SIMPLIFIED PROCEDURE TO ESTIMATE THE

DYNAMIC THERMAL PERFORMANCE

OF EXISTING WALLS P. Fazio, Ph.D. ASHRAE Member

ABSTRACT

R. Zmeureanu

The dynamic thermal performance of existing walls, due to deterioration with age, construction defects, the effect of air infiltration or moisture migration, is unknown, and usually the desi gn val ues are used for the heat trans fer ca 1 cuI at ions in bui 1 di ng renovation activity. In this paper, Balcomb and Hedstrom's technique (1980) for estimat­ing heat fluxes using the temperature measurements within a wall is extended. A multiple linear regression model is used to estimate the conduction transfer function coefficients for both homogeneous and multilayer walls. The hourly heat flux at the inside surface of the wall is then calculated. A microcomputer program has been developed based on this simplified procedure, and analysis indicates an acceptable accuracy.

INTRODUCTION

Estimating the thermal performance of existing walls plays an important role in the con­ceptual stage of building renovation. Usually, the effect of deterioration with age, construction defects, and the effects of air infiltration or moisture migration are un­known; consequently, the design values are used. The heat gain/loss through the wall and the heating/cooling loads of the room are then underestimated. Field experiments on steady-state thermal performance have shown differences greater than 30% between the measured and the design thermal resistance (Fang et al. 1985; Flanders 1985) due to con­vection within wall, construction deficiencies, thermal bridges, and air leakage.

The procedures for in-situ measurements of thermal performance can be classified as:

1. Active methods, where an exterior known power is appl ied on the wall , and then temperatures and/or heat fluxes are measured.

2. Passi ve methods, where the temperatures or the heat fl uxes wi thi n the wall are measured under the weather induced effects.

Simple or complex models are then used in both methods to calculate the thermal resistance or other thermal parameters (e.g., time constant) based on the previous measurements.

So far, researchers have allocated more attention to improvement of the active methods, using more accurate equipment or new mathematical approaches to analyze the measurements (Modera 1985; Sherman et al. 1982; Brown et al. 1979). However, such refine­ments cannot avoid the limitations generated by the basic concept of the active methods, that is, the development of an artificial environment on a .small area of the wall. The effect of climatic factors, such as solar radiation, wind, or rain, has been avoided,

Paul Fazlo, 01 rector and Professor, Centre for Building Studies, Concordia University, Montreal, Quebec, Canada.

Radu Zmeureanu, Research Engi neer, Centre for Building Studies, Concordia University, Montreal, Quebec, Canada.

255

protecting the wall against them (Anderson 1984). Hence, the results do not represent the real behavior of the wall, but rather the response under the controlled conditions. More­over, the lateral heat flow is not taken into consideration, which has an important effect on the results, especially for multilayer walls.

Passive methods have the advantage of analyzing walls under conditions occuring natur­ally, including the combined effect of air infiltration, moisture migration, short- and long-wave radi ati on, and three-dimens i onal pattern of the heat trans fer. Heat fl ux sensors have been used for winter steady-state and summer transient heat flow measurements (Kuehn 1982).

However, the calibration of the heat flux sensors for a particular situation requires elaboration and adequate equipment (Flanders 1985). Since the experience with heat flux meters has not been encouraging, a passive technique for determining heat fluxes from temperature measurements wi thin the wall has been developed (Bal comb and Hedstrom 1980). The one-dimensional heat diffusion equation is solved by the finite difference method, and the thermal properties of the wall are iteratively adjusted until the calculated temper­ature distribution approximates the measurements. Then the heat fluxes at inside and out­side surfaces of the wall are calculated. When applied to a homogeneous wall, the thermal conductivity was estimated at two points within the wall with error between 8.8% and 10.3%, for a root mean square error of the temperature of about 1.5 F (0.83°C). However, the use of this model for a multilayer wall requires information about the real structure and thermal properties of the layers, taking into account the degradation with age or the construction defects. Hence, a destructive procedure of investigation is required to collect these data from existing walls, which is not always possible or appropriate.

