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

Thermal Performance of 

Uninsulated and Partially Filled 

Wall Cavities

Preprint

El Hassan Ridouane and Marcus Bianchi 

Presented at the ASHRAE Annual Conference

Montreal, Quebec

June 25–29, 2011

Conference Paper

NREL/CP-5500-50925

September 2011
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1 

Thermal Performance of Uninsulated and 

Partially Filled Wall Cavities

El Hassan Ridouane, PhD Marcus V. A. Bianchi, PhD

Member ASHRAE Member ASHRAE

ABSTRACT

Low-rise, wood-framed homes are the most common type of residential structures in the United States. Wood wall 

construction supports roofs efficiently and provides a stable frame for attaching interior and exterior wall coverings. Wall 

cavities are prevalent and increase thermal resistance, particularly when they are filled with insulating material. This paper

describes detailed computational fluid dynamics modeling to evaluate the thermal performance of uninsulated or partially 

filled wall cavities and accounts for conduction through framing, convection, and radiation. Parameters are ambient outdoor 

temperature, cavity surface emissivity, cavity aspect ratio, and insulation height. Understanding the thermal performance of 

uninsulated or partially insulated wall cavities is essential for conserving energy in residential buildings. The results can 

serve as input for building energy simulation tools such as DOE2 and EnergyPlus for modeling the temperature dependent 

energy performance of new and older homes with uninsulated or partially insulated walls.

INTRODUCTION

The study of heat transfer and fluid flow inside cavities of various shapes is an attractive area for fundamental and 

applied research. The pioneer studies were summarized by Jaluria (2003), Raithby and Hollands (1998), and Yang (1987). 

Numerous publications discuss natural convection flows in 2-D cavities of square and rectangular cross sections. Earlier 

work concentrated on pure natural convection with various thermal boundary conditions (Abourida et al. 1999, Douamna et 

al. 2000, Fusegi et al. 1992, and Lakhal et al. 1995), and on different aspect ratios and angles of inclination (Rahman and 

Sharif 2003). Experimental studies reported by Catton (1978) 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 

(1997), Pak and Park (1998), and Yucel et al. (1989). Their results showed that surface radiation significantly alters 

temperature distribution and flow patterns.

Barbour et al. (1994) focused on understanding the thermal behavior of steel-framed walls and reported that for metal 

stud walls with uninsulated cavities, the ASHRAE Zone Method overestimates thermal performance by up to 15%. Park et al. 

(1986) calculated heat transfer through the standard stud wall structure of a residential building. The wall cavities contained 

no insulation. They considered five test cases, with different approximations to the coupled heat transfer by convection and 

radiation. The assumption of constant temperature walls led to falsely high predictions for heat loss. This assumption does 

not reveal the substantial temperature differences between the top and bottom of the wall. The authors also found that thermal 

radiation is an important transport mechanism, even with modest temperature differences.

Lorente (2002) 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. Air in wall structures is often falsely considered to be motionless. 

Aviram et al. (2001) used a guarded hot box to experimentally investigate the heat transfer through a variable aspect ratio 

cavity. Circulation intensity decreased and thermal resistance increased with increased aspect ratio. Similar numerical studies 

were conducted by Manz (2003) and Xaman et al. (2005) in rectangular cavities with aspect ratios 20, 40, and 80. Antar and 

Baig (2009) 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 increased thermal resistance significantly. Vafai and Belwafa 

(1990) experimentally investigated heat transfer in cavities that were partially filled with fibrous insulation along the width. 
2 

They tested four samples with different densities and permeabilities in cavities of varying aspect ratios and concluded that 

reducing the insulation thickness (and thereby increasing the air gap thickness) increased heat transfer rates.

