NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Three-Dimensional Numerical 

Evaluation of Thermal 

Performance of Uninsulated 

Wall Assemblies 

Preprint

El Hassan Ridouane and Marcus V. A. Bianchi

Presented at the ASME 2011 International Mechanical Engineering 

Congress and Exposition

Denver, Colorado

November 11-17, 2011

Conference Paper

NREL/CP-5500-52389

November 2011
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1 

THREE-DIMENSIONAL NUMERICAL EVALUATION OF THERMAL PERFORMANCE OF 

UNINSULATED WALL ASSEMBLIES

El Hassan Ridouane, PhD

National Renewable Energy Laboratory

1617 Cole Blvd

Golden, Colorado, USA

Email: elhassan.ridouane@nrel.gov

Marcus V.A. Bianchi, PhD

National Renewable Energy Laboratory

1617 Cole Blvd

Golden, Colorado, USA

Email: marcus.bianchi@nrel.gov

ABSTRACT

Uninsulated wall assemblies are typical in older homes, as 

many were built before building codes required insulation. 

Building engineers need to understand the thermal performance 

of these assemblies as they consider home energy upgrades if 

they are to properly predict pre-upgrade performance and, 

consequently, prospective energy savings from the upgrade. 

Most whole-building energy simulation tools currently use 

simplified, 1D characterizations of building envelopes and 

assume a fixed thermal resistance that does not vary over a 

building’s temperature range.

This study describes a detailed 3D computational fluid 

dynamics model that evaluates the thermal performance of 

uninsulated wall assemblies. It accounts for conduction through 

framing, convection, and radiation and allows for material 

property variations with temperature. Parameters that were 

varied include ambient outdoor temperature and cavity surface 

emissivity. The results may serve as input for building energy 

simulation tools that model the temperature-dependent energy 

performance of homes with uninsulated walls.

INTRODUCTION

The global interest in energy conservation through 

improved building enclosures has driven a steady stream of 

fundamental and applied studies that focus on reducing thermal 

loads and maintaining occupant comfort. Accurate estimates of 

heat transfer through building assemblies, accompanied by lowcost energy upgrades, support efforts to reduce energy 

consumption in older homes. This study evaluates the thermal 

performance of uninsulated walls in low-rise, wood-framed 

homes. Combined heat transfer by natural convection and 

radiation inside wall cavities is an important mechanism in the 

total heat exchange through these walls.

Numerous studies address natural convection flows in 2D 

cavities of square and rectangular cross sections. Early work 

was reviewed by Bejan [1], Jaluria [2], and Raithby and 

Hollands [3]. These studies concentrated on pure natural 

convection with various thermal boundary conditions

(Douamna et al. [4], Fusegi et al. [5], and Lakhal et al. [6], and 

on different aspect ratios and angles of inclination (Rahman and 

Sharif [7]). Experimental studies reported by Catton [8]

provided insight into the complexity of the problem. The 

interaction between natural convection and thermal radiation 

was the subject of numerical studies by Akiyama and Chong 

[9], Pak and Park [10], Ridouane et al. [11], and Yucel et al. 

[12]. Their results showed that surface radiation significantly 

alters temperature distribution and flow patterns.

Park et al. [13] focused on building enclosures and

performed numerical simulations to investigate the heat transfer 

through a standard residential uninsulated stud wall structure. 

Indoor and outdoor air temperatures were fixed at 294 K (70°F) 

and 300 K (80°F), respectively. The authors considered five test 

cases, with different approximations, to address the coupled 

heat transfer by convection and radiation. The results showed 

that thermal radiation is an important transport mechanism in 

uninsulated walls, even with modest temperature differences: 

adding a reflective layer (foil liner) on one inner surface of the 

cavity reduced the heat transfer by 50%. Calculated heat 

transfer rates through the wall were within 3% of the values 

published in the 1977 ASHRAE Handbook of Fundamentals.