In this paper, a simplified passive procedure to define the dynamic thermal perform­ance of existing walls is presented, based on Balcomb and Hedstrom's idea of using temper­ature measurements within the wall. A multiple linear regression model is used to estim­ate the conducti on trans fer functi on coeffi ci ents for both homogeneous and multi 1 ayer walls. A microcomputer program has been developed using this simplified procedure to analyze the temperature measurements and to estimate the hourly heat flow at the inside surface of the wall.

MATHEMATICAL MODEL

The heat flux at the inside surface of a wall can be estimated using the conduction transfer functions (Kusuda 1976), under the general form:

where

qt = heat fl ux at insi de surface (W/m2) X,Y = conduction transfer functions (W/m 2·C)

Z = conduction transfer function

T louts i de surface temperature (OC)

T2 = inside surface temperature (OC)

qt-1 = heat flux at previous time (W/m2)

(1 )

It is assumed for thin layers 6X (Figure 1) that the heat flux, qt' at the inside sur­face can be approximated by:

(2)

256

where

k thermal conductivity of the first layer (W/mOC) AX = thickness of the first layer (m) Tx = temperature at the outside surface of the first layer

substituting Equation 2 into Equation 1:

+ (~ + ~x) T2,t + (~- ~)T2,t-1 + rr T2,t-2 +

Vn 1 + lK T2,t-n + Z -ax Tx,t-1 (3)

The unknown variables in Equation 3, (~, rt, Z) will be defined using the temperature history at three points of the wall (l,X,2). To do this, a multiple linear regression model is assumed for Equation 3:

(4)

A system of normal equations is generated (Appendix A) and then solved to obtain

Xi Vi lK ' ~, Z

In order to verify the accuracy of these results, they are substituted in Equation 5 to solve for temperature at point x.

where

Tx,c = calculated temperature at point X Tx = measured temperature at point X

(5 )

Then, the mean and the standard deviation values of the difference between the measured and the calculated temperature, Tx, are computed.

While the degradation or construction defects usually occur within the wall for multi­layer cases, involving the insulation and the air cavity, the thermal conductivity, k, of the fi rst 1 ayer from ins i de can be estab 1 i shed wi thin acceptabl e accuracy. Then, the estimated thermal conductivity will be used to calculate the conduction transfer function coefficients from the previous results:

Xi = (Xi) k • k (6)

Vi = ( Vi) k • k

Z = Z

Finally, the hourly heat flux at the inside surface of the wall is calculated using Equation 1.

257

A user-friendly software called METCOM has been developed on a microcomputer based on the above procedure. The following input data are required:

- thickness and thermal conductivity of the first layer from the inside, - history of the temperature variation at the inside and outside surfaces of the wall

and at a point within the wall.

Four terms of the conduction transfer functions, X and Y, are used in the actual vers­ion of this software.

ANALYSIS

The simplified procedure has been applied to two wall types:

1. Homogeneous concrete wall (Table 1), in December, for variable and controlled room air temperature, T = 68± 0.5 F (20 ± 1°C).

2. Multilayer wall (Table 2), December and June, for controlled room air temperature at 68 ± 0.5 F (20 ± 1°C).

A detailed computer simulation program, based on the heat balance method and finite difference technique, has been used to assess the temperature history at points 1, X, and 2, for walls with different orientations, under one diurnal cycle.

The s imul ated temperatures have been cons i dered as measured values and then used by the METCOM program to estimate the dynamic thermal behavior of these walls.

Besides the comparison between measured and calculated temperature, Tx, for a supplementary verification of these particular cases, the wall conductance has been determined as follows:

U

U

24 r qi

i =1

wall conductance (W/m 2 C) = heat fl ux as gi ven by Equati on 1 (W/m2)

average temperature difference over 24 hours, between outside and inside surface of the wall (OC)

Appendix B presents the temperature history at points 1, X and 2, as well as the results generated by the METCOM program for some cases under analysis.

