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Building and Environment 44 (2009) 2185–2192

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Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

Numerical analysis of convective heat transfer in fenestration withbetween-the-glass louvered shades

Mike Collins*, Syeda Tasnim, John WrightDepartment of Mechanical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada

a r t i c l e i n f o

Article history:Received 2 February 2009Received in revised form13 March 2009Accepted 23 March 2009

Keywords:FenestrationShadingLouversHeat transferBetween-panes

* Corresponding author. Tel.: þ1 519 888 4567x336E-mail address: mcollins@uwaterloo.ca (M. Collins

0360-1323/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.buildenv.2009.03.017

a b s t r a c t

A two-dimensional steady laminar natural convection model of a window cavity with between-paneslouvers (i.e., slats) was developed by approximating the system as a vertical cavity with isothermal wallsat different temperatures, and with rotatable baffles located midway between the walls. The baffles wereset to a third temperature so that night-time and day-time conditions could be considered. The effects ofwall spacing, baffle angle and temperature, and the wall-to-wall temperature difference were examined.It was found that the system is suited to a traditional one-dimensional analysis, and that the convectiveheat transfer is largely independent of the Rayleigh number for the conditions of practical interest.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The objective of this paper is to numerically examine naturalconvection heat transfer in window cavities containing rotatablelouvered shades. Such systems have become increasingly popular,and accurate heat transfer correlations are required for ratingpurposes and building energy analysis. Such systems have beenexamined extensively in recent times. To date, however, none havelooked at the situation where the system is sunlit.

Rheault and Bilgen [1,2] examined the overall heat transfer ratesof a window system using climatic conditions for a typical Canadianwinter and summer. In their analytical work [1], the temperaturevariation across the louvers and over the thickness of each glazingwas assumed to be minimal, and therefore conduction effects wereignored. Furthermore, the distance between the louver tips and thewindow glazing was relatively large. Therefore, it was assumed thatthe presence of the louvers did not interfere with the cavity flowwhen the louvers were at angles other than vertical. When thelouvers were placed vertically, the problem was treated as two side-by-side cavities with the louvers as a dividing wall. Longwaveradiation and convection transfer rates across the window systemwere considered. The numerical work concluded that the presenceof louvers between the glazings could reduce heating and cooling

55; fax: þ1 519 888 6197.).

All rights reserved.

loads. The analytical results were later verified by the resultsobtained in the experimental study [2].

Garnet [3] measured the centre glass heat transfer of a windowsystem with an aluminum louvered blind between two panes ofglass. Experiments were run at several different blind louver anglesand three different pane spacings. It was observed that, for theblind in the fully open position, the presence of the blind decreasedthe window’s thermal resistance. It was speculated that while inthis position, conduction effects in the blinds was having a signifi-cant effect. For all cavity widths a steady improvement in theperformance of the window was observed as the blind was closed.

Yahoda [4] and Yahoda and Wright [5,6] performed detailedmodeling of the effective longwave radiative and solar/opticalproperties of a louvered blind layer that could be placed anywherein the window system. The effective longwave radiative propertiesmodel was were based on fundamental radiant exchange analysis,and accounted for the louver width, spacing, angle of tilt, andemissivity. The effective solar-optical properties model treatedsolar beam and diffuse radiation separately. Finally, a simplifiedcenter-glass model of thermal transmissivity (U-factor) wasproposed by combining the longwave radiation model with somesimple convection correlations. This model was moderatelysuccessful.

Naylor and Collins [7] developed a two-dimensional numericalmodel of the conjugate convection, conduction and radiative heattransfer in a double glazed window with a between-panes louveredblind. They obtained numerical results both with and without the

y

g

x

H

A

B C

D

P

W

w

a b

Fig. 1. (a) Blind louvers enclosed between glass panes and (b) computational domain.

Nomenclature

A aspect ratio, dimensionlessCp specific heat, J/kgKg gravity, m2/sh heat transfer coefficient, W/m2KH cavity height, mmk conductivity, W/mKNu Nusselt number, dimensionlessp pressure, PaP louver pitch, mmPr Prandtl number, dimensionlessq00 heat flux, W/m2

Ra Rayleigh number, dimensionlessT temperature,�C, KU thermal transmissivity, W/m2Ku, v velocity, m/sw louver width, mm

W cavity width, mma thermal diffusivity, m2/sD change/differencef louver angle, degreesr density, kg/m3

m viscosity, kg/msq temperature, dimensionless

Subscriptsav averagecg centre-glassleft left walllocal localref reference1 left wall/left glass2 right wall/right glass3 louver/baffle

M. Collins et al. / Building and Environment 44 (2009) 2185–21922186

effects of thermal radiation. It was concluded that data froma conjugate convection-conduction CFD model can be subsequentlycombined with a very simple radiation model to estimate the U-factor of the complete window/blind enclosure.

