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4065 (RP-664)

ConvectiveEnergy andHeat TransferThermal Loadin BuildingCalculations

Daniel E. Fisher, Ph.D.Associate MemberASHRAE

Curtis O. Pedersen, Ph.D.Fe/Iow ASHRAE

ABSTRACTValMenclosure film coefficients, required by hourlyenergy and thermal load programs, were experimentallydetermined for ventilative .flow rates below 12 air changes

per hour (ACH).Forty-eight experiments were perfolw~eda full-scale room n order to determine fihn coefficients atlow ventilative flow rates. The experiments, which were per-formed over a range of conditions from .3 to 12 ACH, howedthat for most roomconfigurations, natural convection filmcoefficients significantly underpredict the rate of surfaceconvective heat transfer. The new film coefficients wereimplemented in the BLASTprogram, an hourly heat-bal-ance-based building energy simulation. The significance ofthe error incurred by using natural convection film coeffi-cients in a ventilated space was estimated by comparingBLAST esults obtained with both natural convection and thenew.film coefficients. For the case o[ space cooling, wheresurface-to-air temperature differences are relatively small,errors in calculated space cooling loads were typically onthe order o[10%.INTRODUCTION

Calculation of room urface-to-air heat transmission isdependent n an accurate estimate of the film coefficient. Forty-eight experimentswereperformed n a full-scale room n orderto determine the significance of the error incurred by thecommonractice of using natural convection eat transfer coef-ficients in a mechanically entilated room.

The experimental work, which was sponsored byASHRAEs RP-664, was performed over a range of realisticroomconfigurations. Ventilative flow rates were set between3 and 12 air changesper hour (ACH), nd inlet air temperaturesetpoints were specified between 10C (50F) and 25C(77F). The experimental room was configured with both

isothermal and nonisothermal nteriors and with both ceilingand sidewall diffusers.The research showedhat actual room ilm coefficients maybe up to 20 times higher than natural convectionbased coeffi-cients. BLASTimulations showed hat the error introduced by

the natural convection ssumptionypically results in an annualcalculated cooling oad error on the order of 10%.

Significantly, the research also showed hat roomswithradial ceiling diffusers are relatively well stirred, evenat venti-lative flow rates as lowas 3 ACH. his unexpectedact led to thesimplified engineering correlations that are presented in thispaper: heat transfer coefficients as a function only of ACH. hecorrelations can be easily implementedn room hermal loadprograms, building energy analysis pro~ams,and other engi-neeringcalculations.

Thepaper also demonstrateshe importance f selecting thecorrect reference temperature n defining the film coefficient.The uncertainty analysis associated with the experimentalmethod rgues in favor of a room nlet reference temperature.The temperatureand flow fields of recirculating cavitiesand enclosureshave enjoyedconsiderable ttention in the liter-ature during the last 20 years. Hundreds f papers present theresults of computational tudies, and dozensmorepresent exper-imental results. Althoughmany esearchers have studied thebuoyancy-drivenenclosure (Bauman t al. 1980; Nansteel andGreif 1981, 1983; Bohn nd Anderson 984, 1986; Allard et al.1990; Chenet aL 1990) and a significant number ave investi-gated forced convection t high ventilative flow ates (Spitler etal. 1991b; Nielsen et al. 1978, 1979; van der Kooiand Bedeke1983; van der Kooi and Forch 1985; Murakami t al. 1987;Neiswangert al. 1987), relatively few have nvestigated enclo-sure heat transfer at lowventilative flow ates (Neiswangert aL1987; Chenet al. 1989; Kapoor nd Jaluria 1991; Pavlovic andPenot 1991). Of these, none has developed convective heattransfer correlations for realistic room onfigurations.

DanielE. Fishers a research ngineer ndCurtis O. Pedersens a professoremeritus t the University f Illinois, Urbana.

ASHRAE ransactions: Research 137

1997, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org)Published in ASHRAE Transactions 1997, Vol 103, Part 2. For personal use only. Additional distribution ineither paper or digital form is not permitted without ASHRAEs permission.


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This study used the experimental building enclosureconstructedby Spitler et al. (1991a)and designedoriginally forconvective heat transfer experimentsat high ventilative flowrates. The facility, which was modified to accommodateresearch in the mixedand natural convection flow regimes, isunique n several respects. First, the enclosure is relativelylarge--the size of a smalloffice. Second, ll interior surfaces canbe temperaturecontrolled.

For many f the experiments presented in this paper, allroomsurfaces were controlled at the same temperature. Theisothe~rnal room onfiguration was an important actor in mini-mizing he uncertainty associated with the experimentally eter-mined ilm coefficients. For this configuration, the radiationcomponent f the surface heat transfer was small comparedothe magnitude f the convective flux; even a relatively largeuncertainty n the radiationheat transfer calculationhadan insig-nificant effect on the uncertaintyassociatedwith the convectiveheat transfer coefficient.A number of nonisothermal experiments were alsoperformedn order to validate the application of correlations to

roomswith nonuniform urface temperatures. The nonisother-malroomwas configuredwith three "hot" walls, a "hot" ceiling,a "hot" floor, and one "cold" wall.THE EXPERIMENTALFACILITY

The experimental acility, shownn Figure 1, consisted ofan office-sized chamber ocated inside a larger structure. Thespace between he outer shell and the experimental enclosurewas a temperature-controlled "guard space" that maintained atemperature difference of -0C (32F) across the walls of theexperimentalenclosure.The enclosure, which consisted of 53 individuallycontrolled heated panels, was ventilated through either of twoinlets located in the ceiling and side wall. The layout of theheatedpanels nd the air inlets andoutlets is illustrated in Figure2. Construction nd validation of the facility are discussed by

Fisher (1989).