Despite the wealth of literature about vertical cavities, more information is needed for their application in wholebuilding energy simulation tools. Tools such as DOE2 and EnergyPlus use simplified, 1-D characterization that assumes a 

fixed thermal resistance over a building’s temperature range. In reality, the thermal resistance of uninsulated and partially 

insulated cavities is affected by radiation and convection and is a function of several parameters, including temperature, 

surface emissivity, and aspect ratio. The objective of the present work is to fill this gap by performing direct numerical 

simulations of heat transfer by convection and radiation in air-filled and partially insulated wall cavities. These cavities, 

partially insulated along the height, appear in new and existing construction. In new construction, the walls may not be filled 

all the way, leaving a gap at the top of the cavity. In existing construction, the insulation material may settle. The outcomes of 

this study provide:

• Accurate input for whole-building simulations models such as DOE2 and EnergyPlus in different operating conditions

• Information necessary to provide recommendations for retrofit measures. 

NUMERICAL MODEL

The geometric configuration (see Figure 1(a)) is a section of a standard 2×4 residential stud wall. Starting from the 

inside (left), the wall consists of a 0.5-in. (0.0127-m) gypsum wallboard, a 3.5-in. (0.089-m) air cavity partially filled with 

fiberglass insulation, a 0.5-in. (0.0127-m) layer of sheathing, and a 1-in. (0.025-m) layer of wood siding that is exposed to 

outside air. Table 1 presents the material properties of different layers of the wall assembly (ASHRAE 2009). The table lists

the apparent thermal conductivity for fiberglass insulation, which is based on R-15 in a 3.5-in. (0.089-m) cavity. It includes 

all the thermal phenomena that occur in fibrous insulation: heat conduction through the air, heat conduction through the glass, 

and infrared radiation exchange. The cavity is closed at top and bottom by adiabatic sills. Two cavity heights of 3-ft (found 

under windows) and 8-ft (full length of the wall) are considered. Simulations performed on partially filled cavities were 

limited to 8-ft tall cavity with insulation heights varying from 0 to 8 ft (0 to 2.44 m). 

Table 1. Properties of Building Materials Used in This Study

Material

Density 

lb/ft3 (kg/m3) 

Conductivity 

Btu/h·ft·°F (W/m·K)

Specific Heat

Btu/lb·°F (J/kg·K)

Gypsum wallboard 40 (640.7) 0.0916 (0.1584) 0.27 (1130.4)

Sheathing 18 (288.3) 0.0316 (0.0546) 0.31 (1297.8)

Wood siding 43 (688.8) 0.1054 (0.1823) 0.28 (1172.3)

Fiberglass 1.8 (28.8) 0.0194 (0.0336) 0.2 (837.3)

All thermophysical properties—except air density, which follows the ideal gas law—are assumed to be constant and 

evaluated at the mean temperature for each simulation. The fiberglass insulation is modeled as a porous medium with a 

porosity of 0.88 and uniform air permeability. Experimental measurements for attic insulation reported by Delmas and 

Wilkes (1992) showed that densities varying from 0.4 lb/ft3

 (6.4 kg/m3) to 0.9 lb/ft3 (14.42 kg/m3) correspond to 

permeabilities of 5.84 × 10-8 and 2.7 × 10-9 m2

, respectively. The fiberglass insulation used in wall cavities usually has a 

higher density (1.8 lb/ft3

 [28.8 kg/m3]), for which the permeability will be much smaller1

The fluid flow is assumed to be 2-D, laminar in the porous medium, and turbulent in the air cavity. Under steady-state 

conditions, the governing equations are the heat conduction equation in the structural parts of the wall and mass conservation, 

2-D Navier-Stokes equations, and energy equation in the cavity. The porous medium is modeled with the addition of a 

momentum source term to the standard fluid flow equations. The source term is composed of a viscous loss term (Darcy) and 

an inertial loss term. We used the surface-to-surface method described in Modest (2003) to calculate the radiative exchange 

, but since data is not available for 

higher densities, we used the value of 2.7 × 10-9 m2

, which corresponds to the highest density available. The insulation 

permeability is assumed to be the same horizontally and vertically.