Recently, Huang [8] conducted an experimental investigationsimilar to that of Garnet [3]. He examined the effects of louvers onthe convective and radiative heat transfer inside a vertical windowcavity using two sets of glazings; clear/clear and low-e/clear. Hisexperiment used isothermal vertical surfaces at various panespacings and louver angles to examine the centre-glass U-factor.The results showed better window performance when the louverswere tilted from their fully open position and also when the low-ecoating was used. More importantly, it was discovered that corre-lations used to predict heat transfer in window cavities could beused to predict heat transfer in the present system [9]. To do so, thefollowing assumptions were made:

� The system could be approximated as two vertical cavities ofa width that is a function of louver tip to glass spacing.� There was no transfer of flow across the blind layer except at

the ends of the cavity.� The convective heat transfer was laminar natural convection

correlations [10].

These assumptions were later verified via flow visualizationperformed by Almeida et al. [11]. Those studies further showed thatturbulent transition was expected to begin at cavity widthsexceeding 40 mm.

A simplified convective heat transfer model was developedwhich was subsequently combined with Yahoda’s [4] longwaveradiation model to predict the centre-glass U-factor. The newmodel reproduced experimental data accurately.

In this study, laminar natural convection heat transfer was studiednumerically. A two-dimensional model was used in keeping withestablished window analysis methodology. Convective heat transferwas considered for situations when the blind was at a third prescribedtemperature relative to the glass temperatures. As a 3-temperaureanalysis, simulation of heat transfer can be performed for cases wherethe shade is hotter than the glass; simulating absorbed solar radiation.That is, the system was analyzed for situations that represent sunlitconditions. In future work, the results produced here will be coupledwith Yahoda’s [4] longwave model, and comparisons will be made tothe results of Huang [8].

Numerical results will be examined on two levels. First, thesimulation results will provide information about flow structuresand heat transfer that improve our understanding of the underlyingheat transfer processes. Second, in keeping with a traditional one-dimensional centre-glass analysis, particular attention will be paidto average convective heat transfer across the center portion of thecavity. The development of a correlation and comparison to thework of Huang [8] will be the subject of a future publication.

2. Physical model

A tall vertical enclosure was chosen to represent the glazingcavity, and baffles located on the vertical centre line of the enclo-sure represented the blind louvers (Fig. 1). The two window panes(AB and CD) were set apart at a distance, W, and a height, H, andwere assumed to be isothermal. The end walls (BC and DA) wereassumed to be adiabatic. The blind consisted of a set of evenlyspaced isothermal baffles of width, w, and pitch, P (pitch is the

Table 1Constant geometric parameters used in the numerical model.

H (mm) w (mm) No. of baffles Pitch P (mm)

367.0 14.8 30 11.8

M. Collins et al. / Building and Environment 44 (2009) 2185–2192 2187

vertical distance between two consecutive louvers), which could berotated about their centre to an angle, f, from the horizontal. Thebaffles were assumed to be made of a material with high thermalconductivity, and flat with zero thickness.

Three temperatures were required to model the system. In thisstudy, T1 and T2 are the left wall (AB) and right wall (CD) temper-atures, and T3 is the baffle temperature. For convenience, thetemperature difference across the cavity and dimensionless baffletemperature are defined as DT ¼ T2 � T1 and q3 ¼ (T3 � T1)/(T2 � T1), respectively. Air properties were evaluated at a referencetemperature, Tref., that represents all three temperatures in thesystem with the baffle temperature predominating.

Tref ¼12

�T1 þ T2

2þ T3

�(1)

The air properties at Tref were taken from Hilsenrath [12].The numerical model was an approximation of a real fenestration.

For an actual window, there would be frame effects and only thecenter-glass region would be nearly isothermal. The idealized systemwas, however, consistent with the experimental setup used in theexamination conducted by Huang [8]. Geometric parameters thatremained constant for all numerical simulations are given in Table 1.