Figure I Schematicof experimental facility (Fisher 1989).

One wall of the experimental room (S. Wall) wasconstructedwith plate heat exchangers ehind he heated panels.All of the nonisothermal roomexperiments were performed bycirculating chilled water through these heat exchangers. Theconstruction and instrumentationof the cold wall are discussedby Fisher (1995) and Mansfield 1993).

Eachheated panel was instrumentedwith two surface ther-mocouples.Local heat transfer coefficients were calculatedusing the average of the two panel surface temperatures. Thecalculation of the interior radiant energyexchangewas basedonthe assumptionhat tire panel surface wasuniform t the averageof the twomeasuredemperatures.At the lowairflow rates typi-cal of the mixedconvection regime, temperature differencesbetween ny two points on a single panel were less than 0.5C(0.9F) (Fisher 1989). The uncertainty introduced by this errorwas ncorporatedn the calculation of the surface film coefficientuncertainty.

A chilled-water coil with electric reheat maintained hedesired roomair inlet temperature. Thermocouplerids locatedat the roo~n ir inlets andoutlet measurednteringand leaving irtemperatures. A flow measurementox constructed according toANSI/ASHRAEtandard 51-1985 (ASHRAE985) providedpressure and temperature nformation required to calculate theair mass low rate to the room.

The oom entilation rate was calculated fiom the measuredp~essuredrop across one or two elliptic flow nozzles of knowncharacteristics. Various nozzle combinations were used toobtain ventilative flow rates ranging iom 05 to 2 m3/s.Ceiling

N. Wall

l~oor

fW. Wall E. WallS. Wall

W = Inlet or OutletOpeningsFigure 2 Heated panel layout (Fisher 1989).

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Air speeds and temperatures n the experimental oomweremeasuredby 16 omnidirectional air speed transducers and 16type-T thermocouples ttached to a computer-controlledrolley(Cantillo 1990). The rolley, moving orizontally and vertically,typically collected data at 1,000 ocations in the half-room.

Air temperature measurements ere particularly importantin evaluating possible reference temperatures.A number f bulkair and planar temperatureswere nvestigated as possible refer-ences or defining he heat transfer coefficient.THE EXPERIMENTAL METHOD

Eachunique experimentwas defined by a roomventilativeflow rate, an inlet air temperature, and room urface tempera-tures. Temperatures nd flow rates werecontrolled to specifiedsetpoints until roomair outlet temperatures and time-averagedsurface heat fluxes werenearly constant, indicating hat a quasi-steady state had been reached. The computer-controlledrolleythen traversed the roomon a specified path logging air speedsand air temperatures; a second data-acquisition system oggedexperimentalvariables at 20-second ntervals for at least onehour. Thesurface convective lux and film coefficient calcula-tions were based on periodic and one-time measurementsatthese quasi-steady-stateconditions.Table1 defines he variablesand parameters sed in these calculations.

TABLE 1Film Coefficient Calculation:Parametersand Variables

Ai Area f heatedpanel (m)F0- Gray nterchangeactor between anels andj (m)hi Convectiveeat ransfer coefficient or panel (W/(m2/C))

qi-s=net rate of radiation eat ransfer rom anel to allother surfaces n enclosure W/m)qi-co,n,Rateof convective eat transfer frompanel (W/m)

Rate f electrical resistance eat ransfer o panel (W/m)qi-h! Rateof heat ransfer frompanel to guard pace W/m)Rt Thermal resistance of wall (m2. C/W)Stefan-Boltzmannonstant (W/(m2/K4))Trq Reference emperature C)Ti, T./ Averageurface emperature f panels i andj (C)Guard pace emperature C)Vi Linevoltageonpanel heater volts)

Theconvective lux fromeach of the 53 surfaces, qconv, wascalculated from spatially and temporally averaged data. Anenergybalanceat the surface defines the convective lux. For aheatedsurface, assuming o participation of the enclosure ir inthe radiant exchange, he energybalance is

qi-conv = qi-pwr-qi-s-qi-h/ (1)

whereqi-pwr s the rate of heat transfer to the panel from theelectrical resistance heaters, qi-s represents the radiantexchangebetween oom urfaces, and qi-hl is the "back loss"to the guard space.The electrical power nput to each panel was calculatedfrom he measured oltage, the measuredesistance of the heated

panel, and the measured rea of the panel:V2 (W/m2). (2)qpwr - R. Ai

The net radiant heat transfer from the ith room urface to allthe other surfaces in the enclosure is given by Hottel andSarofim (1967)1 (T~ 4. 2- . ~ Tj)I(W/m ). (3)i-~" Ai.~ [Fi] G" -j=l

