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Building and Environment 59 (2013) 690e700

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Building and Environment

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Experimental study of convective heat transfer from windows with Venetianblinds

Jordan Clark a, Leen Peeters b, Atila Novoselac a,*

aDepartment of Civil, Architectural and Environmental Engineering, University of Texas at Austin, 1 University Station C1752, Austin, TX 78712, USAbDepartment of Mechanical Engineering, University of Brussels (VUB), Pleinlaan 2, 1050 Elsene, Brussels, Belgium

a r t i c l e i n f o

Article history:Received 1 July 2012Received in revised form14 September 2012Accepted 16 September 2012

Keywords:WindowsBlindsConvectionHeat transferPerimeter zone

* Corresponding author. Tel.: þ1 512 475 8175.E-mail address: atila@mail.utexas.edu (A. Novosel

0360-1323/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.buildenv.2012.09.010

a b s t r a c t

To provide for more detailed and accurate load calculations and energy simulation of buildings, the effectof blinds on convection heat transfer at interior window surfaces was analyzed. Based on full-scaleexperiments in an office-size chamber for various diffuser locations, window geometry, and blindangles, the study provides convective heat transfer models for natural convection, forced convection dueto a ceiling slot diffuser, and forced convection due to a floor register. Results are given in the form ofcorrelations which relate either supply volumetric flow rate or room-surface temperature difference toconvection heat transfer at both window and exterior wall surfaces. Results show that heat transfer isdependent on supply flow rate, blind angle, diffuser location and window configuration. Results arecompared against previously reported data and show that convection in cases with blinds follows thesame form as often arises in turbulent forced convection situations, but differs appreciably in magnitudefrom previously given models for bare windows. These results should allow for more accurate simulationof energy use in buildings and contribute to the construction of more energy efficient buildings.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

As load calculation and energy simulation methods becomemore accurate, more detailed models must be created to includethe effects of different architectural components and systems in thecalculations. Heat transfer processes in window assembliesstrongly influence the overall thermal load in a space, and this areaoffers ground for additional research. While heat transfer at barewindow surfaces, and in small isolated window-blind assemblieshas been analyzed, little full-scale work on floor-to-ceilingwindows with blinds, which exist in a large portion of commer-cial construction today, currently can be found in the literature. Tothis end, experiments were conducted to determine the effect ofblinds on heat transfer throughwindows under a variety of thermalconditions and geometries.

Many researchers have investigated convection heat transfer atindoor surfaces. Among these, Waters [1], Alamdari et al. [2] andLomas [3] have demonstrated the importance of selecting a propermodel for indoor convection in accurately performing load calcu-lations. Correlations pertaining to natural convection heat transfer

ac).

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at interior surfaces have been developed [2,4,5], while others [6e8]have analyzed forced convection from interior surfaces. Additionalresearchers [9,10] have created correlations for situations whichcould not be properly classified as either forced or naturalconvection.

Much effort has also been expended toward the goal of under-standing the complex process whereby energy is transferred vianatural convection heat transfer at a blind-window assembly.Collins et al. [11] conducted a numerical study of an isothermal flatplate adjacent to a set of Venetian blinds which were assumed to beirradiated by solar radiationwith a constant flux. Shahid and Naylor[12] numerically analyzed a double-pane windowwith an adjacentset of Venetian blinds. Many investigations of a sealed windowcavity which houses an internal set of Venetian blinds have beenconducted (e.g [13e15]).

Experimental studies in the same vein have been conducted aswell. Machin et al. [16] performed an experimental study ofconvection heat transfer from a small (0.38 m � 0.36 m) window-blind assembly. Results were reported for one surface-air temper-ature difference (20 �C) and four blind angles: �45�,0�, þ45�

and �90�. Flow visualization showed a cellular flow field betweenblinds, of the type expected in an enclosure. Machin et al. [16]observed that heat transfer at the window surface in someinstances was greater when covered with blinds than the similarity

J. Clark et al. / Building and Environment 59 (2013) 690e700 691

solution for a flat plate without blinds. Collins et al. [11] validatedtheir numerical study with an experimental evaluation of theirresults. The main limitation of the experimental setup was that itwould be most valid for a small window (0.2 m � .4 m) which wasembedded into a wall cavity. Cuevas et al. [17] recently studiednatural convection at window surfaces with blinds in a small-scalesetup.

Recently, Wright et al. [18] have attempted to synthesizemost ofthe existing knowledge on radiative and convective heat transferthrough fenestration systems into one complete model. The modelincludes complicated radiative heat transfer processes throughsystems several layers thick, and includes multiple surfaces withinone system which transfer energy through convection. A full-scalefloor-ceiling window, such as is present in much of contemporarycommercial construction has not yet been analyzed. Forcedconvection in window-blind assemblies also has yet to be studied.The objective of the presented study is to bridge some of the gaps inthe knowledge about convective heat transfer at complex surfacessuch as windows with Venetian blinds.