ASHRAE [14] provides a table listing thermal resistance values 

for enclosed air spaces under various conditions, depending on 

cavity surface emissivity. These values are for well-sealed 

cavities and selected combinations of mean temperatures and 

temperature differences, but do not represent a building’s 

operating conditions. For uninsulated 2 × 4 walls, the table 

shows slight variations in cavity resistance with the mean 

temperature and temperature difference.

Barbour et al. [15] used a calibrated hot box to test a 

number of wall assemblies, to provide measured thermal 

resistance for commonly used steel-framed wall configurations. 
2 

They found that insulating sheathing significantly decreases the 

effects of thermal bridging and that the ASHRAE Zone Method 

overestimates thermal performance of metal stud walls with 

uninsulated cavities by up to 15%. Lorente [16] studied heat 

loss through building walls with closed, open, and deformable 

cavities, which appear in double-pane windows that have 

moderate pressure differences between the inner and outer 

panes. Heat losses are largely due to convective heat transfer 

inside vertical wall cavities. 

Aviram et al. [17] used a guarded hot box to 

experimentally investigate the heat transfer through a variable 

aspect ratio cavity. A block and brick wall cavity measuring 1.2 

× 1.2 m2

 (3.94 × 3.94 ft2) was tested at cavity depths of 78, 60, 

and 40 mm (3.1 in., 2.4 in., and 1.6 in.). Results showed that 

circulation intensity decreased and thermal resistance increased 

with increased aspect ratio. The resistance of the cavity 

increased by 66% when the cavity depth decreased from 78 mm 

(3.1 in.) to 40 mm (1.6 in.). Similar numerical studies were 

conducted by Manz [18] and Xaman et al. [19] in rectangular 

cavities with aspect ratios 20, 40, and 80 (typical aspect ratios 

in wall cavities is 27.4 for 2 × 4 construction and 17.5 for 2 × 6 

construction). Antar and Baig [20] studied conjugate heat 

transfer by conduction and convection in a hollow block and 

showed that increasing the number of cavities while keeping 

the block width constant significantly increased thermal 

resistance. 

The objective of the present study is to evaluate the 

thermal performance of uninsulated walls by solving the 3D 

combined heat transfer by conduction, convection, and 

radiation in the wall assembly, including the framing elements. 

The model can be applied over a wide range of operating 

conditions. The results are compared to the output of a 2D 

model [21], which was modified to model variable 

thermophysical properties, and to the current input of wholebuilding energy simulation tools (fixed thermal resistance 

evaluated at 297 K (75 ̊F) mean temperature). 

NUMERICAL MODEL 

Figure 1 presents the geometric configuration, which is a 

0.41-m (16-in.) × 0.14-m (5.5-in.) × 2.44-m (8-ft) section of a 

standard 0.05 × 0.1 m2

 (2 × 4 in.2) residential stud wall. Starting 

from the inside (left), the wall consists of a 0.0127-m (0.5-in.) 

gypsum wallboard, a 0.089-m (3.5-in.) air cavity limited by 2 × 

4 studs, a 0.0127-m (0.5-in.) layer of sheathing, and a 0.025-m 

(1-in.) layer of wood siding that is exposed to outside air. The 

distance between the studs is 0.41-m (16-in.) centers. The 

cavity is closed at top and bottom by adiabatic sills. We took 

advantage of the periodicity and modeled only a section of the 

wall that contains one air cavity and half of each limiting stud. 

The thermophysical properties of air, wood studs, wood siding, 

and sheathing were allowed to vary with temperature. Air 

properties varied as piecewise-linear functions of temperature, 

except density, which follows the ideal gas law. An air property 

ߔሺܶሻ at a temperature T is determined through this equation: 

ߔሺܶሻ ൌ ߔ ൅ ௡ః೙శభିః೙

்೙శభି்೙

ሺܶ െ ܶ௡ሻ (1) 

where (ܶ௡, ߔ௡ሻ are data pairs entered manually into the model. 