Finally, the rate of heat transfer from he inside surface tothe guard space (the "back oss"), qhl, is calculated from hemeasured urface temperatures nd the thermal resistance of thesurfaces:

[ri- Tg,,~ ~qi-h, = ~)(W/m-). (4)Thus, the convective flux was explicitly calculated fromexperimental measurements for each surface in the room.Since the guard space was controlled to the inside surface tem-perature, for the isothermal roomconfiguration the only sig-nificant termon the right-handside of the equation s qi-pwr"

The convective heat transfer coefficient was calculatedfrom the rate of convective heat transfer and the temperaturedifference betweenhe surface and an arbitrarily selected refer-ence temperature.

qi - con vhi - (Ti- Trej)O (5)

Theselection of the reference temperaturewas arbitrary in thesense that for enclosure heat transfer, a clear and obviouschoice for a temperature reference does not exist. An mpor-tant part of the investigation was o examinehe impactof var-ious reference temperatures on the proposedcorrelations andon the experimental ncertainty associated with the heat trans-fer coefficients. The room nlet temperature, the roomoutlettemperature, and spatially averaged planar and bulk air tem-peratures were examined s possible references.SUMMARY OF EXPERIMENTS

Of the 48 experimentsperformedduring the course of theinvestigation, 16 wereperformed ith radial ceiling diffusers inthe isothermal oomand 20 with radial ceiling diffusers in thenonisothermal oom. In addition, several heat gain experimentswere performedwith reduced roomvolume n order to estimatethe effect of furniture. Thebalanceof the experimentstudied hefree, horizontal et andare not discussed n this paper.

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The adial ceiling diffuser, used in many ommercialppli- 7buttcations, is of great practical importance. everal adial diffusers Tintof different design and openarea were used in the ceiling jetexperiments n order to vary the outlet velocity of the jet and Vistudy the effect of diffuser type on surface convection.Table 2 Rishowshe experimentode, he ventilative flow ate, the air inlet Thistemperature, nd the diffuser openarea for eachof the isothermalroomceiling experiments.

TABLE 2Summary f Isothermal RoomCeiling Inlet ExperimentsFile

e0112933e0905921e1010921e1211921e1204922e0828921e101692le1202921e0112932e1204921e0619921e0112931e0827921

FlowRate(ACH)

3.003 ~025.95599

6.059~009.059.07

Inlet Temp.10.8319.9816.7220.049.9815~0419.9514.959.919.9220.0810~0214.99

DiffuserArea(m)0.0220.0085

!0,00510.00510.01160.0085

0.01160.01160.022

0.01160.022

!0~0220.0085

e0624923 11.94 25.03 !0.022e0829921 11.94 15.03 0.022e0618921 11.96 20.02 0.022

Eachdata set was nitially screenedby calculating an over-all room eat balance rom he data. It was equired hat the totalenergy ransferred to the room ir during he courseof the exper-iment, Eair, be within 10% f the total electrical energydissi-pated by all room anels, Epwr:

(Eair -- Epwr)


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9

Figure 3

20ft./min. (0.t0 m/s)plane 15ft./min:(0.076 /s)plane(a) (b)

Measured ir speeds for 9 ACH,10C: above 20 fpm (a) and above 15 fpm (b).

Air

(a)Figure 4 Measuredair speed for 6 ACH, OC: above 20 fpm (a) and above 15 fpm (b).

(b)

flow regions represent the turbulent mixing egion rather thanthe inner flow egionof the .jet.Similar air speed patterns were observed at bothhigher and lower volumetric flow rates. The flow fieldsshown n Figure 3 are typical of the Spitler (1990) data and

the higher volumetric flow rate experiments performed aspart of this investigation. The characteristic flow is alsoobserved at lower volumetric flow rates. Figure 4 showsthe same plane of air speed measurements or inlet condi-tions of 6 ACHt 10C (50 F). Even at this relatively lowvolumetric flow rate and low inlet air temperature, thebuoyancy of the jet is not sufficient to overcome theCoanda effect.

At the lowest volumetric flow rate and lowest air inlettemperature, the effect of buoyancy begins to show. InFigure 5a the ceiling.jet is not visible. This is not becauseit does not exist, but rather because the jet-affected zone

is not penetrated by the air speed probes In contrast, theflow field near the floor, fed by the downwardlow of coldair, is relatively active The "still air core" is discerniblein Figure 5b but is less well defined than at higher flowrates.

The data presented in Figures 3 through 5 indicate thatthe density differential between the cold, mechanicallydriven jet and the roomair has a negligible effect on theflow field in comparison to the Coanda effect. The jetremained tenaciously attached over the entire range ofconditions such that even the flow along the floor appearsto be driven by the attached ceiling and wall jets.

Figure 6 shows measured temperatures for pointscoincident with the air speed measurements shown inFigures 3 through 5. Isotherms at 0.5 C (0.9 F) intervalsare shownon the plots.