 1 We performed a sensitivity analysis using permeability values between 10-9 and 10-12 m2 and the maximum air velocity in 

the insulation varied from 4.17 × 10-3 (2.12 × 10-5) to 1.3 × 10-5 ft/min (6.6 × 10-8 m/s), which had no effect on heat transfer 

across the cavity or on the surface temperatures used to determine the thermal resistance.
3 

between the inner surfaces of the wall cavity. All participating surfaces are assumed to be gray and diffuse. Surface 

emissivities of 0.05, 0.8, and 0.9 were considered. To examine the effect of the aspect ratio on the heat transfer through the 

wall, we compared a 3-ft (0.91-m) tall cavity, which can be found under windows, to the full cavity height of 8 ft (2.44 m). 

The model assumed a tight wall and ignored infiltration and exfiltration.

The governing equations are solved numerically using the finite volume method of FLUENT 6.3 (FLUENT Inc. 2006). 

Turbulence is modeled by the standard k–ε model. An implicit segregated solver is used and all discretization schemes 

employed are of second-order accuracy or higher. The QUICK scheme is used for momentum, energy, and density 

discretization. A second-order scheme is used in the pressure discretization and the SIMPLE scheme is used in pressurevelocity coupling. We assessed simulation convergence by monitoring computed conservation equations residuals and by

converging surface monitors for velocity, temperature, and heat flux at select locations in the domain by setting their absolute 

convergence criterion 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 10,000 to 50,000 quadrilateral elements at the highest ΔT used (70°F 

[39 K]). Grid independence was within 1% with the uniform grid size of 33,304 quadrilateral elements.

COMPARISON WITH PREVIOUS RESULTS

The numerical results obtained were compared against the results published in Chapter 26 of 2009 ASHRAE 

Fundamentals (ASHRAE 2009) and in Park et al. (1986). The thermal resistance of uninsulated wall cavity is compared in 

Tables 2 and 3. Table 2 compares the thermal resistance of a 3.5-in. (0.089-m) × 8 ft (2.44-m) cavity with that of 3.5-in. 

(0.089-m) air space (ASHRAE 2009) with an effective surface emissivity of 0.82. Among the five cases evaluated by Park et 

al. (1986), the present results are compared, in Table 3, with those of the isothermal case with pure natural convection (Case 

1) and when the three heat transfer modes were combined (Case 2). Both comparisons show good agreement.

Table 2. Comparison of Thermal Resistance of an Air Cavity*

Mean 

Temperature 

°F (K)

Temperature

Difference 

°F (K)

Present Work

ft2·h· ̊F/Btu 

(m2·K/W)

ASHRAE (2009)

ft2·h· ̊F/Btu 

(m2·K/W) % Difference

50 (283) 30 (16.6) 0.95 (0.17) 0.91 (0.16) 4.2

50 (283) 10 (5.5) 1.06 (0.19) 1.01 (0.18) 4.7

0 (255) 20 (11.1) 1.15 (0.20) 1.14 (0.20) 0.8

0 (255) 10 (5.5) 1.25 (0.22) 1.23 (0.22) 1.6

-50 (228) 20 (11.1) 1.31 (0.23) 1.37 (0.24) -4.3

-50 (228) 10 (5.5) 1.47 (0.26) 1.50 (0.26) -2.0

*Applies to a 3.5-in. (0.089-m) × 8-ft (2.44-m) air cavity against the data published in ASHRAE (2009). These results are for a surface 

emissivity of 0.82 and constant surface temperatures.

Table 3. Comparison of the Thermal Resistance of a Wall Assembly*

Case No.

Case Description Present Work

ft2·h· ̊F/Btu (m2·K/W)

Park et al. (1986) 

ft2·h· ̊F/Btu (m2·K/W)

1 Isothermal walls 5.48 (0.97) 5.43 (0.96)

2 Combined cond., conv., and rad. 4.31 (0.76) 4.31 (0.76)

* Applies to a wall assembly containing a 3.5-in. (0.089-m) × 8-ft (2.44-m) air cavity against the results of Park et al. (1986).