DISCUSSION

The results provi ded by thi s simp 1 ifi ed procedure i ndi cate that the dynami c thermal performance of exi sti ng wall s (homogeneous and nonhomogeneous) can be estimated wi th acceptable accuracy for building renovation practice.

Both mean and standard devi ati on of the difference between the measured and the calculated temperature, Tx , within the wall are less than 0.3°C for homogeneous walls (Table 3) or 0.6°C for multilayer walls (Table 4). The calculated wall conductance (Equation 7) shows a difference from the theoretical value of about 1.4-11.7% (homogeneous wall) or 1.9-21.8% (multilayer wall), for cases that were analyzed.

The conduction trans fer functi on coeffi ci ents, as defi ned by thi s method, must be calculated for each wall, taking into consideration the orientation. The use of south wall conefficients, for example, to walls with other orientations generates errors of about 30-85% (Appendix C).

258

CONCLUSION

The simplified procedure presented in this paper is useful to those involved in building renovati on for assessi ng the dynami c thermal performance of exi sti ng walls. The temper­ature measurements at three points within the wall are analyzed, and then the conduction transfer function coefficients are defined for that particular situation.

The theoretical analysis of several cases has shown that the results are within an acceptable accuracy for the current practice.

The method should be tested under a succession of different days, using both computer simulation and measurements in-situ.

REFERENCES

Anderson, B.R. 1984. "Site-testing thermal performance a CIB survey." Building Research and Practice, Volume 12, Number 3, May/June.

Balcomb, J.D., and Hedstrom, J.C. 1980. measurements made in massive walls." Conference, October.

"Determi ni ng heat f1 uxes from temperature Proceedings of the 5th National Passive Solar

Brown, W.C., and Schuyler, G.D. 1979. "A calorimeter for measuring heat flow through wa 11 s." Proceedi ngs of the ASHRAE/OOE Conference, Thermal Performance of the Exteri or Envelopes of Bulldlngs. Atlanta: American Society of Heating, Refngerating and Alr Conditionlng Engineers.

Fang, J.B., and Grot, R.A. 1985. "In situ measurements of the thermal resistance of building envelopes of office buildings." ASH RAE Transactions 1985, Vol. 91, Part 1.

Fl anders, S.M. 1985. "Confi dence in heat fl ux transducer measurements of buil di ngs." ASH RAE Transactions 1985, Vol. 91, Part 2.

Kuehn, T.H. 1982. "Field heat-transfer measurements and life-cycle cost analysis of four wood-frame wall constructions." ASHRAE Transactions 1982, Vol. 88, Part 1, pp. 651-656. Atlanta: American Society of Heatlng, Refrlgerating and Air Conditioning Engineers.

Kusuda, T. 1976. "NBSLD, the computer program for hea ti ng and cool i ng loads in buil d-ings." Washington, D.C.: National Bureau of Standards.

Modera, M.P. 1985. "Technical description: The envelope thermal test unit." ASHRAE Transactions 1985, Vol. 91, Part 2.

Sherman, M. H.; Sonderegger, R.C., and Adams, J. W. 1982. "The determi nati on of the dynami c performance of walls.", ASHRAE Transactions 1982, Vol. 88, Part 1, pp. 689-712. Atlanta: American Society of Heatlng, Refrlgeratlng and Air Conditioning Engineers.

