rcctangular enclosure, with beating and cooling OD the opposing 2 x 1 sutfaccs, the cin:ulation for bcatios from bcIow ooosists of two symmetrical roD..,.,U. with their IUS panllcllO the sborter borizontal dimens;oa. These roD-<:dIs each oollSist of two symmetrical bait roll­ceu.. M the coclosurc is iodioed about the lesser horizon­tal dimension as an aDs, the roU-<lC!l whose motion is up­ward along the iodioed swfaoo grows ill size and strength .t the expense of the otbcr rolJ-ccU, which is opposed by the buO)'llI;t force and C\'elltuaUy vanishes. 10 Ibis """' ihc initial roD-ceIIs c:irculated upward at the ceoter and down aIoog the codwaUs owiDg 10 the slight DOD-isothermality of the surfaa:s- M • conscqucnce, the upper roU-<lC!l dimi­Dished and vanished.

The aw:rage rate of beat lraosfer across the CDclosurc .t first dccrcases with iDdination, then B'lCS through a minimum and increases 10 • maximum bigher than tbc va­lue for DO iodioation. This maximum is .ttained when tbc diagonal plane of the enclosure is vertical. FuWIy, the rate of beat transfer dccrcases 10 zero for an iDcIination of" rod, a>rresponding to beating from above. with DO circulation. 11Ic above dcsaiption of the cin:ulation and beat lraosfer is in amtotinity with pur prior obsoeI1lllnoos.

All of the baffle 5izes and locations which were tested in Ihis investigation produced obtiquc roll..,.,lls, particularly for low angles of inclination. As the inclination of 'he heated surface was iDcrea.sed to 71/2 rad the axes of circulation again became paraDel 10 the Ie.ser borizontal dimension.

All of the baffIe-configurations of Ibis investigation redu­ced the overall rate of heat =fer a' aU ang"'s of inclina­tion, presumably bc<:ause of tho obtique panems of Dow and the related dcaeasc ill the rate of circulation.

No one baffIc-amliguration was best for aU angles of incli­nation. For iDdH1alions from 2f119 10 fI rad increasing the height""d/or width of the baffle produced a monotonic de­aeasc in the rate of heat transfer. Location of a baffle of half-width and full-height ocar the elevated eod of the CD­

closure reduced the rate of heat Innsfer relative 10 central or lower location<. A baffIc of half-height and fuU-..idlh produced tho greatest reduction in the rale of beat transfer for aU inelinatioas grealer than flI9 rad.

The maximum reduction in the rate of hcallraosfer whicb was achieved with these baflIes varied from about 10'Yo at no inclination up 10 about 20% at 7f119 rod, and of oourse, dov.n 10 zero at fI rad. It is probable that oomparable reduc­tions C3II be achieved in enclosures of greater aspect ratios.

11Ic effect of the thermaloooduaivity and finite thickness of the Plexiglas eodwalls 011 the rcspe<:tive heat Duxes from the healed plate 10 the Duid and to the cooled plate from the Duid was fortuilously revealed by the usc of beal Dux metetS in both surfaces. For the ease of beating from below, the cooled Duid Ica.ing the oold plate picks up beat while Dov.ing down past tho eoowalls, whi<:h have a mean tempe­rature cquailO the average of the bot- and oold-plalC tem­peratures. 1be amsequence is that the beat lraosferrcd 10 the mid plate is equal 10 that lcavitl& the bol plale plus this ineremenL For the experimental appararw and lXlDdition. of Ibis study, tho beat 0... 10 tho oold plate was about 2.S'Yo greater than that lcavitl& tbc bol plate. U the _ails were perfect iJNllalOtS or vani,hingly thin, this incremenl would approach zero.

As the enclosure is inclined, tho roD-c:clI at the ck.-ated end dccrcases ill size and rate of circulation, and eventually dis­3flI'C'In. Tbcrcafter, the tIow pan.." lXlIlsislS ofa single roD­ceO circulating upward at the elevated end and dmm....ard.t the other, the DC! beat lraosfer be....een the cndv.aDsand the Duid approacbcs zero, and ocarIy the same beat Dux passes between the ftuid and the bol and mid plates.

UDder idealized conditions the opposite direction of circu­lation is equally probable for heating from below, i.e., do..nward in the center and upward along both endv.aU.. A net beat Dux would then occur from the Duid 10 the mlder cndwalIs, and aboul 2.S'Yo less heat cuhange would take place from the Duid 10 the eoId plate than from the bot plate 10 the Duid.

The COttSistently obsoerved direction of circulation for no iII­clination, i.e., upward ocar the center, is presumably an ar­tifact of a slight DOD-isotbcrmility ill the heated and cooled surfaces. This sensitivity of the cin:ulation pattellllO minor perturbations in the boundary a>oditioas sbould alway. be a consideration in interpreting experiments for laminar natural mnvection. 1be minor details of tho circulation patterns observed in this investigation may to some extent have been inDucnced similarly to the direction of circula­tion. However, the main characteristics "'" believed 10 be mrrcct.