RESULTS AND DISCUSSION

Numerical simulations were performed to evaluate the thermal performance of pre-retrofit wall cavities under a wide 

range of ambient conditions. In all numerical results presented in this section, a constant indoor temperature of 70°F (294 K) 

is maintained; the outdoor ambient temperature varies from 0°F (255 K) to 120°F (322 K). The wall exchanged heat with the 

indoor environment at 0.68 h·ft 2

·°F/Btu (0.12 m2·K/W) and with the outdoors at 0.17 h·ft 2·°F/Btu (0.03 m2·K/W). The results 

are presented first for the air-filled cavity without insulation and then for the partially insulated cavity. The effects of surface 

emissivity, ambient temperature, aspect ratio, and insulation height on temperature distribution and thermal resistance are 

presented and discussed. The thermal resistance values correspond to the wall cavity only, which exclude that of the 

structural parts of the wall.
4 

Uninsulated Wall Cavity

Figure 1(b) illustrates the temperature contour plots, in an 8-ft (2.44-m) tall cavity, when the ambient temperature was

30°F (272 K). The cavity dimensions in the temperature distribution plots are not to scale, to allow visualization of the flow 

patterns in the entire domain. Three surface emissivities (0.05, 0.8, and 0.9) are considered. At this high temperature 

difference between the indoors and the outdoors, a strong clockwise flow circulation was formed with high temperature 

gradient near the hot (left) and cold (right) vertical boundaries. Surface emissivity affected circulation intensity significantly. 

Figure 1 (a) Schematic of the wall structure. (b) Effect of surface emissivity, ε, on the temperature distribution in an 

8-ft (2.44-m) tall air-filled wall cavity when the outdoor ambient temperature is 30°F (272 K).

Figure 2(a) reveals the thermal resistance, RC, of the wall cavity as it varied with the ambient temperature and surface 

emissivity. The thermal resistance is low at 0°F (255 K) and increases with the ambient temperature to reach a maximum and 

then decreases at high ambient temperatures. The maximum correspondes to the condition when there is no temperature 

difference between the two surfaces. While the resistance of the cavity when there is no temperature difference is not very 

relevant, it provides an upper bound for the thermal resistance in the cavity. Near this condition, there is no air movement and 

while there is heat conduction through the stagnant air, thermal radiation dominates. The smaller the surface emissivity, the 

higher is the thermal resistance at no temperature difference.

Figure 2 Thermal resistance of a 3.5-in. (0.089-m) × 8-ft (2.44-m) air-filled wall cavity as a function of the outdoor 

ambient temperature. (a) High surface emissivities of 0.8 and 0.9 and (b) low surface emissivity of 0.05.

0.8

1

1.2

1.4

0 20 40 60 80 100 120

RC (h.ft2. ̊F/Btu)

Tamb ( ̊F)

ε = 0.8

ε = 0.9

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120

RC (h.ft2. ̊F/Btu)

Tamb ( ̊F)

ε = 0.05 (a) (b)

T (°F)

H

W

Inside Air Outside 

cavity hout, Tamb hin, Tset = 70°F 

ε = 0.05 ε = 0.8 ε = 0.9

(a) (b)
5 

Figure 3 shows the contour plots of temperature associated with ε = 0.9 and three values of ambient temperature, 

namely, 0°F (255 K), 30°F (272 K), and 60°F (289 K). The flow field consisted of a single circulation with high temperature 

gradients at low temperature (high ΔT) of 0°F (255 K). These gradients weakened as the temperature increased.

 

Figure 3 Effect of temperature differential, ΔT, on the isotherms in an 8-ft (2.44-m) tall air-filled wall cavity when the 

surface emissivity is 0.9.

To examine the thermal behavior of the wall cavity under different aspect ratios, we considered a 3-ft (0.91-m) tall 

cavity (found under windows) and compared the results against those from an 8-ft (2.44-m) tall cavity. Both cavities are 3.5 

in. (0.089 m) wide. When the aspect ratio, A, was reduced from 27.4 (8 ft) to 10.3 (3 ft), the velocity and temperature 

patterns remained qualitatively the same. The only difference was in the size of the isothermal region in the cavity core. This 

region was larger for A = 27.4. Figure 4 shows the comparison of RC as a function of the ambient temperature and surface 

emissivity. RC followed the same trends shown in Figure 2. The higher aspect ratio of 27.4 presented slightly stronger 

resistances at ε = 0.8 and delivered stronger thermal resistance for the cavity. This difference disappeared when the 

emissivity was increased to 0.9.