259

+

APPENDIX A

The System of Normal Equations

Z n 1 n + - ,E T,' tTx t-1 = - E T1 tTx t 8X 1=1 ." 8X. ;=1 ' ,

Z t:.x

1 n = - E T1 t-i Tx t

M.. i =1' ,

260

(1)

(2)

(n)

8-1

APPENDIX B

The Temperature History within the Wall and the Results Provided by METCOM Program

Homogeneous Wall, North, Variable Room Air Temperature - December

* Conduction transfer function coefficients *

X (1) = .2485 Y (1) = -9.8563 X (2) = .1635 Y (2) = 11.8812 X (3) = .1768 Y (3) = -1.3804 X (4) = .4439 Y (4) = - .7202

Z = .8645

* Estimated wall conductance, in W/(m 2·C) = 3.24

Hour Tl(OC) T2(OC) Heat Flow (W/m2) Txc( °C)

1 - 3.68 14.68 - 70.57 9.39 2 - 5.77 14.25 - 69.24 9.06 3 - 6.90 13.90 - 65.17 9.01 4 - 8.44 13.62 - 62.39 8.94 5 - 9.75 13.35 - 62.24 8.68 6 -10.66 13.07 - 62.11 8.41 7 -11.45 12.77 - 62.59 8.08 8 -11.96 12.81 - 66.73 7.80 9 -11. 73 14.20 - 83.60 7.93 10 -11.54 16.51 -106.30 8.54 11 -11.25 18.59 -122.60 9.40 12 -12.3 22.90 -158.93 10.98 13 -12.26 24.15 -149.73 12.92 14 -11.89 25.27 -148.13 14.16 15 -11.48 25.11 -136.88 14.84 16 -11.56 23.49 -115.44 14.83 17 -11. 96 21.53 - 99.01 14.10 18 -12.44 20.5 - 96.55 13.26 19 -11.18 18.71 - 85.07 12.33 20 -11.98 17.85 - 79.03 11.92 21 -12.42 17.03 - 75.65 11.36 22 -12.73 16.36 - 73.74 10.83 23 -13.32 15.71 - 73.25 10.22 24 - 7.63 15.16 - 72.04 9.76

261

Tx(OC)

9.33 9.08 8.94 8.81 8.64 8.41 8.13 7.85 7.83 8.30 9.14

11.27 12.97 14.22 14.90 14.74 13.93 13.08 12.70 12.06 11.44 10.85 10.28 9.75

B-2 Homogeneous Wall, East, Variable Room Air Temperature - December

* Conduction transfer function coefficients * X (1) = -.1138 Y (1) = -10.0482 X (2) = -.1010 Y (2) = 10.0326 X (3) = .4525 Y (3) = - 1.2900 X (4) = .2937 Y (4) = 0.0012

Z = .6851

* Estimated wall conductance, in W/(m 2·C) = 3.28

Hour TWC) T2 (OC) Heat Flow (W/m2) Txc( DC) Tx(OC)

1 - 3.65 14.76 - 73.20 9.27 9.46 2 - 5.75 14.32 - 70.19 9.06 9.19 3 - 6.88 13.96 - 65.01 9.08 9.03 4 - 8.43 13.67 - 62.81 8.96 8.89 5 - 9.73 13.39 - 61.90 8.75 8.71 6 -10.65 13.11 - 61.40 8.50 8.48 7 -11.44 12.80 - 61.14 8.21 8.18 8 -10.64 12.84 - 65.01 7.96 7.90 9 - 6.30 14.24 - 82.40 8.06 7.91 10 - 3.91 16.59 -105.30 8.69 8.50 11 - 5.68 18.75 -119.15 9.81 9.55 12 - 9.18 23.34 .-153.83 11.80 12.14 13 -11.27 24.73 -142.31 14.06 14.01 14 -11.57 25.82 -142.71 15.12 15.16 15 -11.29 25.55 -132.28 15.63 15.66 16 -11.41 23.82 -112.74 15.36 15.32 17 -11.86 21.78 - 96.45 14.55 14.38 18 -12.36 20.69 - 93.55 13.67 13.14 19 -11.11 18.88 - 85.37 12.48 12.99 20 -11.92 18.00 - 78.51 12.11 12.31 21 -12.37 17.16 - 74.19 11.60 11.66 22 -12.69 16.48 - 72 .83 11.02 11.04 23 -13.28 15.81 - 71.64 10.44 10.44 24 - 7.60 15.25 - 72.08 9.84 9.89