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Figure 5

15fi/rnin (0.076m/s)plane

Measured ir speeds for 6 ACH,10C: above I51~pm a) and above ]O fpm (b).(b)

(b)Figure 6 Temperature mapsat 9 ACH a), 6ACH b), and 3 ACH or IOC inlet

At 9 ACH Figure 6a), the room appears to be rela-tively "well stirred" with respect to temperature. There isno sign of stratification, and the temperature in themeasurement lane varies by less than 1 C (1.8F). At 6 ACH(Figure 6b), the room s still relatively well stirred with respectto temperature. The "cold corners" (also clearly visible at9ACH)how he jet leaving the ceiling and reattaching to thesidewallsbut donot indicate a buoyancyffect. Theunistrut trol-ley rails mountedn the upper right and left corners of the roomtend to exaggerate he effect of the upper corners.

Althoughhe room ir temperature s still quite uniform t3 ACHFigure 6c), some emperature tratification is evidentthis volumetric low rate. Buoyantorces are no longer negligi-ble, and one wouldheoretically expect o see their effect on therate of convectiveheat transfer----especially on the floor. Themomentumf the mechanicallydriven jet, however, till domi-nates the flow field, even at these extreme onditions.Selecting the Reference Temperature

Two riteria wereapplied in selecting the reference temper-ature for room onvectiveheat transfer calculations. The first

(c)criterion required hat the reference emperature e readily avail-able both in energysimulation programs nd to building design-ers in general. Thesecondcriterion required that the referencetemperature minimize he experimental uncertainty associatedwith the calculation of the heat transfer coefficients. Basedonthese criteria, the room nlet temperaturewas he best referencefor defining oom onvective eat transfer coefficients,

The izst criterion eliminated ll but three possibilities: theroom nlet temperature, the roomoutlet ternperature, and the"bulk" (or mean)air temperature Other possible referencetemperatures, such as near-wall air temperatures, can only beobtained n the laborato~3.Of the three possibilities, the roominlet and outlet temperatures re most eadily available both inpractice and in energy simulation programs.

AlthoughSpider used the roomoutlet temperature as thereference or the convective eat ransfer coefficient Spitler et al.1991b),at lowventilative flow rates the uncertainty n the filmcoefficient associated with an outlet reference temperature sunacceptably high. At low volumetric flow rates, the outlettemperature pproaches he room urface temperature. This smallAT eads directly to high unce~Xaintiesn the film coefficients.142 ASHRAEransactions:Research


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20.015.010.05.0o.o

-lO.O__ - I0 5 10 15Air Changes er Hour ACH)

2.52.01.51.00.5o.o-o.5

-1.0

Figure 7 Uncertainty n wall h for outlet reference (a) and inlet reference (bFigure 7 shows he calculated uncertainty in film coeffi-cients using inlet and outlet reference temperatures.The igureshowsaverage wall heat transfer coefficients for 15C 59F)inlet air experiments.Theuncertainties shownn the figure aretypical of room eat transfer coefficients over the rangeof exper-imentaldataBasedon the experimentaluncertainty, the inlet tempera-ture is clearly the better choice or a reference emperature.Theplots also indicate that the inlet reference emperature ay orre-late the data better. Theheat transfer coefficients basedon theinlet temperature showedgood sensitivity to ACH ver theentire rangeof conditions.The Effect of the Radial Diffuser onRoomConvective Heat Transfer

For a givenvolumetric low ate, the "open rea" of a ceilingdiffuser determines he velocity of the .jet at the room nlet.Experimentswere designed o answer he question of whetherornot the rate of convective eat transfer is dependent n the inletjet velocity The experimental videncepresented n the follow-ing paragraphs indicates that for a radial diffuser, surfaceconvections independent f the inlet jet velocity.A numberof tests at 12 and 6 ACH ere performed n theisothermal roomwith 20C (68F) inlet air and 30C (86F)surfaces For each test, the velocity of the jet at the inlet wasvaried for a constant volumetric low rate by changing he openarea of the radial ceiling diffuser.

Two ypes of diffusers were used for the tests, as shownnFigures 8 and 9. The first type was simply a cylindrical coverwith evenlyspaced lots or holes on the cylinder wall; the secondtype wasan adjustable pan-typediffuser.The measured ate of convective heat transfer showed osensitivity to the inlet velocity regardlessof the proximityo theinlet jet. Figure 10 shows he averagerate of convective heattransfer for the three heatedceiling panelsclosest to the ceilingdiffuser. The irst case, with an approximatenlet jet velocity of1.19 m/s (3.9 fds), is for the pan-type iffuser with a 2-in~ (51-mm) ap between the cover plate and the diffuser pan. Thesecond ase, withan inlet jet velocityof 2.37 m/s 7.7 ft/s), is for

t

I5 10Air Changes er Hour ACH)(b)a 1-in. (25.4-mm)ap with the pan-type iffuser. The hird case,withan inlet jet velocityof5.11 n/s (16.7 ft/s), is for the cylin-drical-type diffuser shownn Figure8. As he inlet velocity ischangedby greater than a factor of four with a constant volu-metric flow rate of 12 ACH,he convective flux remains rela-tively constant. The variations in the convective flux areexplained by slight variations in inlet temperature, volumetricflow ate, and perhapsalso by the jet attachment oint.EXPERIMENTAL RESULTSDevelopment f Correlations

Severalconclusionscan be drawn rom he evaluation of theflow and temperature ields. First, due to the dominance f theCoanda ffect, the flow field is momentumriven and is rela-tively unaffected by buoyancy.Second, he temperature of theinlet jet is the best reference or the definitionof the surfaceheattransfer coefficients. Finally, notwithstandinghe importance fmomentumn determining he flow field, the surface heat trans-fer is independentf the inlet .jet velocity.

