A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

A Model for Naturally Ventilated 

Cavities on the Exteriors of 

Opaque Building Thermal 

Envelopes 

B. Griffith 

Presented at Simbuild 2006 Conference 

Cambridge, Massachusetts 

August 2−4, 2006 

Conference Paper 

NREL/CP-550-39829 

November 2006 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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A MODEL FOR NATURALLY VENTILATED CAVITIES ON THE EXTERIORS OF 

OPAQUE BUILDING THERMAL ENVELOPES1

Brent Griffith 

National Renewable Energy Laboratory, Golden, CO 

 

1 This work has been authored by an employee or employees of the Midwest Research Institute under Contract No. DE-AC36-

99GO10337 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the 

article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide 

license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes. 

ABSTRACT

This paper describes a model for naturally ventilated 

cavities that are formed by lightweight baffles on the 

exteriors of opaque building thermal envelopes. The 

model can be used for building components that are 

slightly detached from the main envelope (but do not 

connect to the interior), such as photovoltaic panels, 

double roofs, rain screens, and unglazed transpired 

collectors. The model provides values for baffle 

surface temperature as well as exterior boundary 

conditions for convection and radiation to use in 

modeling heat transfer in the underlying surface. Two 

quasi-steady energy balances are used to solve for 

temperatures: one for the baffle surface and the other 

for the air in the cavity. The model assumes that the 

heat capacity in the baffle can be neglected, since it is 

much lower than the underlying mass surface. Natural 

ventilation rates are calculated with simplistic 

correlations that are based on user-provided discharge 

coefficients. Convection coefficients inside the cavity 

are based on those used for window gaps as 

documented in ISO (2003) Standard 15099. Radiation 

coefficients are linearized. The model has been 

implemented in EnergyPlus. 

INTRODUCTION

Buildings form complicated systems and present 

numerous modeling challenges for whole-building 

energy simulation programs. The exterior surfaces that 

form the thermal envelope of buildings are fundamental 

elements of whole-building simulation programs. Most 

building simulation programs intended for modeling 

annual energy performance treat surfaces as solid 

constructions with uniform (one-dimensional) heat 

flows. Boundary conditions for modeling surface heat 

transfer are also treated as uniform across the area. For 

the outside face of exterior surfaces, the boundary 

conditions typically represent the surrounding weather. 

Building simulation programs often provide 

mechanisms for other boundary conditions on the 

outside faces of exterior surfaces, such as for ground 

contact and neighboring thermal zones. 

Many wall and roof constructions used in buildings can 

be considered solid, but in special cases surfaces are 

constructed such that their exteriors are not solid with 

the rest of the assembly. They instead have cavities 

underneath that are partially vented to the outside. 

Examples include vented roof tiles, certain rain screens, 

photovoltaic mounting configurations with standoffs 

(e.g., roof paver systems from PowerLighttm, see 

www.powerlight.com), unglazed transpired solar 

collectors (e.g., solar ventilation preheat systems such 

as Solar Walltm, see www.solarwall.com), and various 

other double-skin designs that have been proposed for 

alternative, low-energy architecture. Such constructions 

share the following characteristics: 

• Air-filled cavities located toward the exterior 

• A solid portion of the construction assembly 

located toward the interior 

• Opaque outer layers on the exterior with 

openings that allow airflow in and out of the 

cavities. 

This paper presents a simple model for exterior surfaces 

with these characteristics. Ciampi et. al. (2003) studied 

such systems for opaque facades and developed a 

simple analytical model that predicts the impact that 

ventilation has on the thermal load. However, whole1
building simulation programs do not appear to provide 

explicit models for vented exterior cavities. Advanced 

users who need to model such systems could, for 

example, modify surface and material properties to 

attempt to account for changes in thermal performance. 

However, little guidance is available. Ideally, an 

explicit model would be available for building 

simulation. In the case of ventilated photovoltaic 

modules, having a more detailed model is especially 

important because the resulting temperature affects the 

device’s performance. This model was originally 

developed to represent unglazed transpired solar 

collectors when they are not being actively operated for 

solar ventilation preheat (but are still present on the 

facade). 