262

B-3 Homogeneous Wall, South, Variable Room Air Temperature - December

* Conduction transfer function coefficients *

X (1) = -.1128 Y (1) = - 8.7181 X (2) = .5608 Y (2) = 10.3550 X (3) = -.1368 Y (3) = - 1.4121 X (4) = .2294 Y (4) = - .7495

Z = .8328

* Estimated wall conductance, in W/(m 2·C) = 3.17

Hour T1 (OC) T2(OC) Heat Flow (W/m2) Txc( °C) Tx (OC)

1 - 4.51 15.08 - 64.82 10.22 10.16 2 - 6.64 14.52 - 63.40 9.76 9.70 3 - 7.77 14.06 - 62.98 9.34 9.38 4 - 9.34 13.68 - 60.87 9.11 9.10 5 -10.65 13.33 - 60.64 8.78 8.81 6 -11. 57 12.98 - 60.34 8.45 8.47 7 -12.36 12.62 - 60.55 8.08 8.08 8 -11.91 12.31 - 61.82 7.67 7.68 9 - 7.02 12.27 - 65.31 7.37 7.34 10 - 1.14 12.98 - 72.70 7.53 7.29 11 2.39 14.96 - 88.43 8.33 7.81 12 4.57 19.67 -124.12 10.36 10.41 13 5.22 21.71 -117.87 12.87 13.16 14 4.36 23.81 -114.34 15.23 15.50 15 1.46 24.96 -106.11 17.00 17.15 16 - 4.35 25.38 - 97.51 18.07 17.91 17 - 9.49 24.70 - 89.13 18.02 17.60 18 -11.39 22.49 - 76.79 16.73 16.24 19 -11.89 20.28 - 71.96 14.88 15.43 20 -12.49 19.18 - 67.22 14.14 14.38 21 -13.07 18.14 - 64.84 13.28 13.40 22 -13.44 17.26 - 64.38 12.43 12.46 23 -14.06 16.42 - 64.74 11.56 11.60 24 - 8.45 15.71 - 66.51 10.72 10.80

263

•

8-4 Multilayer wall, North - December

* Conduction transfer function coefficients *

X (1) = 0.0981 Y (1) = -6.6914 X (2) = 0.0486 Y (2) = 8.2500 X (3) = 0.0967 Y (3) = - .8438 X (4) = 0.0654 Y (4) = - .7656

Z = .6016

* Estimated wall conductance, in W/(m 2·C) = .375

Hour Tl (·C) T2(·C) Heat Flow (W/m2) Txc( ·C) Tx(·C)

1 - 7.61 20.34 -10.46 19.29 19.22 2 - 9.70 20.26 -11.46 19.11 19.12 3 -10.11 19.74 - 7.66 18.97 18.87 4 -11. 74 20.10 -12.62 18.84 18.79 5 -12.82 19.46 - 7.88 18.67 18.59 6 -13.79 19.91 -13.76 18.53 18.50 7 -14.38 19.24 - 8.86 18.35 18.32 8 -15.16 20.09 -17.29 18.36 18.36 9 -15.00 21.37 -23.64 19.01 18.99 10 -15.02 24.95 -41.26 20.82 20.83 11 -14.80 27.31 -39.73 23.34 23.36 12 -14.62 27.52 -24.60 25.06 25.05 13 -14.66 28.74 -26.84 26.06 26.09 14 -14.31 28.59 -18.77 26.71 26.79 15 -14.10 27.53 - 8.95 26.64 26.66 16 -14.39 24.82 5.24 25.34 25.38 17 -14.83 24.71 - 6.78 24.03 24.09 18 -15.26 23.33 - 2.53 23.08 23.11 19 -15.45 22.82 - 6.03 22.22 22.15 20 -16.04 22.23 - 7.89 21.44 21.45 21 -16.49 21.85 - 9.51 20.90 20.90 22 -16.79 21.25 - 8.88 20.36 20.38 23 -17.38 20.96 -10.79 19.88 19.90 24 -11.03 20.61 -10.65 19.54 19.55