The act that the film coefficients are independentf the .jetvelocity precludes the possibility of correlating surface filmcoefficients to jet-velocity-based parameters uch as the outletReynolds number:UoLRe- v (7)

whereUo is the .jet velocity at the diffuser, L is a diffuser-based length scale, and v is the kinematicviscosity. Attempts. diffuser

ceilin~~,~ /fixture

Figure 8 Cylindrical-o,pe radial diffuser.



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Diffuser F~ Fixture

Figure 9 Pan-type radial diffuser.at correlating the heat transfer coefficients to the Reynoldsnumber and other velocity-based parameters predictablyfailed.

Momentumependencewas tested by calculating the jetmomentumumber, , which had been previously used to corre-late room eat transfer coefficients at high ventilative flow ates.The esults of this test showedhat room urface heat transferwas also independent of jet momentumor the ceiling inletconfiguration.

The jet momentumumber s defined asJ - (8)9g~room

where,h =

=p =g =

mass low rate of ventilation air,jet velocityat the diffuser,densityof air,acceleration due to gravity, andvolumeof room.

For high ventilative flow rates in the enclosure, Spitler corre-lated the forced convection eat transfer coefficient to the jetmomentumumber Spitler et al. 1991b). Variable diffuserarea tests performed or the sidewall inlet at high ventilationrates showed hat for the conditions under consideration, therate of surface heat transfer was sensitive to changes n theinlet momentum.owever, or the radial ceiling diffuser, therate of surface heat transfer is completelynsensitive to varia-tions in the jet momentumumber. Figure 11, which showsheat transfer coefficients based on an inlet air reference tem-perature, illustrates the independencef surface heat transferand the momentumf the inlet jet.The development f successful correlations was based onthe observation hat although he heat transfer coefficient wasindependent f both the inlet jet velocity and he inlet jet momen-tum, it wasdependent n the jet mass low rate. For incompress-ible flow over the temperature range studied, volumetric flowrate also resulted in reasonablecorrelations of the surface heattransfer. The mplicationof this observation s that in developingwhole-roomonvective heat transfer coefficients, the physics

160,]._. 140~,--. 120.

10o.80=

~ 60.o 20-O-

Jet Inlet Velocity (m/s)

2enterPaneN. CenterPanel

S. CenterPanel

Figure 10 Convective flux for three heated panels near theradial diffuser.

must be understood in terms of the roomcontrol volume atherthan in terms of the surface boundaryayer.The ventilative flow rate is proportional to the totalenergy delivered to the room t a given inlet air temperatureWhen ormalized to the roomvolume, this paratneter scalesthe roomconvective heat transfer to its fundamentaldrivingpotential--the difference between the surface temperatureand the air inlet temperature. Preliminary experimentalevidence ndicates that the validity of the correlations dependonly on a basic similarity of the flow field. Thus single corre-

lation for each surface orientation described the roomconvective heat transfer from 3 ACHo 100 ACH or a variety ofdiffusers, including the diffusers described in this paper andthe commercial iffuser used by Spitlero

As shownn Figures 12 through14, the volumetric low ratedependence is of the form (h-ACH). The figures show roomconvectiveheat transfer coefficients as a function of volumetriflow rate for an inlet air reference emperature.Experimental Uncertainty andRangeof Correlations

The rt of uncertainty nalysis s well established n the ther-mal sciences; numerous exts and papers address the topic,including excellent texts by Taylor (1982) and Holman1989).Of patlicular importance o this investigation is the fact thatSpitler validated both the experimental rocedure nd the perfor-mancef the facility at high ventilative flow ates (Spitler 1990)

Theclassic paper on uncertainties in single-sample xperi-ments was published by Kline and McClintock (1953), whshowedhat for the special case of a linear function with inde-pendent variables, each of which s notxnally distributed, therelation betweenhe uncertainty nterval for the variable and theuncertainty nterval for the result is givenby

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[(~R e ~2 {OR "~2 (OR )2"11/2e. -- Lt,~n ,j (9)whereR = calculatedesult,R=R(vl, v2 ..... Vn),eR = uncertaintynterval n the result, andei = uncertaintynterval n the ith variable.

The artialderivative, Rl~vn, is a measuref the sensitivityof the result to a singlevariable.Multiplyinghe sensitivityor"influence"oefficientby the estimated ncertaintyn the vari-ableprovides n estimate f the variables ontributiono uncer-tainty in the result. Themethod f influence oefficientshastraditionallybeen xtendedo nonlinear elationships yfirst-orderexpansionf the governingquation ndevaluation f thepartial derivatives t the basevalues Holman989).This method asused o calculate the uncertainty ssoci-ated with the experimentallyeterminedeat transfer coeffi-cients. Figures15 through17 show he uncertainty in heattransfer coefficients for a room onfiguredwith a ceilingdiffuser.The ilmcoefficients re basedona jet inlet referencetemperature.