The specific objectives of the present study are to: (1) determinewhether existing correlations for natural convection at windowscovered with blinds, which were developed for small windows, areapplicable to floor-to-ceiling windows and (2) develop new corre-lations describing forced convection in the same situation. The twobasic hypotheses investigated in this study are (A) floor-to-ceilingwindows will experience heat transfer that is appreciablydifferent from a small window under buoyant flow conditions dueto the larger length scales inherent in the process, and (B) forcedconvection at windows with blinds will be less effective than thebare window situation.

The following sections describe the experimental methodologyused to analyze convection in blind-window assemblies. Results ofthese experiments are then given and compared with existingwork. Models for predicting convection in these situations aregiven and their applicability is discussed.

2. Methodology

The basic research tools for the investigation described in thispaper were experiments in a full-scale test room. The experimentswere conducted in the Center for Energy and EnvironmentalResources (CEER) at the University of Texas at Austin. This sectionprovides a description of the experimental setup used, themethodsemployed in the experiments, methods and assumptions made incalculation of radiative and convective heat transfer, and themethod used for the formulation of the experimental results.

Fig. 1. Schematic of chamber characteristic surfac

2.1. Test room setup

Experiments were conducted in a full-scale test room/envi-ronmental chamber at the CEER. The environmental chamber hasinterior dimensions of 4.5 m � 5.5 m � 2.7 m high. U-values ofthe chamber walls are 0.2 W/m2 K. For experiments analyzingforced convection from surfaces near a ceiling slot diffuser,a 0.3 m deep drop ceiling was built into the chamber. The ceilingwas sealed on its bottom surface to prevent air infiltrationbetween the space proper and the plenum above the ceiling. Thedrop ceiling housed an insulated flexible duct along its lengthleading to two diffuser boxes and two ceiling double-slotdiffusers (Titus ML 39), 1.2 m long each, spaced 0.5 m apart. Forfloor register experiments, the ceiling was removed, and the ductplaced in a 0.3 m high raised floor. The plenum beneath the floorwas sealed and the duct attached to diffuser boxes were fittedwith two standard, 1.2 m long grille registers with 0� pitch (TitusCT-PP-0).

The chamber itself has a dedicated and modifiable controlsystem capable of supplying air between 6 and 50 �C, with a relativehumidity between 2% and 99%. Flow rates corresponding toventilation rates between 0 and 15 air changes per hour (ACH) areachievable. The chamber contains supply and return fans capable ofmaintaining a pressure of 0 � 0.5 Pa gage in the chamber. Flow ratemeasurements were calibrated prior to commencement of theexperiments and found to be accurate within 5%. The chamber alsocontains hydronic cooling coils embedded into one wall capable ofsimulating a winter condition. Thin electrical resistance heaters areplaced on walls and floor to simulated internal loads and conductnatural convection investigations.

The chamber walls, floor and ceiling were divided into 14sections as shown in Fig. 1. Short-wave solar radiation transmittedthrough the window and internal loads such as computers andoccupants were also simulated with electrical resistance heaters onthe floor and portions of the side walls, respectively. In calculatingthe radiation heat transfer during the course of the experiments,each section was assumed to be isothermal and the temperature ofthe surface was given as the average of at least two temperaturemeasurements on the surface.

One wall of the environmental chamber was designated the“window” of the chamber (see Fig. 1) and was heated with thinelectrical resistance heaters to simulate a pane of glass absorbinglong-wave solar radiation. For the winter condition, the windowwas cooled with hydronic cooling coils to simulate losses to theexterior environment. Two window configurations were analyzed,corresponding to the two most common window configurationsfound in typical contemporary commercial construction. A

es with wall, window, and diffuser location.

J. Clark et al. / Building and Environment 59 (2013) 690e700692

depiction is shown in Fig. 2. “Configuration A” was that of a floor-ceiling window. “Configuration B” was comprised of a 1.03 mhigh wall below a 1.37 m high window in the same plane. Thinelectrical resistance heaters simulating the heated wall were tapedcontinuously to the chamber surface and then additionally tapedcontinuously to each other to avoid any air movement between theheaters and the wall.

The specific configuration of the wall designated the “window”

changed based on the particular situation being analyzed. Inexperiments simulating Configuration A, equal heat fluxes weresent to all portions of the wall. In Configuration B, a flux corre-sponding to only conduction heat transfer through the wall wassent to the “wall” portion, and a larger flux simulating the absorbedlong-wave solar radiation was sent to the window. Standardcommercial Venetian blinds, 2.5 cm wide and spaced at 2.2 cmvertically, were placed 2.5 cm from the window surface, which isthe standard distance of installation in commercial construction.

Table 1Instruments used and accuracy.

Variable Instrument used Accuracy Comments

Supply and returnvolume flow rate

EBTRON GTType A 116

5% ofmeasured

Verified withduct bluster

2.2. Instrumentation

During the selection of themeasurement instrumentation, focuswas placed on increasing the accuracy of instrumentation whichmeasured the variables which had the largest impact on theuncertainty of the results. The following describes the equipmentused.

Electrical power sent to the resistance heaters was measuredwith a power meter, accurate to 3% of the measured value. For thecalculation of conductive losses through the wall an ITI GHT-1C-(210) electric power meter was used, calibrated to an accuracy of1% of the measured value. Temperatures of all surfaces weremeasured with Omega 44033 thermistors accurate to �0.1 �C. Thetemperature of each of the surfaces was taken to be the average ofat least two thermistor readings. When blinds were employed, sixdedicated thermistors were attached to the blinds’ surfaces. Thesetemperatures were averaged to give one temperature, which wasassumed to be the isothermal temperature of all blinds. Supply air,return air, and center-of-room air temperatures were alsomeasured and included in the calculations.