Density of wood products was considered independent of 

temperature. The thermal conductivity of dry wood (studs, 

siding, and sheathing) was obtained from the Wood Handbook 

[22]: as the temperature increases, the thermal conductivity 

increases 3% per 10 K. Due to lack of information, the gypsum 

properties were assumed to be constant. As a reference point, 

Tables 1 and 2 list the material properties of different layers of 

the wall assembly evaluated at 297 K (75 ̊F) [14].

Figure 1 Schematic of the wall structure, which consists of a 

0.41-m (16-in.) long × 0.14-m (5.5-in.) wide × 2.44-m (8-ft) 

high section of a standard 2 × 4 residential stud wall. 

Table 1. Properties of Building Materials Used in This 

Study Evaluated at 297 K – SI units 

Material 

Density 

kg/m3

Conductivity 

W/m·K 

Specific Heat 

J/kg·K 

Gypsum board 641 0.158 1130 

Sheathing 288 0.055 1298 

Wood siding 689 0.182 1172 

Wood stud 689 0.182 1172 

Table 2. Properties of Building Materials Used in This 

Study Evaluated at 75 ̊F – English units 

Material 

Density 

lb/ft3

Conductivity 

Btu/h·ft·°F 

Specific Heat 

Btu/lb·°F 

Gypsum board 40 0.0916 0.27 

Sheathing 18 0.0316 0.31 

Wood siding 43 0.1054 0.28 

Wood stud 43 0.1054 0.28 

The operating conditions considered resulted in high 

values of the Rayleigh number (~ 109

 and higher), so the 

Inside 

Outside 

Stud 

hout, Tamb hin, 

Tset = 294 K (70°F) 

Air cavity 

2.44 m 

0.41 m 

0.14 m 
3 

airflow is assumed to be turbulent. Under steady-state 

conditions, the governing equations are the heat conduction 

equation in the solid parts of the wall and 3D Navier-Stokes 

and energy equations in the air. We used the surface-to-surface 

method described by Modest [23] to calculate the radiative 

exchange between the inner surfaces of the wall cavity. Two 

surface emissivities of 0.05 and 0.8 were considered and all 

participating surfaces were assumed to be gray and diffuse. The 

emissivity of 0.8 represents common building materials and 

emissivity of 0.05 corresponds to a highly reflective aluminum 

foil surface when a reflective insulation (radiant barrier) is 

added to reduce radiation transfer. The model assumes a tight 

wall and ignores infiltration and exfiltration.

We used the finite volume method of the commercial 

software FLUENT 6.3 [24] to numerically solve the governing 

equations. Turbulence is modeled by the standard k–ε model. 

An implicit segregated solver is employed and all discretization

schemes are of second-order accuracy or higher. The QUICK 

scheme is used for momentum, energy, and density 

discretization. A second-order scheme is applied in the pressure 

discretization and the SIMPLE scheme is used in pressurevelocity coupling. We assessed simulation convergence by 

monitoring computed conservation equations residuals and 

converging surface monitors. The absolute convergence criteria 

for velocity, temperature, and heat flux monitors, at select 

locations in the domain, were set to 10-6. We conducted a 

formal grid sensitivity study to ensure the numerical results 

were independent of grid resolution. We examined grid sizes 

ranging from 150,000 to 350,000 hexahedral elements at the 

highest ΔT used (61 K [110°F]). Grid independence was within 

1% with the nonuniform grid size of 259,200 hexahedral

elements.

Verification of the numerical model was done in a 

previous study (Ridouane and Bianchi [21]) by comparing the 

results of a 2D model with those published 2009 ASHRAE 

Fundamentals [14] and in Park et al. [13]. Both comparisons 

showed good agreement.