Thecorrelations shownn Table3 are applicable o anisothermal oomwith a radial ceiling jet between 0C 50F)and25 C (77 F) andan enclosure ir changeate (ACH) ithinthe range 3 < ACH 100). Theconvective eat transfer coef-ficient, h, is basedon a reference emperature easuredn thesupply ir duct.TABLE3Heat TransferCoefficientsfor Ceiling nlet Configuration

SurfaceType CorrelationWalls h = 0.19~ACH8Floor h = 0.13ACH8Ceiling h = 0.49ACH8

Althoughhe correlationsre subject o restrictions, heyaresuitable for manyHVACpplications.Theexperimentalangeofbothvolumetriclow ate and nlet air temperatureovers henormalperatingange f most uildings.n spite of the fact that anumberf variablessuch s roomspect atio, interaction f inletjets frommultipleiffusers, urnishings,nd nternalheat ources)were otcheckedy he parametricet of experiments,he fact that12 ACH Ceiling Convection5---

4

04.0 104 8.010-4 1.210"3 1.6 lff 4~0104J

12 ACH Wall Convection5 i i I I I ~

8.010,4 1,210"3 1.6103J

Figure 11

6 ACH5 t4-

~3-

1 -0 ~0.0 10

Ceiling 6 ACHI ~ 5

~3

ConvectionI

I4.010 -4 6.010-4

I IWall Convection

I 1 I I I

I I 02.0104 5.01~51.510-42.51~3.510-44.51~J JConvective eat transfer coefficient as a function of jet momentumumbet:ASHRAEransactions: Research 145


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2O

15 ~

5

2 16 30 44 58 72 86 100ACHLEGEND O Fisher [95] V Spider [90]

Figure12 Ceiling h vs. ACHor a radial ceiling diffuserwith an inlet air reference temperature.

0 I I ~ ~ I ~2 16 30 44 58 72 86 100ACHLEGENDFisher [95] V Spitlez [90]

Figure 13 Wall h vs. ACHbr a radial ceiling diffuser withan inlet air reference temperature,

10 , ~ ~ , , ~...................

6

0 t I ~ t2 16 30 44 58 72 86 100LEGENDFisher [95] V Spitler [90]Figure 14 Floor h vs, ACHbr a radial ceiling diffuser

with an inlet air reference emperature~ceiling heat transfer dominates verall room onvections expectedto mitigate he sensitivity of the conelationso these variables~

Twenty xperiments were performed n the nonisothermalroom o determine he applicability of the correlations (derivedfrom sothermal oom ata) to realistic room urface temperatureprofiles. This set of experimentshowedhat the correlationscan beapplied to nonisothermal oomswith surface temperaturediffer-encesof less than 20C 68 F) without erious error. Althoughheroom low fields are significantly different, the maximumevia-

2.0 4.6 7.2 9.8 15.0ACH

12.4

Figure 15 Floor heat transfer coefficients with uncertaintyintervals.

4

0 ~ --t t ~2.0 4.6 7.2 9.8 12.4 15.0ACH

Figure 16 Wall heat transfer coefficients with uncertaintyintervals.

4

0 ~2.0 4.6 7.2 9.8 12.4 15~0ACH

Figure17 Ceiling heat transfer coefficients with uncet;tain~.,intervals.

tion in the heat transfer coefficient at 6 ACH ith a 20C 68F)surface temperaturedifferential was15%, s shownn Figure 18.APPLICATIONSImplementing the Correlations

The expressions for roomconvective heat transfer coeffi-cients presented n Table3 are suitable for implementationn anyheat balance based building energyor thermal load programwith

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sufficient detail to support he calculations.Asignificant require-ment s that the radiation and convection coefficients not becombinedor computationalpurposes. The correlations cannotbe easily incorporated in roomweightingfactors or in surfaceresponse actors that include the air nodes. Likewise, implifiedfenestration models with combined adiation and convectioncoefficientswill not be able to utilize the results of this study.

The new convective heat transfer coefficients wereimplemented in the BLASTBuilding Loads and SystemThermodynamics)program. BLASTmplementation of time-varying film coefficients was essentially demonstrated inAppendixG of Spitler (1990). The correlations can alsoimplemented n computational fluid dynamiccodes, where inmost cases they will represent a significant improvementvertypical wall functions.Significance of Results: A Case Study

ABLASTodel f a 1.4 million ft 2 office wasused for thisexercise. The acility, a seven-storybuilding with masonry alls(24% lass) and a built-up asphalt roof with fiberglass and feltinsulation, was modeled s seven occupiedzones with an inter-nal occupancyoad of 1 person/100t 2, a lighting load of 2.0 W/ft 2, and an equipmentoad of 0.4 W/ft2. The "dead air spaces"between he suspended eilings (with recessed lighting) and thenext floor (or roof) were modeled s separate, "uncontrolled"zones. "High nternal loads" were simulated by increasing theoccupancyoad to 1 person/50 ft 2 and increasing the equipmentload to 2.0 W/ft2. High olar loads weresimulatedby increasingthe glazing area to 54% f the total wall surface area. For thepurposes of this exercise, both buildings were located in thecentral MidwestSt. Louis, Missouri).