Additional measurements and calculations were performed toverify the accuracy of the measured results, but not used directly tocalculate convection correlations. These included calibration of theflow rate readings, which was accomplished with a duct blasteraccurate to 5%. Also, general knowledge of flow fields near the wallwas gained through the use of omni-directional anemometers

Fig. 2. Distinction between two analyzed configurations. Configuration A is a floor-to-ceiling window while Configuration B is a window above a small wall.

accurate to 0.02 m/s. A summary of the equipment used andassociated uncertainties are given in Table 1.

2.3. Calculation procedure

The calculation of convective heat flux, was accomplished byperforming an energy balance at the window or wall surface asdescribed by Eq. (1):

_Qgen þ _Qconvection þ _Q radiation ¼ 0 (1)

where _Qgen is the energy dissipated by the resistance heaters (W),_Qconvection is the convective heat flux (W) and _Q radiation is theradiative heat flux (W).

Since the heat flux generated at the surface is known from theamount of energy sent to the surface, and the radiation heattransfer is calculated as described below, _Qconvection can be calcu-lated. Once _Qconvection is known, h (convective heat transfer coef-ficient) is calculated according to Eq. (2), given the measured air-surface temperature difference and the area of the surface:

Qconvection ¼ Asurface h�Tsurface � Tair

�(2)

where A is the surface area in question (m2), and T is temperature(K).

Once several particular values of h are calculated for particularventilation rates and room-surface temperature differences, theyare correlated together into an equation as a function of eithertemperature difference (natural convection), or flow rate (forcedconvection). The air temperature, to which Eq. (2) refers, changeswith the situation being analyzed. In natural convection experi-ments, it refers to the bulk air temperature. In forced convectionexperiments, it refers to the inlet temperature at the diffuser. Theseare the temperatures driving convection heat transfer from thesurface.

To properly determine the radiative component of heat transferfrom the window surface, view factors between various surfaces

Interior surfacetemperature

Omega 44033thermistors

�0.1 �C Additionaluncertaintyintroducedin averagingand radiationcalc.

Supplytemperature

Omega 44033thermistors

�0.1 �C

Electric power Brand ElectronicPower Meter

3% ofmeasured

Exterior air androom-surfacetemperature

Omega 44033thermistors

�0.1 �C

Surface emissivity Measured byOak RidgeNationalLaboratories

Assumedto be exact

Sensitivity analysisshown to negligiblyaffect final calculation

Conductive lossesthrough wall

ITI GHT-1CFlux meter

1% ofmeasured

Used for calculationof UA value of chamber

Hydronic coilsflow rate

Omega FTB-9500 2% ofmeasured

Hydronic coilstemperature

EncapsulatedOmega 44033thermistors

�0.17 �C

J. Clark et al. / Building and Environment 59 (2013) 690e700 693

were calculated. All view factors used in radiation calculations werecalculated with a Monte Carlo simulation. View factors betweensurfaces change with the angle at which blinds are set, and thusa new Monte Carlo simulation was conducted for each blind angle.The geometry of the enclosure, including the blinds, was drawnwith AutoCAD for each experiment. This drawing was thenimported into Sinda/Fluint RadCAD and a calculation for the viewfactors between each surface was performed by running a MonteCarlo simulationwith twomillion rays.With this number of rays, anaccuracy of 0.5% was achieved for the view factors. These viewfactors were then imported into a program developed by theresearchers and radiation heat transfer between each surface in theexperiment was calculated. Emissivities of surfaces were deter-mined by Oak Ridge National Laboratories. Emissivities used in theradiation calculation were 0.89 for electric heaters, 0.87 for paper,0.9 for the blinds, 0.84 for tape, and 0.2 for aluminum and stainlesssteel. For more information on the radiation calculation please referto reference [8].

To provide correlations which are readily usable by energyanalysts, a few modifications to the traditional form of correla-tions were made. First, correlations are given which relate heattransfer at a surface to the difference between the surfacetemperature, and either the bulk room temperature (naturalconvection) or the supply inlet temperature (forced convection).Secondly, forced convection correlations are given as a function ofsupply volumetric flow rate. This convention is adopted fromSpitler et al. [6].

2.4. Quality control and uncertainty analysis

Measures were taken to minimize error in experimentaldesign, experiment execution, and data processing. The uncer-tainty in the measured and processed data for all developedcorrelations was investigated in detail. Also, substantial efforthas been dedicated to the design of experimental set-ups toensure the robustness of the newly developed convectioncorrelations and their applicability to a wide range of possiblesituations. A set of control measures was introduced to minimizethe systematic or specific errors in the correlation developmentprocedure. The following subsections briefly describe thesecontrol measures.