RESULTS AND DISCUSSION

The 3D numerical model was used to simulate the 

performance of uninsulated wall assemblies typical in older 

wood frame homes. A parametric study was performed varying 

the ambient outdoor temperature from 233 K (-40 ̊F) to 311 K 

(100 ̊F) and using two surface emissivities of 0.05 and 0.8. The 

indoor temperature was maintained at 294 K (70°F). The 

convective heat transfer coefficients at the indoor and outdoor 

surfaces were assumed to be 8.33 W/m2

·K (1.47 Btu/h·ft 2·°F) 

and 33.33 W/m2

·K (5.88 Btu/h·ft 2·°F), respectively. Local and 

average quantities are provided for different operating 

conditions. The output of the 3D model is compared to the 

results of a 2D model to verify the need for the additional 

dimension to accurately predict the thermal characteristics of 

uninsulated wall assemblies. The effects of surface emissivity 

and ambient temperature on temperature distribution, thermal

resistance, and heat flux through the wall are presented and 

discussed.

Local Quantities

Figure 2 illustrates the temperature distribution at two 

typical cross sections of the wall for winter conditions when the 

ambient temperature was 255 K (0°F). Cross section A is the

vertical midplane perpendicular to the wall; cross section B is 

the vertical midplane parallel to the wall. Both divide the air 

cavity in half. The dimensions in the temperature plots are not 

to scale, to allow visualization of the flow patterns in the entire 

domain. Building materials, other than metals, have a high 

thermal emissivity around 0.8. For illustration purposes, we 

also simulated the case of foil faced materials (reflective 

insulation) having an emissivity of 0.05. At this high

temperature difference between the indoors and outdoors (ΔT), 

strong clockwise flow circulation was formed in the cavity with 

high temperature gradients near the hot (left) and cold (right) 

vertical boundaries. The temperature distribution associated 

with this circulation is clearly seen in cross section A; cross 

section B provides the temperature gradients along the depth of 

the wall and shows the effects of the studs on airflow at both 

ends of the wall section. This effect is not accounted for in 1D 

and 2D models. Changes in the scale of the color bar between ε 

= 0.05 and ε = 0.8 plots show how significant the effect of 

surface emissivity is on temperature distribution. Except for the 

change in flow direction, similar trends were observed for 

summer conditions when the ambient temperature was 311 K 

(100°F) (Figure 3). Also, the indoor/outdoor temperature 

difference in Figure 3 is much smaller than that in Figure 2.

Convection boundary conditions imposed at the internal 

and external surfaces of the wall assembly allow the surface 

temperatures to vary in space. This variation is depicted in 

Figure 4 along the vertical symmetry line of the internal and 

external surfaces of the wall for 255 K (0°F) and 311 K (100°F) 

ambient temperatures. A 3.6 K (6.5°F) difference was found 

between the top and the bottom of the internal surface at an 

ambient temperature of 255 K (0°F). This difference is a 

function of the temperature difference and the overall thermal 

resistances.

Figure 5 presents the variations of the local heat flux, q, 

along the vertical symmetry line of the internal and external 

surfaces of the wall with an emissivity of 0.8 when the ambient 

temperature is 255 K (0°F). For this ΔT there was a clockwise 

airflow circulation in the cavity (see Figure 2(b)). Starting with 

the inside surface (dashed curve), the heat flux is high at the 

floor level where the cold air first hits the hot surface and 

decreased as the height increased. The opposite occurred on the 

outside surface with the hot air hitting the cold surface at the 

top resulting in a high value of q, which decreased as the height 

decreased toward the floor.
4 

 Cross section A Cross section B

 

 Cross section A Cross section B

Figure 2 Effect of surface emissivity, ε, on the temperature 

distribution in the wall when the outdoor ambient temperature 

is 255 K (0°F). 

 Cross section A Cross section B

 Cross section A Cross section B

Figure 3 Effect of surface emissivity, ε, on the temperature 

distribution in the wall when the outdoor ambient temperature 

is 311 K (100°F). 

Figure 4 Temperature profile along the vertical symmetry line 

of the internal and external surfaces of the wall. The graph 

shows changes in temperature relative to the bottom of the wall 

with an emissivity, ε, of 0.8.