To understand the flow field and heat transfer characteristics ofthe system, three different wall spacings (W ¼ 17.8 mm, 25.4 mm,and 40.0 mm), three different wall-to-wall temperatures(DT ¼ 35 �C, 10 �C, and �15 �C), three different baffle temperatures(q3 ¼ 0, 0.5, and 1), and three different baffle angles (f ¼ 0�, 45�,and �45�) were considered. Table 2 presents the matrix of condi-tions considered in this study.

Nu a

v

1.2

1.3

1.4

1.5

1.6

Present StudyWright & Sullivan

Lee & Korpela

A=15

A=20

A=40

3. Governing equations

Steady laminar natural convective heat transfer in the system isdescribed by the fundamental conservation laws of mass,momentum, and energy. The Boussinesq approximation has beenapplied to the y-momentum equation, and the assumptions of anincompressible fluid flow with negligible viscous dissipation, andconstant thermo-physical properties has been made.

The dimensional forms of the conservation equations are

vuvxþ vv

vy¼ 0 (2)

r

�u

vuvxþ v

vuvy

�¼ �vp

vxþ m

v2uvx2 þ

v2uvy2

!(3)

Table 2

Input variables used in the numerical model.

T1 (�C) T2 (�C) q3 T3 (�C) DT (�C) W (mm) f (degrees)

�10.0 25.0 0.0 �10.0 35.0 17.8/25.4/40.0 �45, 0, 45�10.0 25.0 0.5 7.5 35.0�10.0 25.0 1.0 25.0 35.015.0 25.0 0.0 15.0 10.015.0 25.0 0.5 20.0 10.015.0 25.0 1.0 25.0 10.040.0 25.0 0.0 40.0 �15.040.0 25.0 0.5 32.5 �15.040.0 25.0 1.0 25.0 �15.0

r

�u

vv þ vvv�¼ �vpþ m

v2v2 þ

v2v2 þ grb

�T � Tref

�(4)

vx vy vy

vx vy

!

uvTvxþ v

vTvy¼ a

v2Tvx2 þ

v2Tvy2

!(5)

Here, u, v, and T are velocity components in the x, y directionsand temperature, respectively. r, m, and a are the density, dynamicviscosity and thermal diffusivity respectively. b is the volumeexpansion coefficient where b ¼ 1/Tref. g is gravitational accelera-tion, and p is the pressure.

To solve Eqs. (2)–(5), the boundary conditions must be specified.No slip conditions were applied to all surfaces, the temperaturewas specified for both side walls and the baffles, and the endsurfaces were adiabatic. The dimensional forms of the boundaryconditions are:

AB u ¼ v ¼ 0; T ¼ T1CD u ¼ v ¼ 0; T ¼ T2

BC; DA u ¼ v ¼ 0; vT=vy ¼ 0On the baffles u ¼ v ¼ 0; T ¼ T3

(6)

The steady state governing equations were discretized by thefinite-volume method using a third-order Quick scheme [13].The solution procedures included the conjugate gradient methodand the PISO algorithm (Pressure-Implicit with Splitting ofOperations) [14] to ensure correct linkage between pressure andvelocity. The typical number of iterations needed to obtainconvergence was between 5000 and 10,000. The tolerance of thenormalized residuals upon convergence was set to 10�5 for everycalculation case.

4. Model checks

To provide confidence in the numerical model, steady laminarnatural convection in a vertical cavity was also studied numerically,and compared to published solutions by Lee and Korpela [15], andWright and Sullivan [16]. Comparisons were made by plotting the

Ra4000 6000 8000 10000 12000 14000

1

1.1

Fig. 2. Comparison of the Nuav for the hot wall of the cavity versus Lee and Korpela[12] and Wright and Sullivan [13].

Fig. 3. Isothermal lines and velocity vectors for f ¼ 0� (top), 45� (middle), and �45� (bottom). W ¼ 17.8 mm, T1 ¼15 �C and T2 ¼ 25 �C.

M. Collins et al. / Building and Environment 44 (2009) 2185–21922188

average Nusselt number, Nuav, versus Rayleigh number, Ra, atdifferent aspect ratios, A ¼ H/W. Nuav as given by

Nuav ¼1H

ZH

0

Nulocaldy (7)

where Nulocal is the local Nusselt number and is given by

Nulocal ¼ local

k(8)

h W

Here, k is the conductivity of the air, and hlocal is the local convectiveheat transfer coefficient and is defined by

hlocal ¼q00

DT(9)

q00 is output by the software at q00 ¼ �kwT=wx at the wall.