In the first phase of the project, a group of experiments wasrepeated to identify faulty sensors. For each experiment, multipletemperature and velocity sensors switched positions in thechamber. In addition, air flow rate was measured in the supply andreturn air ducts to prevent the failure of an experiment due toa faulty flow measurement. Furthermore, the symmetry in theexperimental setup and comparison of temperatures and heatfluxes at the symmetric surfaces was used to check if there was anydiscrepancy in the experimental results. For example, very similarvalues of measured variables on surfaces of side walls improve thereliability of meshed values.

dqsurface convective ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�dqsurface total

�2þ�dqsurface radiative

�2þ�dqwall loss�2r

(7)

To test thewhole correlation development process, experimentswere conducted for an environment in which well-establishedcorrelations already exist. For this purpose we mimicked experi-ments for the development of correlations for natural convection atvertical surfaces in a confined space [5]. The agreement between

experimentally measured coefficients and the previously devel-oped correlationwas good, and the details of this test are presentedin the results section of this report.

Bulk room air temperatureswithin the chamberweremaintainedat or near the temperature immediately outside the chamber tominimize any conductive losses through the chamber walls. This,combined with maintaining the same pressure in the chamber as inthe surrounding environment, provided for very good thermal insu-lation and air tightness of the chamber and a precisemass and energybalance. Nonetheless, very small losses through the insulated wallswere calculated to account for conductive losses. The energy balancewas checked for each experiment. If the balancewas satisfied, energysupplied to the chamber would equal energy removed according to:

_Qgen � _mcpðTair inlet � Tair outletÞ� _Qconduction losses ¼ X/0 (3)

wherem is the mass flow rate of air (kg/s) and cp is the specific heatcapacity of air (J/kg K). The normalized energy balance was calcu-lated by:

Balance ¼ X= _Q internal sources (4)

where Qinternal sources indicates the power released in the chamberby the electrical heaters or absorbed by hydronic cooling panels. Inexperiments where the difference was greater than 10%, it wasdetermined that the steady state condition in the chamber had notbeen reached and the experiments were discarded and/or repeated.

With the systematic error minimized as described in the textabove, care was taken to precisely evaluate the uncertainty asso-ciated with each reported value. Uncertainty is given as a functionof the imprecision inherent in all measured variables used tocalculate a reported value. With the uncertainty in each measure-ment calculated, the effect on the final value calculated is deter-mined based on the general uncertainty theory given in ASHRAEEngineering Analysis of Experimental Data [19]. As the convectioncoefficient is derived from the convective heat flux (qsurface_-convective) and reference temperature difference (DT, surface e

supply air or surface e room air) the uncertainty in the convectioncoefficient is calculated based on:

dh ¼ h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dqsurface convective

qsurface convective

!2

þ�dDTDT

�2vuut (5)

The uncertainty in temperature difference is calculated byuncertainty in surface (dTsurface) and air (dTair) temperature:

dDT ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�dTsurface

�2þðdTairÞ2r

(6)

The uncertainty in the specific convective heat flux for a givensurface (Qsurface_convective) consists of the uncertainties in the heatfluxes used for its calculation:

where Qsurface_total is the uncertainty in an electric heat fluxmeasurement for surfaces where electric heaters controlled thesurface temperature. For surfaces where the hydronic system isused, the uncertainty in total heat flux was calculated with an

Table 2Experimental matrix.

Configuration HVAC regime Ventilationrates

Blind angle

Configuration A,natural convection

Cooling small,medium, andlarge DT

NA �45� , 0� , 45�

Configuration A,ceiling diffuser

Cooling large DT 2, 12 ACH 0� , 45� , 80�

Configuration B,ceiling diffuser

Cooling and heatingsmall, medium,large DT

2e12 ACH �80� , �45� , 0� ,45� , 80�

Configuration A,floor register

Cooling large DT 2e12 ACH �80� , �45� , 0� ,45� , 80�

Configuration B,floor register

Cooling large DT 2e12 ACH �80� , �45� , 0� ,45� , 80�

J. Clark et al. / Building and Environment 59 (2013) 690e700694

equation similar to Eq. (6) based on the uncertainty in the waterflow measurement and supply-return water temperature differ-ence. Losses were calculated based on the U value of the chamberwalls and the surface outdoor air temperature difference. The cor-responding uncertainty Qwall_loss is calculated based on themeasured Qwall_loss and the uncertainty in these two temperatures.

Due to the complex long-wave radiation heat exchange betweenindoor surfaces, calculation of radiative heat flux is computation-ally very intensive and the calculation of the uncertainty in Qsurfa-

ce_radiative is correspondingly intensive. The uncertainty calculationof Qsurface_radiative for each surface was built into the program codedeveloped for the radiative heat flux calculation. The uncertainty inradiative heat flux for specific surfaces is based on view factors andincludes uncertainties in radiative heat flux in-between thisspecific surface and all outer characteristic surfaces in the testchamber. These were calculated based on uncertainties in surfacetemperatures and uncertainty in surface emissivity coefficients.