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 

Height along the wall, y [m]

T(y) - T(y = 0) [K]

Tamb = 255 K

Tamb = 255 K

Tamb = 311 K

Tamb = 311 K

(a)

ε = 0.05

Tamb = 255 

K (0 ̊F)

(b)

ε = 0.8

Tamb = 255 

K (0 ̊F)

K

K

(a)

ε = 0.05

Tamb = 311 

K (100 ̊F)

K

(b)

ε = 0.8

Tamb = 311 

K (100 ̊F)

K

Outside 

surface

Inside 

surface
5 

Figure 5 Local heat flux along the vertical symmetry line of the 

internal and external surfaces of the wall with an emissivity, ε,

of 0.8 when the ambient temperature is 255 K (0°F).

Average Quantities

The total resistance, Rtot, of the wall assembly, including 

that of framing, air cavity, and inside and outside films, is 

shown in Figure 6 as a function of the ambient temperature and 

surface emissivity. The output of the 2D model, which also 

accounts for the effect of variable material properties, includes 

the resistance of the studs in parallel with the air cavity 

resistance. When the emissivity is equal to 0.8, the resistance 

predicted by both 2D and 3D models is high at 233 K (-40°F) 

and decreases with the ambient temperature to reach a 

minimum around 283 K (50 ̊F) for ambient temperatures below 

the interior temperatures. Rtot decreases quickly at higher

ambient temperatures. Good agreement is observed between the 

2D and 3D predictions; differences are within 1%. The 

horizontal dashed line indicates the resistance used in the 

traditional approach, which is evaluated at 297 K (75 ̊F). When 

the emissivity is lowered to 0.05 (Figure 6(b)), the minimum 

does not take place in the range investigated and the thermal 

resistance is characterized by a monotonic increase between 

233 K (-40°F) and 294 K (69°F). For heating conditions the 

maximum deviation between 2D and 3D model predictions is 

4%. When the ambient temperature is higher than the exterior 

temperature, the thermal resistance predicted by the 2D model 

can be up to 14% higher. However, larger differences are found 

at temperature differences below 5.4 K (10°F), where the heat 

transfer rate is small.

The effect of allowing the thermophysical properties of 

air and wood to vary with the local temperature is illustrated in 

Figure 7, where the total resistance is shown as a function of 

the ambient temperature. The 3D model was used to predict the 

total resistance of the assembly for constant1

 1 All properties are fixed, except air density, which followed the ideal gas 

law.

and variable 

material properties. The assumption of constant thermophysical

properties, evaluated at 297 K (75 ̊F), underpredicted the wall 

performance when the ambient temperature was below the set 

point of 294 K (70 ̊F): the lower the ambient temperature, the 

greater the difference is, reaching 8% at 232 K (-40°F). Good 

agreement is observed around Tamb of 297 K (75 ̊F) where the 

constant properties were evaluated. Opposite trends occurred at 

ambient temperatures higher than 300 K (80°F): constant 

properties predicted higher resistances for the wall, but the 

temperature differences are smaller, so the discrepancy is 

smaller (2% at 311 K).

Figure 6 Thermal resistance of the wall assembly, predicted 

using 2D and 3D models, as a function of the outdoor ambient 

temperature. (a) High surface emissivity of 0.8 and (b) low 

surface emissivity of 0.05.