37

•�

1bese are apparent!} the fu>t experimental results fOT the effect on natural eonvection of a partial baflle nonnal to the isothermal surfaces. A finite-dilIerence solution for the same beba,ioris presenled in a eompanion ""per [13J.

Although the results are for glycerol aDd a 2 x I x 1 enclo­sure !bey are expected to be applicabl< qualitatively for air in an codosure with large aspect ratios.

Ref"",......

[1)� CIlao, P. K..-B, Ozoc, H.. and CIlurcbil1, S.W., The Effect of a Non-Uniform Surbce Temperature on Uminar Natural Convection in a Re=ngular Enc1o­sure, ChmL Eng. Commun., ""L 9, pp. 245-2.54, 1981.

(2)� Chao, P. K..-B., Ozoe, H., Churchill, S.W., and Uor, N., Uminar Natural Conyection in an Inclined Roc­rangular Bol with the LDwer Surface Half-Healed and HaIf-lnsulaled, J. H<tIl Transfer, yol. lOS, pp.425-432. 1983.

(3)� Cane, R.LD., Hollands, K..G.T.• Railhby, G.D., and Uany, T ..E., Free Conyection in Heal Transfer Across Inclined Honeycomb Panels, J. H_ Trruuf'" vol. 99C, pp. 86-91, 1977.

(4)� Arnold, J.N, Edwards, D.K.., and Canon, I., Effect of Till and Horizontal Aspect Ra~o OIl Natural ConYec­tion in a Rectangular Honeycomb, J. Hms Transier_ ""L 99C, pp. 120-122, 1977.

(5)� Emery, A.F, Eap/oratory Studies of Free-Conyection Heal Transfer Through an Endosed Vertical Lay« with a Vertical Baffle, J. Hms Tramf'" voL 91C, pp. 163-165, 1969.

(6)� Proben. S.D, ODd Ward, J, Improvements 011 the Thermal Resistance of Vertical Air-Filled Enclosed Cavities, Proc. 5d11nl. H_ Tran.if" Con!, Tokyo, NeJ.9. pp. 124-128. 1974.

(7) Janikowski, H.E, Ward, I., and Proben, S.D., Free Convection in Venical, Air-Filled Re=ngular Cavi­ties Firted with Bam... Proc. 6dI lnL H_ Transf" Coftf, TorolUD, vol 2. pp. 257-262, Hemisphere Publishing. Washingtoa, D.e., 1978.

(8) Nansteel, M.W., and Greif, R, Narural Convection in Undivided and PaniaIIy Divided Rectangular Endo­sures,J. H<tJl Transfer, voI.103C, pp. 623-629,1981.

Acknowledgement

1bis worlt was 5Up?Ofted in part by the U.S. Department of Energy Solar Heating and Cooling R + 0 Branch througb Contract EM-78-04-5365, and in part by Special Research Projects on Energy Problems of Grants-in-Aid for Scientific Rcoean:h, Ministry of Education, Japan (No. 57040075). The participation ofProf. Ozoe in the work althe University of Pennsylvania was cosponsored by the Japan Society for the Promotion of Science ODd the U.S. National Science Foundation.

[91� Bauman, F., Gadgil, A., ICammerud, R., and Greif. R., Buoyaocy-Dr;'en Convection in Rectangular En­closures: Experimental Results and Numerical Calcu­lations, 19rJo NaJionol H<tJl Transfer Con!, Orlando, ASME Paper llO-JIT-66, 1980.

(10) Chang, Le., Yang, K..T.and 1Joyd,J.R, Radiation­. Natural Convection Interactions in Two-Dimensional

Complex Endosures,A1AAIASMEJrdJoint TMmw­physia, FWids. PIamuJ <l HeaJ TroM[er Confmna, SL LoWs, Paper 82-JIT49.

(11)� W'mlers, K..H.. The Effect of Conducting Divisions on the Natural Convection of Air in a Rectangular Cavity with Heated Side Walls. AlAAJASME Jrd Joint Thcnnophysin, FIuUb, pu.sma <l He., Tronsfer Con­ferena. SL LoWs, Paper 82-JIT-69.

(12)� Duxbury, D, An Inlerferometrie Study of NatuIa1 Con'-.ction in Enclosed Plane Air Layers with Com­pIele and Partial Central Vertical Divisions, Pb.D. Thesis, University of Salford, U.K.., 1981.

[131� CIao, P. K..-B., Ozoe, H., OJurcbiIl. S.W., and Lior. N., The Effect of Partial Baffles on Natural Convec­tion in an 1DC\ined Rectangular Endosure, Part U. Fwite-Difference Calculations, CJu:m. Eng. Fundam., in this paper.

(14)� Newman, A.A., Glyuro~ Neill &. Co.• Ltd, Edin­burgh, 1968.

[151� Ozoe, H., SalO. N., and Churchill, S.W.• Experimental Confumation of the Tbree-Dimcnsional Helical Strealdines Previously Computed for NatuIa1 Convec­tion in Inclined Rectangular Enclosures. Kagaku KCJ!dkll Ronbunshll, ""I, 5, pp. 19-2.5. 1979; English transl. lru. Own. Eng., voL 19, pp. 454-462, 1979.