2.5. Experimental matrix

During the course of the investigation, several different windowconfigurations, HVAC regimes, and flow rates were tested. Thefollowing experimental matrix (Table 2) categorizes the experi-ments by the configuration analyzed, HVAC regime tested, venti-lation rates (ACH) at which the experiments were conducted, andthe different blind angles which were tested. In the HVAC regime

Fig. 3. Natural convection coefficient at window surf

column, cooling signifies the summer condition inwhich supply airis cooler than room air. Large DT corresponds to a supply-return airtemperature difference of 12 � 1 �C; medium DT to 8 � 1 �C; andsmall DT to 4 � 1 �C. Room set point was maintained at 23 �C for allexperiments.

3. Results and discussion

In this section, results of the various sets of experiments arepresented. Results of natural convection experiments are presentedfirst, followed by ceiling slot diffuser results, and then floor registerresults.

3.1. Natural convection

3.1.1. Window surfaceAn experimental analysis of the phenomenon of natural

convection in a window-blind assembly was conducted for a floor-to-ceiling window with blinds. Results are correlated to thetemperature difference between the window and the bulk room air(defined as the average of eight sensors spread throughout theinterior of the chamber) or between the blinds and the bulk roomair, according towhich surface the correlation describes. The resultsare given in the following paragraphs. In Fig. 3 and others to follow,“hroom” designates a convection coefficient developed with the bulkroom temperature as the reference temperature. Similarly “hsupply”uses the supply temperature as a reference. Troom refers to the bulkroom temperature and Tsupply to the supply temperature.

Convection coefficients which describe heat transfer at thewindow surface under natural convection conditions are given inFig. 3. The results show that when blinds are present, convection atthe window surface is best described by a correlation of the form of

h ¼ C�Tsurface � Troom

�1=4(8)

while the bare window case results correlate better to an equationof the form :

h ¼ C�Tsurface � Troom

�1=3(9)

As correlations for laminar floware typically given in the form ofEq. (8) and those for turbulent flow in the form of Eq. (9), these

ace for Configuration A with and without blinds.

Fig. 4. Boundary layer obstruction by blinds with the schematic of jet entrainment asa function of blind angle.

0 5 10 15 20 25 300

1

2

3

4

Experimental Data from Current Study for Various Blind Angles and Temperature Differences, Scaled for Comparison

Wright et al. (2009)

h room

[W/m

2 K]

Glass-Blinds Spacing [mm]

Fig. 6. Comparison of results at all blind angles tested with Wright et al. [18] model (allresults plotted are for Configuration A in Fig. 2).

J. Clark et al. / Building and Environment 59 (2013) 690e700 695

results suggest different near-windowflowcharacters for situationsin which blinds are present and those in which they are absent.

One conjecture as to the reason for this is that when the blindsare present, the distance between the window surface and thenearest tip of the blinds is such that the boundary layer is neverable to grow past a certain thickness, and thus eddies cannotdevelop and the flow never reaches turbulence (Fig. 4). Thisconjecture is given some credence by flat plate natural convectiontheory which predicts a boundary layer with a thickness of theorder 2 cm for laminar flow and a transition to turbulent flowoccurring on the wall in all situations analyzed [20]. Thisphenomenon would not be captured in an experimental setupshorter than roughly 1.5 m.

The variation of the effectiveness of heat transfer with blindangle is most likely due to the variation in the ease of entrainmentof room air into the gap between the blinds and the windowsurface, and thus the mass flow rate of air in the gap (Fig. 4). At anangle of �45�, blinds are oriented nearly parallel with the naturaldirection of entrainment into the boundary layer, and thus

Fig. 5. Comparison of results from this study with the results previously obtained byWright et al. [18] (model given in Wright et al. [18] with superimposed experimentalresults from this study).

entrainment is relatively easy. At a blind angle ofþ45�, blinds act asa barrier to the entrainment, which would naturally occur if blindswere not present. It should be noted that for blind angles of morethan 45�, or less than �45�, the trend witnessed in the analyzedrange would most likely not continue, as the path for entrainmentthrough the blinds would become smaller and eventually reachzero, preventing entrainment altogether and significantly damp-ening the effectiveness of heat transfer at the window.

The current investigation can be employed to validate theapproach put forth in ASHRAE RP-1311 [18]. The natural convectioncorrelations suggested byWright et al. [18] are presented in Fig. 5 ingraphical form. The correlations assume the user has selecteda convection coefficient of 3.5 W/m2 K to describe heat transferunder natural convection conditions from a bare wall or windowsurface. As can be seen, correlations are given as a function of thedistance between the glass and the shading layer, which in the caseof the current investigation are the Venetian blinds. In the current

0 1 2 3 40

1

2

3

4

5

6

7

45 degree blinds 0 degree blinds -45 degree blinds

h ro

om [W

/m2 K]

ΔTroom [°C]

h=2.0*ΔT0.33

Fig. 7. Natural convection coefficient at blind surfaces for Configuration A. DTroomrefers to the difference between the average blind surface temperature and the averagebulk room temperature. Solid line is a best-fits correlation with an exponent of 0.33 forthe data.

0 1 2 3 40

1

2

3

4

5

6

7

8

This study: -45 degree blinds This study: 0 degree blinds This study: 45 degree blinds Wright et al. 2009: -45 or 45 degree blinds Wright et al. 2009: 0 degree blinds

h ro

om [W

/m2 K]

ΔTroom [°C]

Fig. 8. Comparison of Wright [18] model for convection at blind surfaces withexperimental results.