264

8-5 Multilayer wall, East, - December

* Conduction transfer function coefficients *

X (1) = 0.0928 Y (1) = -6.7363 X (2) = 0.0508 Y (2) = 8.4063 X (3) = 0.0864 Y (3) = - .9844 X (4) = 0.0889 Y (4) = - .7031

Z = .6250

* Estimated wall conductance, in W/(m 2·C) = .362

Hour T1 (OC) T2 (OC) Heat Flow (W/m2) Txc( °C) Tx( °C)

1 - 7.59 20.35 -10.08 19.34 19.24 2 - 9.69 20.27 -11. 25 19.14 19.13 3 -10.10 19.75 - 7.37 19.01 18.88 4 -11. 74 20.10 -12.19 18.88 18.79 5 -12.82 19.46 - 7.52 18.71 18.60 6 -13.78 19.91 -13.42 18.57 18.51 7 -14.58 19.24 - 8.48 18.39 18.32 8 -13.71 20.09 -16.97 18.39 18.36 9 - 9.23 21.37 -22.86 19.08 19.01 10 - 7.31 24.97 -40.25 20.95 20.90 11 - 9.18 27.34 -38.11 23.53 23.50 12 -11.62 27.58 -22.56 25.32 25.25 13 -13.36 28.82 -24.60 26.36 26.31 14 -13.42 28.68 -16.73 27.01 26.99 15 -13.49 27.62 - 7.41 26.88 26.83 16 -13.97 24.90 6.68 25.57 25.53 17 -14.54 24.78 - 5.44 24.24 24.21 18 -15.06 23.39 - 1.29 23.26 23.21 19 -15.32 22.87 - 5.15 22.36 22.23 20 -15.94 22.27 - 7.07 21.56 21.51 21 -16.43 21.88 - 8.89 20.99 20.95 22 -16.74 21.27 - 8.29 20.44 20.41 23 -17.34 20.98 -10.39 19.94 19.92 24 -11.01 20.63 -10.36 19.59 19.58

265

8-6 Multilayer wall, North, June

* Conduction transfer function coefficients * X (1) = 0.0800 Y (1) = -6.8760 X (2) = .0625 Y (2) = 6.1875 X (3) =- .0938 Y (3) = .3906 X (4) = .1514 Y (4) = .0938

Z = .2891

* Estimated wall conductance, in W/(m 2·C) = .278

Hour T1 (·C) T2(·C) Heat Flow (W/m2) Txc( ·C) Tx (·C)

1 20.38 19.34 - 4.10 18.93 19.09 2 20.27 19.21 - .17 19.19 19.20 3 20.62 19.88 - 4.64 19.42 19.44 4 20.80 19.53 .90 19.62 19.61 5 21.96 20.24 - 4.34 19.81 19.81 6 24.15 19.89 1.20 20.01 19.99 7 23.75 20.49 - 3.29 20.16 20.18 8 21.81 20.13 1.43 20.27 20.31 9 21.29 20.75 - 3.24 20.43 20.46 10 21.79 20.54 .73 20.61 20.61 11 22.58 20.70 - .57 20.64 20.64 12 22.00 20.79 - .72 20.72 20.74 13 21.59 20.90 - .92 20.81 20.86 14 22.48 15.74 35.54 19.29 19.33 15 22.88 14.75 21.00 16.85 16.86 16 23.59 12.42 24.55 14.88 14.91 17 25.14 16.50 -17.42 14.76 14.77 18 26.74 15.85 - .69 15.78 15.79 19 25.95 17 .21 - 7.86 16.42 16.44 20 23.30 17.24 - 1.76 17.06 17.10 21 21.41 17 .80 - 3.13 17.49 17.51 22 19.79 18.04 - 1.73 17.87 17.86 23 18.25 18.59 - 3.93 18.20 18.20 24 19.08 18.84 - 2.88 18.55 18.58