Table4 shows he error in the daily cooling load due to anerror in the ceiling convectiveheat transfer coefficient. Columnone showshe daily cooling oad for each case with the currentlyused BLASTonvective heat transfer coefficients. Columnwoshows he daily cooling load for each case calculated with theheat transfer coefficients that are associated with a moderate

1

%0.8"=~13.6

0.4."~ 0.:2..~.~ 0.

15% Error Line-2" .... ......Surface Panel Number

Figure 18 Deviation o.[ non-isothermal tvom fromisothermal room eat transfer coefficients.

ventilation rate of 6 ACH ith a 10C 50F) reference temper-ature. Thedeadair spaceheat transfer coefficients were et at theBLASTefaults (natural convection) for all 12 cases. Columnthree shows the percent difference between columnone andcolumnwo The example, hough valid for only one building inone location, showsup to an 11% rror in the daily calculatedload on the system.

TABLE 4BLAST oads for Natural and MixedConvectionHeat Transfer CoefficientsSens. Load Sens. LoadCase (kBtu/h),Natural (kBm/h),LowConvection Momentum

Single tory, low 3.520E+ 03 3.897E+ 03internal loadsMultistory, ow 2.534E+ 04 2.662E+ 04internal loadsSingle tory,high internal 4.743E+ 03 5.149E+ 03loadsMultistory,high 3o438E 04 3~580E 04internal loadsSingle tory, 4.57E+ 03 5.092E+ 03high solar loadsMultistory, high 3.372E+ 04 3o598E 04solar loads

PercentError10.7%5.05%

8.5%

4A%116.7%

SUMMARY AND CONCLUSIONSHeat balancebased calculation of building energyor thermal

loads requireseither explicit or implicit estimation f the surfacefilm coefficients. Simulation tudies, whichwere performed oestimate the impactof film coefficients on overall room eatingand cooling loads, indicated that commonlysed film coeffi-cients can result in a daily cooling oad error on the order of 10%.Equationselating room onvective eat transfer coefficients othe air change ate of ceiling-ventilated oomsweredevelopedromexperimental ata. Thecorrelations that wereoriginally developedfor ventilative flow rotes ranging rom3 to 12 ACH ereextended

to cover he Spitler data set (15 ACHo 100ACH). heconvectiveheat ransfer coefficientswere ased n an inlet jet referenceemper-ature, which ot only resulted n the lowestexperimentalncemaintybut also significantly mprovedhe correlations.Severalobservationsed to the selection of ACHs the corre-lating parameteror the convective eat transfer coefficient. First,it wasobserved hat the ceiling jet did not detachfrom he roomsurfaces over he entire rangeof experimental arameters.Thus heflow field in the roomwas roughly similar from 3 to 100 ACH.Second,t wasdemonstratedhat the rate of convective eat trans-fer was ndependent f both the velocity and the momentumf theinlet jet. The choice of ACH s the correlating parameter issupported y the physicsof the control volume,which equires theoverall roomconvectiveheat transfer to be proportional to theventilative low ate at a constant nlet air temperature.



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Theexperimentalnvestigationalso left a numberf questionsunanswered.irst, sensitivity of the con:elationso the aspectratioof the roomwasnot investigated. A elated problemnvolves theinteraction of mtdtiple diffusers in a large room.The effect offurnishings and heat sources in roomsalso requires additionalexperimentalnvestigation.REFERENCESAllard, F., C. Inard, and J.P. Simoneau.990. Experimentaltudyof numerical imulationof natural convection n a roomwithheated ceiling or floor. Roomvent roceedings 0.ASHRAE.985. A NSff ASHRAEtandard 51-1985, Laboratory

methods f testing fans for rating. Atlanta: Americanocietyof Heating, Refrigerating and Air-ConditioningEngineers,Inc.

Bauman, ., A. Gadgil, R. Kammemd,nd R. Greif. 1980. Buoy-ancy-driven convection n rectangular enclosures: Experi-mental results and numericalcalculations. ASME0-Ht-66.NewYork: American ociety of MechanicalEngineers.Bohn, M.S., and R. Anderson.1984. Temperature nd heat fluxdistribution in a natural convection enclosure flow. SERITechnical Paper 252-2482. Golden, Colo.: Solar EnergyResearchnstitute.

Bohn, M.S., and R. Anderson.1986. Temperature nd heat fluxdistribution in a natural convection nclosure low. Journalof HeatTransfer 108(May):471-475.

Cantillo, J. 1990. Air velocity and temperaturemeasurementsn afull-scale ventilative coolingresearch acility. M.S.Thesis,Department f Mechanical nd Industrial Engineering, Uni-versity of Illinois at Urbana-Champaign.