MODEL FORMULATION

The Exterior Naturally Vented Cavity model is 

provided as a special case for the outside boundary 

conditions of opaque heat transfer surfaces when they 

include a multi-skin exterior. Figure 1 shows the 

overall configuration. From the thermal envelope’s 

point of view, a vented cavity on the outside of the 

surface modifies the conditions experienced by the 

underlying heat transfer surfaces. This exterior cavity 

acts as a radiation and convection baffle situated 

between the exterior environment and the outside face 

of the underlying heat transfer surface. The actual outer 

surface is referred to as the “baffle.” The modeling here 

assumes that the heat capacity in the outer baffle can be 

neglected, since it is much lower than the underlying 

mass surface. This assumption may not hold for 

ventilated exterior facade systems that use a more 

massive outer layer, such as heavy tiles; the model 

should not be used for these cases without modification. 

Figure 1 Overall configuration 

Baffle Heat Balance 

The baffle is assumed to be thin and have high enough 

conductivity that it can be modeled with a single 

temperature (for both sides and along its area). This 

temperature Ts,baff is determined by formulating a heat 

balance on a control volume that just encapsulates the 

baffle surface. The heat balance is diagrammed in 

Figure 2. 

Figure 2 Baffle surface heat balance 

The heat balance on the baffle surface’s control volume 

is: 

,, ,

, 0

sol LWR Env conv Env LWR cav

conv cav source

qq q q

q q

α

′′ ′′ ′′ ′′ + + +

+ ′′ ′′ + =

 (1) 

Where, 

sol qα

′′ is absorbed direct and diffuse solar 

(short wavelength) radiation heat flux, 

LWR Env , q′′ is net long wavelength (thermal) 

radiation flux exchange with the air and surroundings, 

conv Env , q′′ is surface convection flux exchange 

with outside air, 

LWR cav , q′′ is net long wavelength (thermal) 

radiation flux exchange with the outside face of the 

underlying surface(s), 

conv cav , q′′ is surface convection flux exchange 

with cavity air, 

2
source q′′ is a source/sink term that accounts for 

energy exported out of the control volume when the 

baffle is a hybrid device such as a photovoltaic module 

or an active thermal collector. 

All terms are positive for net flux to the baffle. Each 

heat balance component is introduced briefly here. 

External SW Radiation 

sol qα

′′ is calculated by using models for sky conditions, 

solar radiation, shading, and reflections that are typical 

of building simulation, and generally includes both 

direct and diffuse incident solar radiation that is 

absorbed by the surface face . This is influenced by 

location, surface facing angle and tilt, shading surfaces, 

surface face material properties, weather conditions, etc. 

The sky, solar, and shading models used in the current 

implementation are documented in the engineering 

reference for EnergyPlus (DOE 2006). 

External LW Radiation 

LWR Env , q′′ is formulated as the radiation exchange 

between the surface, the sky, the ground, and the 

atmosphere, which is typical of building simulation. In 

the current implementation, radiation heat flux is 

calculated from the surface absorptivity, surface 

temperature, sky, air, and ground temperatures, and sky 

and ground view factors (DOE 2006). Linearized 

coefficients, rather than the full fourth-order relation, 

are typically used to model radiation coefficients to 

greatly simplify solving Eq. 1. 

External Convection 

conv Env , q′′ is modeled with the classical formulation: 

( , where h conv Env co amb s baff , q hT T ′′ = −

Cavity LW Radiation 

LWR cav , q′′ is modeled with a radiation exchange 

formulation between the baffle surface and the 

underlying heat transfer surface across the cavity. 

Radiation across the cavity is also modeled with 

linearized coefficients. 

Cavity Convection 

conv cav , q′′ is modeled with the classical formulation: 

q hT T conv cav c cav a cav s baff ′′ , ,, , = − ( ), where hc,cav, is the 

convection coefficient. Although ventilation air 

exchanges will affect the actual airflow patterns within 

the cavity, a simple model would have great difficulty 

predicting the consequences of this on surface 

convection rates. Therefore, we assume that the 

cavity’s geometry and temperature regimes are similar 

to the gaps found inside the glazing units used in 

windows. ISO (2003) standard 15099 provides a 

concise collection of accepted correlations for hc,cav that 

were selected because they were the best identified. 

The correlations were synthesized from a large number 

of relevant engineering studies. They cover a wide 

range of tilts providing a set of correlations that apply to 

arbitrary angles, including vertical and horizontal 

orientations. 