266

B-7 Multilayer wall, East, June

* Conduction transfer function coefficients *

X (1) = 0.0051 Y (1) = -6.9316 X (2) = .1200 Y (2) = 6.6328 X (3) = -0.0700 Y (3) = .1016 X (4) = .1455 Y (4) = -0.0117

Z = .3516

* Estimated wall conductance, in W/(m 2·C) = .298

Hour T1 (OC) T2 (OC) Heat Flow (W/m2) Txc( °C) Tx(OC)

1 20.27 19.35 - 4.44 18.91 19.08 2 20.18 19.21 - .24 19.19 19.20 3 20.55 19.87 - 4.76 19.39 19.43 4 20.75 19.53 .69 19.60 19.60 5 22.94 20.24 - 4.63 19.78 19.81 6 29.98 19.89 1.04 19.99 20.00 7 36.13 20.50 - 2.78 20.22 20.25 8 38.62 20.16 2.88 20.45 20.50 9 39.11 20.84 - 1.05 20.73 20.80 10 37.50 20.69 3.88 21.08 21.12 11 34.51 20.92 3.14 21.23 21.26 12 28.65 21.06 3.15 21.38 21.42 13 25.36 21.19 2.53 21.44 21.52 14 25.58 16.03 38.66 19.90 19.94 15 25.02 15.03 23.36 17.37 17.39 16 25.20 12.66 26.62 15.32 15.36 17 24.97 16.71 -15.92 15.12 15.14 18 24.12 16.03 .29 16.06 16.08 19 23.43 17.35 - 7.30 16.62 16.64 20 22.45 17.33 - 1.26 17 .20 17.22 21 21.07 17.86 - 3.01 17.56 17.58 22 19.47 18.08 - 1.84 17.90 17.89 23 18.04 18.61 - 3.93 18.22 18.22 24 18.92 18.85 - 3.02 18.55 18.58

267

Hour

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

APPENDIX C

The Effect of the Use of NOI'th Wall Coefficients to Other Orientations Mult, layer Wall, December

Heat flux at inside surface

North Wall East Wall South Wall

Btu/h.ft 2 W/m2 Btu/h .ft 2 W/m2 Btu/h .ft 2 W/m2

- 2.45 -10.87 - 3.10 - 9.78 - 1.11 - 3.49 - 3.55 -11.19 - 3.35 -10.56 - 1.23 - 3.88 - 2.42 - 7.62 - 2.16 - 6.79 - 0.28 - .87 - 3.80 -11. 99 - 3.53 -11.12 - 1.83 - 5.77 - 2.29 - 7.23 - 1.99 - 6.27 - 0.34 - 1.07 - 4.09 -12.89 - 3.80 -11.97 - 2.16 - 6.81 - 2.59 - 8.17 - 2.28 - 7.19 - 0.59 - 1.85 - 5.29 -16.68 - 5.03 -15.85 - 3.24 -10.20 - 7.39 -23.29 - 7.16 -22.54 - 5.14 -16.20 -13 .01 -40.97 -12.88 -40.56 -10.55 -33.23 -12.58 -39.62 -12.55 -39.53 - 9.90 -31.17 - 7.85 -24.74 - 7.88 -24.83 - 5.23 -16.48 - 8.53 -26.86 - 8.56 -26.95 - 5.93 -18.68 - 6.05 -19.06 - 5.95 -18.75 - 3.39 -10.69 - 3.04 - 9.57 - 2.90 - 9.12 - 0.48 - 1.52