Figure 4 Effect of the cavity aspect ratio, A, on the thermal resistance of a 3.5-in. (0.089-m) wide cavity filled with air. A 

= 10.3 corresponds to a 3-ft (0.91-m) tall cavity; A = 27.4 is for an 8-ft (2.44-m) tall cavity.

0.8

0.9

1

1.1

1.2

1.3

1.4

0 20 40 60 80 100 120

RC (h·ft2· ̊F/Btu)

Tamb ( ̊F)

A = 10.3, ε = 0.8

A = 27.4, ε = 0.8

A = 10.3, ε = 0.9

A = 27.4, ε = 0.9

Tamb = 0oF Tamb = 30oF Tamb = 60oF

T (°F) T (°F) T (°F)
6 

Partially Insulated Wall Cavity

As stated in the introduction section, partially insulated wall cavities appear in new and existing construction. Air gaps, 

even a few inches tall, when left uninsulated at the top of these cavities will cause significant reduction in the thermal 

resistance of the wall. This section discusses the impact of thermal shorts caused by these air gaps on the overall thermal 

resistance of the wall cavity.

Figure 5 illustrates the temperature distribution in the upper region of the wall, which has an air gap above the 

insulation. The corresponding heat flux profiles along the warmer inner surface of the wall exchanging heat with the room air

are presented in Figure 6. Three insulation heights with a 4-in. (0.1 m), a 1-ft (0.3 m), and a 2-ft (0.61 m) tall air gaps are 

presented from left to right. At this ambient temperature of 30°F (272 K), there is a strong air circulation in the uninsulated 

part of the cavity with higher temperature gradient in the smallest air cavity. The isotherms in the insulation are straight over 

the entire length of the insulation, except in the region between the insulation and the air gap where the isotherms are 

deformed by the heat exchange caused by the air circulation in the uninsulated part. The 1-D temperature profiles indicate 

that heat transfer across the insulated domain does not experience convection. Each curve of Figure 6 illustrates the 

distribution of the local heat flux at a typical insulation height. The heat flux dominated by diffusion at the bottom of the wall

remains uniform up to the interface of the insulation and the air gap. Over the air gap height, at the upper region, the heat flux 

increased quickly to reach a maximum at the bottom of the air gap and decreased again near the top. The high heat flux in the 

air gap is attributed to radiation and natural convection. 

 

Figure 5 Temperature distribution in the upper section of an 8-ft (2.44-m) tall partially insulated wall cavity. (a) 4-in tall 

air gap, (b) 1-ft tall air gap, and (c) 2-ft tall air gap. These results are for 0.9 surface emissivity and 30°F (272 

K) ambient temperature. 

(a) (b) (c)

T (°F)

4-in. 

1-ft

1-ft
7 

Figure 6 Heat flux along the inner surface of the wall exchanging heat with the room air. These results for an 8-ft (2.44-

m) tall partially filled wall cavity when the surface emissivity is 0.9 and 30°F (272 K) ambient temperature. 

Figure 7 shows the cavity thermal resistance as a function of the ambient temperature and insulation height. Each curve 

represents one insulation level and the figure covers different insulation levels from an uninsulated cavity to a fully insulated 

cavity. Regarding the upper curve representative of the fully insulated cavity, which constitutes a base case for comparison, 

RC is constant and equal 15 h·ft2

· ̊F/Btu (2.64 m2·K/W). With a 3.8-in. (0.089 m) tall air gap, the thermal resistance drops by 

15%. Similarly, a 1-ft tall air gap led to a 35% decrease and a 2-ft tall air gap led to a 54% decrease in thermal resistance. 

Figure 7 Thermal resistance of a partially insulated wall cavity as a function of insulation height and ambient 

temperature. These results are for a 3.5-in. (0.089-m)× 8-ft (2.44-m) cavity with 0.9 surface emissivity. 