Fig. 4. Isothermal lines and velocity vectors for q3 ¼ 0 (top), 0.5 (middle), and 1 (bottom). f ¼ 0� , T1 ¼15 �C, and T2 ¼ 25 �C.

M. Collins et al. / Building and Environment 44 (2009) 2185–2192 2189

Ra is given by

Ra ¼ r2gbDTW3

m2 Pr (10)

where Pr is the Prandtl number

Pr ¼ mCp

k(11)

Here, Cp is the specific heat of the air. Fluid properties were eval-uated at a reference temperature

Tref ¼�

T1 þ T2

2

�(12)

Results were determined for cavities with aspect ratios of A ¼ 15, 20and 40 using a uniform grid size of (W � H) of 60 � 300 (Fig. 2). Forthe cases of A ¼ 15 and 20, the predictions of Lee and Korpela [15]agree with the present numerical simulation to within 0.7%, whilethe predictions of Wright and Sullivan [16] agree to within 1.5%. AtA ¼ 40, agreement is not as good, although Nuav is still predicted towithin 0.1.

In order to determine the proper grid size for this study, a griddependency test was also conducted for the vertical cavity(W ¼ 17.78 mm) with the baffles in the horizontal position, and forthe geometry presented in Table 1 and Fig. 1. Temperatures were setto T1 ¼ �10 �C, T2 ¼ 25 �C, and T3 ¼ 7.5 �C. These variables resultedin Ra¼ 2.92 � 104. Seven different grid densities were used for thegrid independence study. Considering both the accuracy and the

Fig. 5. Isothermal lines and velocity vectors for W ¼ 17.8 mm (top) and 25.4 mm (bottom). f ¼ 0� and q3 ¼ 0.5.

M. Collins et al. / Building and Environment 44 (2009) 2185–21922190

computational time involved, a grid density (W � H) of 80 � 434was chosen for W ¼ 17.8 mm. By the same method, grid densities of120 � 434 and 200 � 434 were chosen for W ¼ 25.4 mm, and40.0 mm spacings, respectively.

5. Analysis and discussion

It is useful to first examine the flow structures and heat transferto improve our understanding of the underlying heat transferprocesses. Figs. 3–5 show isothermal lines and velocity vectors atthe top of selected cavities. Fig. 3 shows the effect of baffle angleand temperature for W ¼ 17.8 mm, T1 ¼15 �C, and T2 ¼ 25 �C, Fig. 4shows the effect of cavity width and baffle temperature for f ¼ 0�,T1 ¼15 �C, and T2 ¼ 25 �C, and Fig. 5 shows the effects of cavitywidth and wall temperatures for f ¼ 0�, T1 ¼15 �C, and T2 ¼ 25 �Cfor W ¼ 17.8 mm and 25.4 mm.

The effect of baffle temperature is shown in Figs. 3 and 4. Forq3 ¼ 0.5, the system is geometrically and thermally symmetric. Assuch, the isotherms on both sides of the cavity are also symmetric(albeit in the opposite direction), indicating an equal amount ofheat transfer at both surfaces. When q3 ¼ 0, however, there is notemperature difference between the left wall and the baffles. Assuch, the isotherms are all between the right wall and the baffles.The opposite occurs when q3 ¼ 1. Finally, while the vector plots

show a turn-around region at the tops of the cavities, theisothermal lines do not penetrate appreciably to the opposite sideof the cavity for any of the cases. It appears as if the turn-aroundregion at the cavity ends is very short. This suggests that the endregions of the cavity have little effect on the heat transfer betweenthe walls.

The effects of baffle angle are demonstrated by Fig. 3. In all cases,the heat transfer at the baffle tips is increased due to increased fluidflow when the baffle tips are in close proximity to the walls. Thiseffect was also seen in the results of Huang [8] and Garnet [3] whofound that an open blind, when the louvers and glass were in closeproximity, resulted in larger thermal transmission then a similarsystem with no blind present. Furthermore, it is noted that theisotherms extend into, but not beyond the baffle layer in all cases.The corresponding vector plots show that convective cells formbetween the baffles, and no significant transfer of fluid occursbetween opposite sides of the cavity via the baffle layer. Thisphenomenon supports the treatment of the system as two verticalcavities (right wall–baffles and baffles–left wall).