J. Clark et al. / Building and Environment 59 (2013) 690e700696

investigation, blind-glass spacing is maintained at 25mm. From thecorrelation given in the current investigation, a no-blinds convec-tion coefficient of 3.5 W/m2 K corresponds to a temperaturedifference of 8.1 �C. Points are plotted for this temperature differ-ence, using the current correlations, superimposed on the graphdepicting the correlations ofWright et al. [18] In Fig. 5, h g-a (dottedline) describes heat transfer between the glass and the room air.

Results in Fig. 5 show that current results are in relatively goodagreement with theWright et al. model, albeit slightly higher, likelybecause of the different experimental setup. Results of the currentinvestigation also vary with blind angle, as the Wright et al. [18]model does not. This trend is further demonstrated by Fig. 6,which shows all results for the Configuration A, with convectioncoefficients scaled to compare them to a baseline hc value of 3.5 W/m2 K. As can be seen from the two figures, an allowance for changein the model due to blind angle would represent an improvementto the Wright et al. [18] model.

3.1.2. Blind surfacesNatural convection heat transfer at the blind surfaces was also

analyzed and convection coefficients specifically for the blindswere calculated. Fig. 7 shows the large degree of error inherent in

Fig. 9. Comparison of convection coefficient for window surface with no blinds versus winddiffusers. Blinds are at zero degrees for both geometries: A and B.

the calculation precludes any definitive conclusion being drawnfrom the results. As the blinds used were not heated, the temper-ature difference between the blinds and ambient air was often verysmall, resulting in the accuracy of the thermistors becoming rela-tively important. Future experiments with heated blinds will likelyproduce results with less uncertainty.

These results can also be qualitatively compared with the modelgiven in Wright et al. [18] to describe the effect of blind angle onconvection heat transfer at the shading surface (Fig. 8). It should benoted that data from the current experiment contains a large degreeof error, as correlations are based on a small temperature differencebetween blinds and room air, thus inflating the significance of the�0.1 �C precision of the thermistors used. The comparison showsvery good agreement between experimental data and the Wrightet al. [18] model for blind angles of 0� and �45�. However, theWright et al. [18]model could be improved by including the effect ofthe blinds at 45� blocking the flow into the assembly and decreasingthe effectiveness of heat transfer at the blind surfaces.

3.2. Forced convection with ceiling slot diffusers

This section presents the results of experiments run witha ceiling slot diffuser. It shows the results for the window surface inthe form of comparisons with the bare window case, for variousconfigurations. These results are followed by results for blindsurfaces given as a function of blind angle.

3.2.1. Window surfaceThe first comparison made in the ceiling slot diffuser experi-

ments is between the situations in which blinds were present andfully open (0�) and that in which they were absent. The results areshown as a function of volumetric flow rate in Fig. 9. Fig. 9a showsthat in Configuration A, blinds reduce convection heat transfer byapproximately 40%. Fig. 9b shows that the open blinds have theeffect of reducing convective heat transfer by roughly 30% at allflow rates in Configuration B.

Another important observation to notice in Fig. 9 is the tightclustering of points for each flow rate representing differenttemperature differences. These results show that the temperaturedifference has a negligible effect on the convective heat transfer.This suggests that the forced mode of convection is dominant at allflow rates. This implies that separate models need not be generatedto account for the possible competing effects of buoyancy caused bythe heated air and the downward supply momentum. Thisphenomenon was witnessed for the bare window configuration aswell, which was analyzed by Goldstein and Novoselac [8].

ow surface with blinds for configurations A (left graph) and B (right graph) with ceiling

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7

h=0.019 V0.8

half wall window full window

h ΔTSu

pply [W

/m2 K]

Flow Rate [m3/h]

h=0.025 V0.8

Fig. 11. Impact of window height on convection heat transfer at window surface nearceiling slot diffuser for the configuration with open blinds.

J. Clark et al. / Building and Environment 59 (2013) 690e700 697

The next parameter studied was the effect of the angle at whichthe blinds were set. As can be seen in Fig. 10, blind angle can affectthe overall convective heat transfer by as much as 40%. The blindangle at which convection was observed to be the greatest waspositive 45�. In this situation the blinds are oriented roughlyparallel with the direction of the bulk momentum of the jet, and assuch impede jet momentum to a lesser degree than angles inwhichthe jet and the blinds are perpendicular and thus the jet is retardedmost effectively by the blinds.

Two sensitivity studies were conducted in order to deter-mine if other relevant parameters were potentially influentialenough to warrant further research. The first looked at theeffect of the surface-air temperature difference as mentionedpreviously, which was embedded into the experiments quanti-fying the effect of blind presence (Fig. 9b). This showed that forthe ceiling slot diffuser experiments, temperature differenceaffected heat transfer very little. The second sensitivity studyconducted was on the relationship between the heating and thecooling condition. Theoretically, a warm jet issuing downwardinto a relatively cool room could experience buoyancy forcesdue to the room airejet air temperature difference that actedcontrary to the momentum forces of the jet. Ultimately, thesensitivity study showed that convection heat transfer in theheating or cooling conditions were virtually identical. Thissuggests again that the jet momentum is sufficiently larger thanthe buoyancy forces as to render the buoyancy effectsnegligible.