Figure 8 compares the thermal performance of the wall assembly, with temperature dependent RC, against the results of 

constant RC when the surface emissivity is 0.8. The comparison was done in terms of the total heat flux through the wall 

assembly for the two limiting cases of uninsulated and fully insulated wall cavities. For the temperature independent case, we 

used the value of RC corresponding to an average temperature of 75 ̊F and a temperature difference, ΔT, of 50 ̊F. The heat 

flux increases almost linearly with ΔT. Differences between the two approaches are up to 6% for |∆ܶ| greater than 10 ̊F. The 

larger variations at very low temperature differences that can be seen in the figure are not significant because of the small 

heat transfer rates at low temperature differences. While both radiation and convection heat fluxes through the uninsulated 

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

Height along the wall (ft)

Heat flux (W/m2)

3.8-in tall air gap

1-ft tall air gap

2-ft tall air gap

0

3

6

9

12

15

18

0 20 40 60 80 100 120

R

C (h·ft2· ̊F/Btu)

Tamb ( ̊F)

fully insulated 1-ft tall air gap Uninsulated

3.8-in tall air gap 2-ft tall air gap

4-in tall air gap 

4-in tall air gap
8 

cavity depend on the temperature, the resistance of the uninsulated cavity is small compared to the air films and the other 

layers in the wall assembly, which makes the effect on the overall heat flux small. The fully insulated case is also shown in 

Figure 8 for comparison.

Figure 8 Total heat flux through a wall assembly containing an 8-ft (2.44-m) tall cavity as a function of temperature 

difference between the indoor and the outdoors when the surface emissivity is 0.8. 

Figure 9 shows the total thermal resistance, Rtot, of the wall assembly including the cavity, wallboard, sheathing, wood 

siding, and the inside and the outside film resistances. This resistance was evaluated as a function of insulation height in an 8-

ft (2.44-m) tall cavity at 30°F (272 K) ambient temperature. Also presented in this figure are the results from the approach 

based on two parallel resistances: one through the insulation and one through the air gap. We used the ASHRAE (2009) data 

for the resistance of the air gap. As the insulation height increases, the thermal resistance increases. When comparing the two 

approaches, the results are almost identical with a maximum difference of 3%. This difference occurred for the uninsulated 

limiting case.

Figure 9 Evolution of thermal resistance with insulation height with 30°F (272 K) ambient outdoor temperature. 

-40

-30

-20

-10

0

10

20

30

40

50

-50 -30 -10 10 30 50 70

Heat flux (W/m2)

Tset - Tamb (oF)

Variable Rc - Uninsulated

Constant Rc - Uninsulated

Fully insulated

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7 8

Rtot (h·ft2· ̊F/Btu)

Insulation height (ft)

CFD, ε = 0.9

CFD, ε = 0.8

Parallel Resistances, ε = 0.82
9 

CONCLUSIONS

Numerical simulations were performed to evaluate the thermal performance of wall cavities, presented by temperature 

distribution, local heat flux along the wall, and thermal resistance of the wall cavity for different temperature differences and 

average temperatures. Parameters were ambient outdoor temperature, cavity surface emissivity, cavity aspect ratio, and 

insulation height. A detailed study of the thermal performance of partially (vertically) insulated wall cavities is revealed by 

presenting the evolution of the thermal resistance, with insulation height, in a 3.5-in. (0.089-m) × 8-ft (2.44-m) wall cavity.

The followings are the key findings of this study:

• As expected, for a partially filled cavity, a small air gap can lead to a significant reduction in resistance. For 

instance, a 4-in. tall (0.1-m) air gap led to a 15% reduction in resistance. Similarly, a 2-ft (0.6-m) tall air gap led to 

54% reduction in thermal resistance.

• While the thermal resistance of an uninsulated cavity varies with temperature, since it is small when compared to 

the resistance of the other layers and of the external and internal air films, the difference in heat flux through the 

wall assembly does not vary much with temperatures. The difference in the total heat flux between constant and 

variable cavity resistances varied between 2% and 6% when the temperature difference is greater 10 ̊F. 

• The parallel resistance approach predicts well the resistance of wall assemblies with partially filled wall cavities, 

with maximum error of 3%.

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