The effects of cavity width are demonstrated by Figs. 4 and 5.The fluid velocity increases as the spacing increases, resulting inlarger turn-around regions near the cavity ends. In practice,fortunately, a 40.0 mm wide window cavity is extremely rare. Theturn-around regions that represent the more realistic windows

0.00.51.01.52.02.53.03.54.04.55.0

-1.0E+05 0.0E+00 1.0E+05 2.0E+05 3.0E+05

Nu c

g

W=17.8 mm / θ3 = 0.0 W=17.8 mm / θ3 = 0.5 W=17.8 mm / θ3 = 1.0 W=25.4 mm / θ3 = 0.0 W=25.4 mm / θ3 = 0.5 W=25.4 mm / θ3 = 1.0 W=40.0 mm / θ3 = 0.0 W=40.0 mm / θ3 = 0.5 W=40.0 mm / θ3 = 1.0

M. Collins et al. / Building and Environment 44 (2009) 2185–2192 2191

(17.8 mm and 25.4 mm) is still small. It is also noted that in general,the isothermal lines become denser at the walls as the cavityspacing decreases. Heat transfer is therefore highest for the lowestpane spacing.

The effects of wall temperature are shown in Fig. 5. The fluidvelocity increases only slightly with the increase of DT for bothwidths. Furthermore, the cells located between the louvers reversedirection depending on which wall is hotter. Overall however, thetemperature difference has little impact on the flow structures.

To evaluate how the baffles affect the heat transfer, it is neces-sary to observe the variations of Nulocal on the walls. Due to the factthat this is a three temperature problem, negative and positiveNusselt numbers can result where the sign is not indicative of thedirection of heat flow. For this discussion, positive Nuavg indicatesthat heat flux is from the surface, while negative Nuavg indicatesthat heat flux is into the surface.

Fig. 6 shows an example of Nulocal along the right wall of thecavity for W ¼ 17.78 mm, f ¼ 0�, T1 ¼15 �C, and T2 ¼ 25 �C. As waspredicted in the preceding paragraphs, one can observe that theproximity of the baffle tips producing a significant periodic effecton the Nulocal distribution, where the peak values of Nulocal indicatethe positions of the louvers. The small turn-around region the topand bottom of the cavity are also confirmed. More importantly, theheat transfer is shown to be steady-periodic after the 1st bafflefrom either end of the cavity. The baffles prevent boundary layergrowth on the cavity walls. As the problem is symmetric, Nulocal atthe left wall can be examined via the same plot whereq3;left ¼ jq3 � 1j and the Nulocal,left ¼ �Nulocal. For example, toexamine Nulocal on the left wall for q3 ¼ 1, then look at the resultsfor q3 ¼ 0, and take the negative value of the resulting Nulocal.

The previous result is a fortunate occurrence in that most windowsare analyzed from a one-dimensional center-glass perspective, andultimately a center-glass U-factor would be required for use inwindow rating software and building energy studies. As such,a center-glass Nusselt number, Nucg, has been calculated at the centerof the cavity between two consecutive louvers

Vertical Distance in mm

Nu l

ocal

100 200 300 400

0

1

2

3

4

5

6

7

3=0.5

3=0

3=1

Fig. 6. Variation of Nulocal along the right wall of the cavity for W ¼ 17.8 mm, f ¼ 0� ,T1 ¼15 �C, and T2 ¼ 25 �C. For left wall: q3;left ¼ jq3 � 1j and Nulocal,left ¼ �Nulocal.

1Zye

Nucg ¼ 2Pys

Nulocaldy (13)

Fig. 7 shows Nucg for all situations of 0�, 45�, and�45�, respectively,and on the right wall.

The symmetry of the heat transfer is further demonstrated inFig. 7. As before, Nucg at the left wall can be examined via the sameplot where q3;left ¼ jq3 � 1j and the Nucg,left ¼ �Nucg. Therefore,when q3 ¼ 0.5, and the baffle temperature is at the average ofthe two vertical walls temperatures, Nucg on the left wall equals thenegative of that on the right wall. Furthermore, when q3 ¼ 1, thelouver and the right wall are at the same temperature, and whenq3 ¼ 0, the louver and the left wall are at the same temperature.Under these circumstances, there should be little heat transferbetween the baffle and the wall. The figures show that this isindeed the case, and a value of Nucg near zero results. For theopposite situation of heat transfer between the baffle and the leftwall when q3 ¼ 1, and between the baffle and the right wall whenq3 ¼ 0, the maximum Nucg occurs. Practically, the symmetricalnature of the problem means that the same correlation wouldsuffice for both sides of the system.