Further simulations were performed separating the effects 

of variable properties of air and wood to evaluate the relative 

importance of each of them. When only the thermophysical 

properties of air were allowed to vary, no effect on the thermal 

resistance was observed. The difference shown in Figure 7 is 

0.0

0.5

1.0

1.5

2.0

30 35 40 45 50 55 60 65

Height along the wall (m)

q (W/m2) 

inside surface

outside surface

0.78

0.8

0.82

0.84

0.86

0.88

0.9

231 241 251 261 271 281 291 301 311

Rtot (m2·K/W)

Tamb (K)

2D Variable Properties, ε = 0.8

3D Variable Properties, ε = 0.8

Traditional Approach

0.9

1.1

1.3

1.5

1.7

1.9

231 241 251 261 271 281 291 301 311

Rtot (m2·K/W)

Tamb (K)

2D Variable Properties, ε = 0.05

3D Variable Properties, ε = 0.05

(a)

(b)
6 

due solely to the effect of variable thermophysical properties of 

wood: at lower temperatures, the thermal conductivity is 

smaller, leading to an increase in the thermal resistance of the 

assembly due to the sheathing and siding higher resistance. 

Figure 7 Effect of temperature-dependent material properties 

on thermal resistance of the wall assembly for 0.8 surface 

emissivity.

To understand the impact of the studs on the heat transfer 

through the assembly, we examined the distribution of the local 

heat flux at midheight of the wall. A low ambient temperature 

of 233 K (-40°F) was selected (see Figure 8(a)). This 

distribution is slightly affected by the studs; their effect has 

reduced the heat extracted by the air circulation from solid 

surfaces because of lower air velocities in these regions. The 

order of magnitude of this reduction is quantified in Figure 8(b) 

by the variation of q on line 1 at the interface between 

wallboard and air cavity. The heat flux in 3D was equal to that 

of 2D in the middle of the cavity and decreased toward the 

studs. Lower values of q translate into higher resistances. 

A detailed 3D model is implemented to contrast the 

thermal performance of the uninsulated wall assembly with the 

predictions of the 2D model and with the traditional approach 

that assumes constant Rtot. The latter, which evaluates Rtot at 

297 K (75 ̊F) mean temperature, is currently used in many 

whole-building energy simulation tools. 

Figure 9(a) compares predictions of the thermal 

performance of the wall assembly using 2D and 3D models 

when the surface emissivity is 0.8. The comparison was done in 

terms of the total heat flux through the wall as a function of the 

ambient temperature. The heat flux decreases with the ambient 

temperature, and crosses the x-axis at the indoor set 

temperature of 294 K (70 ̊F). The 2D model predicted 

comparable heat fluxes to those of 3D model for winter and 

summer conditions. The traditional approach, however, 

predicted slightly higher heat fluxes for winter conditions and 

lower heat fluxes for summer conditions when the outdoor 

temperature is higher than 300 K (80 ̊F) (Figure 9 (b)). 

Figure 8 Heat flux at ambient temperature of 233 K (-40°F) 

and emissivity of 0.8. (a) Distribution on the horizontal 

symmetry plane of the wall. (b) Profile on line 1 from right to 

left.

Table 5 summarizes the output of the different approaches 

and lists the relative differences between each model prediction 

and those of the 3D model. Significant differences between the 

3D and the traditional approach were obtained, which ranged 

from 11.4% at 291 K (65 ̊F)2

 to -2.4% at 311 K (100 ̊F). Of 

particular interest are the differences at lower ambient 

temperatures, where they can be as high as 9.3% on very cold 

days; both the 2D and 3D models predict lower heat transfer 

rates through the wall compared to the traditional approach. 

Smaller differences were found when comparing the 3D and 2D 

model results, with the highest difference of -3.1% at 300 K 

(80 ̊F)3

. If these results are implemented into building energy 

simulation tools, they would reduce the predicted heating load. 

For summer conditions the 3D model predicted slightly higher 

cooling loads for Tamb higher than 300 K (80 ̊F). 

 2

 Differences that take place near a zero temperature difference may be 

interesting for model testing, but not for their effect on heating and cooling load 

predictions. 3

 See previous footnote. 