Chen,K.S., A.C.Ku, and C.H. Chou.1990. Investigation of natu-ral convection n patlially divided rectangular enclosuresboth with and withoutan opening n the partition plate: Mea-surement esults. Journalof HeatTransfer112(8): 648-652.

Chen, Q., C. Meyers, nd J. van der Kooi. 1989. Convective eattransfer in roomswith mixedconvection. In Proceedings fAir FlowPatterns bz Ventilated Spaces,February,Liege, pp.69-82.

Fisher, D.E. 1989. Design of an experimental acility for theinvestigation of convective eat transfer in enclosures. M.S.Thesis, Department f Mechanical nd Industrial Engineer-ing, Universityof Illinois at Urbana-Champaign.

Fisher, D.E. 1995. Anexperimental nvestigation of mixed6on-vectiveheat transfer in a rectangular nclosure.Ph.D.Thesis,Department f Mechanical nd Industrial Engineering, Uni-versity of Illinois at Urbana-Champaign.

Holman, .Po 1989. Experimental methods for engineers. NewYork: McGraw-Hill.Hottel, H.C., and A.F. Sarofim. 1967. Radiative transfer. NewYork: McGraw-Hill.Kapoor,K., and Y. Jaluria. 1991. Mixed onvectiveheat transfercharacteristics of a downwardurning buoyantceiling jet.ASME-ITID-Vol.163, pp. 9-17. New York: American

Society of Mechanical ngineers.

Kline, S.J., and F.A. McClintock.953. Describing ncertaintiesin single-sarnple experiments. MechanicalEngineering57(1):3-8.

Mansfield,B.D.1993. Developmentf a cold wall for investiga-tion of convective nd radiative heat transfer in enclosures.M.S.Thesis, Department f Mechanical nd Industrial Engi-neering, Universityof Illinois at Urbana-Champaign.

Murakami, ., S. Kato, and Y. Suyama. 987. Three-dimensionalnumerical imulation of turbulent airflow in a ventilatedroomby meansof a two-equation model. ASHRAEransac-tions 93(2): 621-642.

Nansteel, M.W., nd R. Greif. 1981. Natural convection n undi-vided and partially divided rectangular enclosures. Jourt~lof Heat Transfer103: 623-629.

Nansteel, M.W.,and R. Greif. 1983. Natural convection heattransfer in complex nclosures at large Prandtl numbers.Journal of Heat Transfer105: 912-915.

Neiswanger, ., G.A.Johnson, and V.P. Carey. 1987. Anexperi-mental study of high Rayleighnumbermixedconvection ina rectangularenclosurewith restricted inlet and outlet open-ings. Journalof HeatTransfer109: 446-453.

Nielsen,P.V., A. Resfivo, and J. H. Whitelaw. 978. Thevelocitycharacteristics of ventilated rooms. ournalof Fluids Engi-neering100: 291-298.

Nielsen, P.V, A. Restivo, and J.H. Whitelaw.1979. Buoyancy-affected flows in ventilated rooms.NumericalHeatTransfer2: 115-127.

Pavlovic, M.D., and F. Penot. 1991. Experiments n the rnixedconvection reNme n an isothermal open cubic cavity.ExperimentalThermal nd Fluid Science4: 648-655.

Spitler, J.D. 1990.Anexperimentalnvestigation of air flow andconvective eat transfer in enclosureshaving arge ventila-rive flow rates. Ph.D. Thesis, Departmentf MechanicalndIndustrial Engineering,Universityof Illinois at U~bana.-Champaign.

Spitler, J., C. Pedersen, D. Fisher, P. Menne, nd J. Cantillo.1991a.Designof an Experimentalacility for investigationof interior convective eat transfer underventilative coolingconditions. ASHRAEransactions97(1).

Spitler, J., C. Pedersen, nd D. Fisher. 1991b. nterior convectiveheat transfer in buildingswith large ventilative flow ates.ASHRAEransactions 97(1).

Taylor, J.R. 1982.An introduction to error analysis--The sttMyof uncertainties in physical measurements.Mill Valley,Calif.: UniversityScienceBooks.

van der Kooi, J., and K. Bedeke.1983. Improvementf coolingload progams by measurements n a climate morn withmass. XVlth h~ternational Congressof Refrigeration Pro-ceedings, TomeV, pp. 71-77.

van der Kooi, J., and E. Forch. 1985. Calculationof the coolingload by meansof a "more-air-points-model." roceedings fthe CLIMA000 WorldCongress on Heating, VentilatingandAir-Condiaonh,g: 395-40l.

148 ASHRAEransactions:Research


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This paper has been downloaded from the Building and Environmental Thermal SystemsResearch Group at Oklahoma State University (www.hvac.okstate.edu)

The correct citation for the paper is:

Fisher, D.E. and C.O. Pedersen. 1997. Convective Heat Transfer in Building Energy

and Thermal Load Calculations, ASHRAE Transactions, vol. 103, Pt. 2, pp.137-148

(Winner of the ASHRAE Best Technical Merit Award).

Reprinted by permission from ASHRAE Transactions (Vol. #103 Part 2, pp. 137-148).

1997 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.
http://www.hvac.okstate.edu/http://www.hvac.okstate.edu/

contoh perhtangan beban

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