Ra

0.00.51.01.52.02.53.03.54.04.55.0

-1.0E+05 0.0E+00 1.0E+05 2.0E+05 3.0E+05

Ra

Nu c

g

0.00.51.01.52.02.53.03.54.04.55.0

-1.0E+05 0.0E+00 1.0E+05 2.0E+05 3.0E+05

Ra

Nu c

g

Fig. 7. Nucg for f ¼ 45� (top), f ¼ 0� (middle), and f ¼ �45� (bottom) on the right wall.For left wall: q3;left ¼ jq3 � 1j and Nucg,left ¼ �Nucg.

M. Collins et al. / Building and Environment 44 (2009) 2185–21922192

The effects of pane spacings and temperature difference on Nucg

are also presented in these figures. Nucg is highest for the lowestwall spacing in all cases. Furthermore, in most cases, Nucg is almostindependent of Ra. The exceptions are the high Ra cases (i.e., whenW ¼ 40 mm) and the high temperature cases (DT ¼ 35 K) coupledwith a small baffle tip to wall spacing (i.e. f ¼ 0� and W ¼ 17.8 mm),and a large baffle–wall temperature difference (i.e., q3 ¼ 1 at rightwall or q3 ¼ 0 at the left wall). Considering the 40 mm spacing, thecalculated Ra’s are large and heat transfer in those cavities may bedominated by advection. It is also likely that the assumption ofsteady laminar flow for the widest pane spacing is not valid.Practically, however, windows are rarely built with 40 mm spacingsdue to structural considerations. These cases were examined out ofcuriosity. Concerning the second exception, the proximity of thebaffle to the wall likely enhanced the cellular flow between thebaffles, and enhanced the heat transfer. However, the conditionsrequired for this to occur are at the limits of the practical cases thatwould be considered in a building energy analysis, and the result-ing change in Nucg was not significant. Practically, it may bepossible to represent the heat transfer in the system in a way thatdecouples Ra and Nucg. As was suggested by Huang [8], the baffletip–wall spacing appears to be the main geometric parameterneeded for a correlation.

6. Conclusions

A finite-volume model of a glazing cavity with between-paneslouvers has been developed and validated. Examination of thenumerical results suggested that a number of assumptions can beapplied to the formulation of a simplified heat transfer model.These assumptions relate to the treatment of direct convectionbetween the glass, the intra-louver heat transfer, and the glass-to-louver heat transfer characteristics.

� The energy transfer that would occur at the end regions, whenthe flow reverses cavity sides, and by air entrainment directlythrough the louvers, was found to be negligible. From thenumerical model, Nulocal was influenced at the ends of thecavity over a small distance, and therefore, the turn-aroundregion is also small. Flow across the cavity was also negligibledue to the formation of cells between the louvers. For thesereasons, the convective heat transfer could be represented asthe convective heat transfer from the glass-to-blind and blind-to-glass, without including a glass-to-glass term.� Nulocal reached a steady-periodic state over a very short

distance. Practically, this supports the one-dimensional centre-glass analysis preferred by building modelers.� It was shown that the temperature drop across the cavity exists

mostly between the blind tips and the glass. The convectivecells that form between the slats create mixing which makesthe blind-section of the cavity essentially isothermal (i.e., withnegligible resistance to heat flow). Therefore, no resistanceneeds to be assigned to the blind section.� The isotherms spread slightly into the spaces between the

louvers. On the basis of this observation it seemed reasonableto treat convective heat transfer between the glass and the

blind using established vertical cavity correlations, where thewidth of the cavity is based on the glass-to-blind spacing withsome sort of geometric correction factor applied. That is Rawould be calculated on the basis of a cavity width which isa strong function of slat angle.

Combining these conclusions, the convective heat transfer ina window cavity with a blind can be treated as a combination of twovertical cavities from the glass-to-blind and blind-to-glass withoutaccounting for the blind section. The cavity width will be somemodified width based on the slat geometry and the slat tip-to-glassspacing.

A correlation can be produced from these results; however, suchan exercise is outside the scope of this paper. A future paper will bededicated to the development of a Nucg correlation, and thecomparison of results to the work of Huang [8].

Acknowledgements

The Natural Sciences and Engineering Research Council ofCanada and The CANMET Energy Technology Centre are gratefullyacknowledged for their support of this work.

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