Since the final purpose of this project was to provide for moreaccurate calculation of cooling and heating loads in energymodeling software, an additional effort was introduced to quantifythe effect of the size of the window. The two most commonconfigurations found in commercial buildings are that of floor-to-ceiling windows and that of a 1.37 m window with a small wallbeneath it. These situations were each simulated as explainedpreviously and the results are contained in Fig. 11. The “halfwindow” situation corresponds to Configuration B.

As expected, the convection coefficients are consistently higherfor the situation inwhich only half the wall is a window. This is dueto the convention of using the supply temperature as a reference. Inthe case of the full-height window, the jet has a chance to heat upor cool down as it moves along the window, thus rendering thelocal temperature difference at lower portions of the windowsmaller, and affecting convective heat transfer accordingly. Whilethe physical heat transfer mechanism is unchanged, the averageheat transfer for the entire window surface as a function of supplytemperature is relatively smaller for the full-height window. This isdue to fact that the actual local temperature difference, the driving

Fig. 10. Effect of blind orientation on convection heat transfer at window surface

force behind the convective heat transfer, is smaller at lowerportions of the window.

3.2.2. Blind surfacesCorrelations were also developed for blind surfaces. Results are

given in Fig. 12 for both configurations. As fluid movement nearblind surfaces is complex, characterized by recirculating flowbetween the blinds and entrainment from both sides of the blinds,no attempt is made to make a strong connection between resultsand theory. Results indicate that the jet results in correlationssimilar to those for turbulent forced convection heat transfer atblinds surfaces and correlations are given in the form typicallyused, h¼CV0.8.

For Configuration B, in which the jet moving along the rela-tively short height of window results in a strong correlationbetween h and blind angle (b), a relationship between blind angleand heat transfer can be given in the form of an equation for theconstant C in the correlation h ¼ C _V

0:8, as shown in Fig. 13.

Comparison of the coefficient C for blind and window surfacesshow opposite trends. Unlike the correlation for windows, blindsurface convection is greatest when the jet is presented witha smooth surface to move along (i.e. the blinds-closed situation).When blinds are open, the jet approaches the blinds at largerangle and less of the blind surface is exposed to the strong jetflow; thus the convective heat transfer is less intense. The

for Configurations A (left graph) and B (right graph) with ceiling diffusers.

Fig. 12. Impact of blind orientation on convection heat transfer at blind surfaces for Configurations A (left graph) and B (right graph) with ceiling diffusers.

0 100 200 300 400 500 600 7000

1

2

3

4

Configuration A

h=0.0165V0.8

h=0.017V0.8

h=0.0135V0.8

h=0.013V0.8

h=0.0158V0.8

Blinds -45O

Blinds -80O

Blinds 0O

Blinds +45O

Blinds +80O

h ΑTs

uppl

y [W

/m2 /K

]

No blinds h=0.024V0.8

J. Clark et al. / Building and Environment 59 (2013) 690e700698

increased convection coefficient at the blinds corresponds toa reduced convection coefficient at the windows.

3.3. Forced convection with floor registers

Convection heat transfer at a window surface near a floorregister was analyzed as well. Experiments were conducted forseveral blind angles. The results for Configuration A are displayedin Fig. 14. Comparison of results for configurations with andwithout blinds (Fig. 14, left graph) shows that heat transfer ishindered up to 45% by the presence of the blinds and that theeffect of blinds is somewhat dependent on blind angle. Also, theresults indicate a small dependency on blind angle. The right graphin Fig. 14 show this dependency and compares it with thedependency for the ceiling diffuser. The variable C for the config-uration with the floor register has the reverse profile of the vari-able C for the ceiling slot diffuser. This reverse profile is due to thejet direction relative to the blinds. With a ceiling diffuser themaximum value of C (which indicates maximum convection at thewindow) is at 45� since this angle enables maximum air flowthrough the blinds; with a floor register the jet approaches fromthe opposite direction and thus the maximum flow through theblinds occurs at an angle of �45�.

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 900.00

0.01

0.02

0.03

0.04

0.05

Window Surfaces: C =0.024+1.480E-4 β- 1.303E-6 β

2-1.82E-8 β

3

Blind Surfaces: C=0.012+5.18E-5 β+9.87E-7 β

2-3.65E-9 β

h = C·V 0.8

Coe

ffice

nt "C

"

Blind angle β [ o ]

Fig. 13. Effect of blind angle on convection coefficient for window and blind surfaces inConfiguration B with a ceiling diffuser (blind angle is defined in Fig. 4).

Flow Rate [m3/h]

-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 900.00

0.01

0.02

0.03

0.04

0.05

Floor Diffuser C =0.0156-4.67E-5 β-1.467β2+3.89E-9 β3

Ceiling DiffuserC =0.024+1.480E-4 β-1.303E-6 β2-1.82E-8 β3

h = C·V 0.8

Coe

ffice

nt "C

"

Blind angle β [ o ]

Fig. 14. Forced convection coefficient at window surface for Configuration A with floorregisters (left graph) with the impact of blind angle (right graph).