0.78

0.8

0.82

0.84

0.86

0.88

0.9

231 241 251 261 271 281 291 301 311

Rtot (m2·K/W)

Tamb (K)

3D Constant Properties, ε = 0.8

3D Variable Properties, ε = 0.8

Traditinal Approach

0

20

40

60

80

0.00 0.10 0.20 0.30 0.40

q(w/m2)

Distance along line 1 (m)

2D Variable Properties

3D Variable Properties

W/m2

(a) 

line 1 

air cavity 

wallboard 

sheathing 

siding 

1⁄2 

stud 

1⁄2 

stud

1⁄2 stud 1⁄2 stud

(b) 
7 

Figure 9 Total heat flux through the wall assembly as a 

function of Tamb when the surface emissivity is 0.8. (a) 

comparison of 3D with 2D and (b) comparison of 3D with the 

traditional approach, assuming constant resistance evaluated 

at 297 K (75 ̊F) mean temperature.

Table 5. Comparison of the Total Heat Flux 

Through the Wall Assembly (ε = 0.8)

Tamb

K

Traditional 

Approach

W/m2

2D

W/m2 

3D

W/m2 

% Diff 

3D/Traditional 

Approach

% 

Diff 

3D/2D

233 76.4 70.2 69.3 9.3 1.3

255 48.6 45.1 45.4 6.6 -0.6

277 20.8 19.3 19.8 4.8 -2.6

291 3.5 3.1 3.1 11.4 0.0

300 -6.9 -6.5 -6.7 2.9 -3.1

311 -20.6 -20.8 -21.1 -2.4 -1.4

CONCLUSIONS

Three-dimensional computational fluid dynamic simulations of 

a standard 2 × 4, uninsulated 2.44-m (8-ft) tall, wall assembly 

were performed to evaluate its performance over a wide range 

of operating conditions. The thermophysical properties of air 

and wood wall materials were allowed to vary with 

temperature. Parameters that were varied in this study include 

the ambient outdoor temperature and cavity surface emissivity. 

The results can be implemented into building energy simulation 

tools to improve their accuracy in predicting building energy 

use in older homes that have uninsulated cavities.

The findings of this study include: 

• The variable thermal conductivity of wood products has a 

significant impact on the assembly’s thermal resistance: 

the assumption of constant thermal conductivity resulted in

up to 8% underprediction for colder ambient temperatures

(lower thermal conductivity of wood) and 2% 

overprediction for warmer conditions.

• The variable thermophysical properties of air have no 

effect on the thermal performance of the wall assembly.

• Three-dimensional flow structures, induced by the wood 

framing elements, were identified, but they led to minor 

differences between 3D and 2D predictions of the wall’s 

total resistance. This indicates that a 2D model may be 

sufficient to predict the thermal resistance of uninsulated 

wall assemblies. 

• In terms of the total heat flux through the wall, 3D and 2D

models showed comparable results for winter and summer 

conditions. Significant differences were found relative to 

the traditional approach, where the thermal resistance of 

the assembly is assumed to be constant: 9.3% at 233 K 

(-40 ̊F). 

The results indicate a potential source of inaccuracy in 

determining the thermal resistance of uninsulated cavities when 

the traditional approach is used: at low ambient temperatures, 

the thermal resistance of wood products may be higher than 

that evaluated at a fixed temperature.

Future work includes the use of model results to develop 

correlations that can be used in building energy simulation tools 

and modifying the model to address air infiltration through the 

uninsulated assembly. More data on the variable thermal 

conductivity of wood products are necessary to properly 

characterize different wood products (siding, sheathing, and 

stud). 

REFERENCES

[1] Bejan, A., 1995, Convection Heat Transfer, 2nd ed., Wiley, 

CA.

-35

-13

9 

31

53

75

231 241 251 261 271 281 291 301 311

q (W/m2) 

Tamb (K)

2D Variable Properties, ε = 0.8

3D Variable Properties, ε = 0.8

-30

-8 

14

36

58

80

231 241 251 261 271 281 291 301 311

q (W/m2) 

Tamb (K)

Traditional Approach, ε = 0.8

3D Variable Properties, ε = 0.8

(a)

(b)
8 

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