1.48 4.66 - 1.79 5.63 3.90 12.29 - 2.31 - 7.29 - 1.95 - 6.13 0.07 .22 - 0.99 - 3.12 - 0.52 - 1.65 1.48 4.66 - 2.02 - 6.37 - 1.62 - 5.10 0.38 1.19 - 2.41 - 7.61 - 1.95 - 6.15 0.03 9.29 - 3.00 - 9.45 - 2.53 - 7.97 - 0.56 - 1.75 - 2.79 - 8.79 - 2.40 - 7.57 - 0.34 - 1.07 - 3.46 -10.89 - 3.07 - 9.68 - 1.00 - 3.15 - 3.46 -10.91 - 3.11 - 9.81 - 1.05 - 3.30

268

Layer

Concrete

TABLE 1

Description of the Homogeneous Wall

Thickness ft

em)

0.98 (0.30)

Thermal Thermal . Conduct i vity resistance

Btu .in/h·ft.F ft 2.h .F /Btu (W/m. DC) (m 2•DC/w)

6.94 1. 70 ( 1.0) (0.3)

Wall conductance = 0.59 Btu/ft 2.h.F (3.33 W/m 2 • D C)

TABLE 2

Description of the Multilayer Wall

Thickness Layer ft

em)

Concrete 0.33 (O.l)

Air cavity 0.07 (0.02)

Insul ati on 0.33 (O.l)

Concrete 0.33 (O.l)

Thermal Thermal Conductivity resistance Btu.in/h.ft·F ft 2.h.F /Btu

(W/m.DC) (m 2•DC/W)

6.94 0.57 (1.0 ) (O.l)

1.56* 0.64 (8.90) (0.l12)

0.28 14.20 (0.04) (2.5)

6.94 0.57 (1.0) (0.1 )

Wall conductance = 0.063 Btu/ft 2'h 'F (0.355 W/m 2•D C)

* Btu/h.ft 2·F for 0.75 in (0.02 m) ventilated air cavity

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TABLE 3

Analysis of the Results for a Homogeneous Wall, December

Variable Room Air Controlled room air Temperature Temperature 68±0.5 F (20±lOC)

North East South North East South

Mean di fference 0.002 0.003 0.001 0.02 0.03 0.0016 F

lOCI (0.004) (0.0042) (0.003) (0.04) (0.06) (0.003)

Standard 0.08 0.11 0.134 0.049 0.007 0.0039 deviation F locI (0.147) (0.202) (0.24l) (0.088) (0.014) (0.007)

Cal cul ated Wall 0.57 0.58 0.56 0.63 0.64 0.65 Conductance Btu/ft 2 .h.F (w/m 2 .oC)

(3.24) (3.283) (3.l74) (3.58) (3.65) (3.72)

Design wall Conductance 0.59 Btu/ft2 .h.F (W/m 2 .oC)

(3.33)

Error 2.7 1.4 4.7 7.5 9.6 11.7 X

270

TABLE 4

Analysis of the Results for a Multila er Wall. with Controlled Room Air emperature at ±. ±

December June

North East South North East South

Mean di fference 0.028 0.031 0.16 0.012 0.019 0.006 F

(OC) (0.05) (0.056) (0.28) (0.022) (0.035) (0.01)

Standard 0.026 0.07 0.32 0.019 0.02 0.02 deviati on F (OC) (0.046) (0.12) (0.577) (0.034) (0.036) (0.039)

Calculated Wall 0.066 0.064 0.051 0.049 0.052 0.064 Conductance Btu/ft 2 .h·F (W/m 2 .oC)

(0.375) (0.362) (0.287) (0.278) (0.298) (0.363)

Design wall Conductance 0.063 Btu/ft 2 .h ·F (W/m2 .oC) (0.355)

Error 5.6 1.9 19.1 21.8 16.1 2.1 %

OUTSIDE INSIDE

Figure 1. Schema of wall

271