0 100 200 300 400 500 600 7000

1

2

3

4

With blinds

No blinds h=0.017V0.8

Configuration B

Blinds -45o

Blinds -80o

Blinds 0o

Blinds +45o

Blinds +80o

h ΑTs

uppl

y [W/m

2 /K]

Flow Rate [m3/h]

h=0.0125V0.8

Fig. 15. Forced convection coefficient at window surface for Configuration B with floorregisters.

J. Clark et al. / Building and Environment 59 (2013) 690e700 699

Results for Configuration B are presented in Fig. 15 and, like forConfiguration A, blinds reduce convection coefficients at windowsurfaces by approximately 35%. When analyzing the impact of blindangle in this configuration, the results show a large degree ofscatter, and therefore no correlations predicting the dependency onblind angle were derived. This scattering of results for Configura-tion B is likely due to the lesser strength of the floor jet. Under thesecircumstances, the effect of the obstructions (blinds) becomesmorepronounced. However, the correlation for the window surface withblinds in Configuration B should be able to be employed in loadcalculation applications with an acceptable degree of uncertaintyfor most engineering applications.

Table 3Summary of results.

Configuration Surface Convection correlation h [W/m2 K]

Natural convection with blindsA Window h ¼ 1.89DT0.25 (blinds �45�)

h ¼ 1.67DT0.25 (blinds 0�)h ¼ 1.48DT0.25 (blinds 45�)

Blinds h ¼ 2.0DT0.33

Ceiling slot diffusers heating and coolingA Window h ¼ c$ð _V=LÞ0:8

c ¼ 0.063 (blinds 0� or closed)c ¼ 0.079 (blinds at 45�)

Blinds h ¼ 0:060ð _V=LÞ0:8 (bl. closed)h ¼ 0:030ð _V=LÞ0:8 (blinds open)

B Window h ¼ c$ð _V=LÞ0:8c ¼ 0.080 þ 4.93E�4b � 4.34E�6b2 � 6.06E�8b3

b e blind angle: 0 for open þ90 for closedBlinds h ¼ c$ð _V=LÞ0:8

c ¼ 0.040 þ 1.72E�4b � 3.29E�6b2 � 1.22E�8b3

b e blind angle: 0 for open þ90 for closed

Floor registersA Window h ¼ c$ð _V=LÞ0:8

c ¼ 0.052 þ 1.561E�4b � 4.867E�7b2 þ 1.30E�8b3

b e blind angle: 0 for open þ90 for closedB Window h ¼ 0:042ð _V=LÞ0:8

All temperatures (DT) are given in degrees Celsius and the normalized flow rate (V/L)is in m3 per hour of supply air per meter of perimeter wall.

The convection coefficients measured at blind surfaces forConfigurations A and B with floor registers are not shown in thisstudy because of the large degree scattering and uncertainty.

4. Summary

Through the course of more than 100 experiments, convectionheat transfer at window surfaces was characterized for differentwindow geometries, diffuser locations, and HVAC operatingregimes. In general, it was found that blind presence stronglyaffects forced convection at window surfaces, as does windowgeometry and supply conditions. HVAC regime (i.e. heating condi-tion or cooling condition) was found to be nearly irrelevant, as wassurface-air temperature difference.

Results are summarized in Table 3. For the purpose of providingcorrelations which can be adopted and used by industry profes-sionals and energy modeling programs, all correlations are given interms of the total volumetric flow rate along the length of the wallin question normalized by the length of the wall ð _V=LÞ. Thisconvention will introduce a source of uncertainty into the corre-lations, as the correlations were developed for a certain layout (2e1.2 m long registers per 4.5 m of wall length). However, thisconvention will allow the results to be readily used and representsan improvement over previous assumptions, such as naturalconvection or a single value of h in a perimeter zone. Results showthat improvements should be made to existing models of naturalconvection in window-blind assemblies to account for largergeometries and different blind angles. In situations where forcedconvection is present, new correlations are given.

There are several limitations to this study. While this studyanalyzes convection at window and blind surfaces for a diffuserpositioning which was deemed to be the most representative ofwhat is installed in commercial construction currently (50e70% ofperimeter zone length covered by diffusers), the investigationcould be extended to other diffuser types and layouts. Otherdiffuser types and spacings of floor registers or ceiling slot diffusersare likely to affect the applicability of the correlations. Larger ormore complex window configurations, such as a 12-foot high floor-to-ceiling window, an angled window, or a bay window, wouldcertainly experience heat transfer differently than the situationanalyzed and would require individual analysis. Blinds analyzedwere also chosen because of their prevalence, but other types suchas vertical blinds will produce different heat transfer characteris-tics. Lastly, while a 25 mm gap between blind and window surfacewas determined to be the standard gap in the vast majority ofcommercial construction, variation of the distance between blindand window may produce a more refined model that may bedesirable for a specific application.

Acknowledgements

This project was funded by the American Society of Heating,Ventilation, and Refrigeration Engineers (ASHRAE) RP 1416,a National Science Foundation Integrated Graduate EngineeringResearch Traineeship (NSF IGERT) in Indoor Environmental Scienceand Engineering, grant# nDGE-0549428, and a University of TexasEngineering Thrust Fellowship.

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