Baffle Temperature 

Substituting models into (1) and solving for Ts,baff

yields the following equation: 

( )

, ,

, , ,,

,

,,, , ,

s co amb r atm amb r sky sky

r gnd amb r cav so c cav a cav source

s baff

co r air r sky r gnd r cav c cav

I hT h T h T

h T hT hT q T

hh h h h h

⎛ ⎞ α ++ + +

⎜ ⎟

++ + ′′ ⎝ ⎠ = +++ ++

(2) 

, ) co, is the 

convection coefficient. The value for hco is treated in 

the usual way for surfaces that are exposed to exterior 

(weather) conditions. In addition, when it is raining, the 

current implementation of this model assumes the baffle 

becomes wet and models the rain-enhanced surface heat 

transfer by using a large value for of 1000.0 

W/m

co h 2

·K. In the current implementation, this value is 

fixed inside the program and was selected to be 

consistent with what EnergyPlus uses for rain on normal 

exterior surfaces. This arbitrary and high value for 

drives the baffle temperature to be very close to the 

outdoor air temperature. This is consistent with the 

assumptions that the baffle is lightweight and the rain 

drops area at the outdoor temperature. 

co h

where, 

s I is the incident solar radiation of all types 

[W/m2

], 

α is the solar absorptivity of the baffle 

[dimensionless], 

is the linearized radiation coefficient for 

the surrounding atmosphere [W/m

r atm , h 2

·K], 

 is the outdoor dry bulb from the weather 

data, also assumed for ground surface [oC], 

Tamb

 is the linearized radiation coefficient for 

the sky [W/m

r sky , h 2

·K], 

3
Tsky is the effective sky temperature [oC], 

 is the linearized radiation coefficient for 

the ground [W/m

r gnd , h 2

·K], 

 is the linearized radiation coefficient for 

the underlying surface [W/m

r cav , h 2

·K], 

Tso is the temperature of the outside face of 

the underlying heat transfer surface [oC], 

 is the convection coefficient for the 

outdoor environment [W/m

co h 2

·K], 

 is the convection coefficient for the 

surfaces facing the cavity [W/m

c cav , h 2

·K], and 

 is the dry bulb temperature for air in the 

cavity [oC]. 

Ta cav ,

Cavity Heat Balance 

The cavity is the volume of air between the baffle and 

the underlying heat transfer surface. The cavity air is 

modeled as well-mixed. The uniform temperature of 

the cavity air, , is determined by formulating a 

heat balance on a control volume of air as diagrammed 

in Figure 3. 

Ta cav ,

Figure 3 Cavity heat balance 

The heat balance on the plenum air control volume is: 

, 0 Q QQ vent co c baff ++ = & && (3) 

where, 

 is the net rate of energy added from 

natural ventilation, where outdoor ambient air 

exchanges with the cavity air. 

Qvent

&

Qco

& is the net rate of energy added by surface 

convection heat transfer with the underlying surface. 

is the net rate of energy added by 

surface convection heat transfer with the baffle. 

Qc baff , &

Cavity Temperature 

Substituting into Eq. (3) yields the following equation: 

( )

,

, ,

,

, ,

c cav so vent p amb

c cav s baff

a cav

c cav vent p c cav

h AT m c T

h AT

T

h Am c h A

⎛ ⎞ +

⎜ ⎟

+ ⎝ ⎠ = + +

&

& (4) 

where, 

A is the surface area [m2

] 

mvent & is the air mass flow from natural forces 

[kg/s] 

Modeling natural ventilation air exchanges in a general 

way is challenging. Therefore, simplistic engineering 

models are used to model resulting from natural 

buoyancy and wind forces. Reasoning that the 

configuration is similar to single-side natural 

ventilation, we elect to use correlations for natural 

ventilation presented as Eq. (29) and (30) in Chapter 26 

of ASHRAE HOF (2001). 

mvent &

mvent = ρ Vtot

& & (5) 

where, 

ρ is the density of air [kg/m3], and 

VV V && &

tot wind thermal = + is the total volumetric 

flow rate of air ventilating in and out of the cavity from 

wind-driven and buoyancy-driven flows, where, 

Vwind = CAU v in ∞ & (6) 

( ) ,

thermal

,

V 2 a cav amb

D in NPL

a cav

T T

CA gH T

− & = Δ (7) 

 (if ) T T a cav amb , >

4
( ) , V 2 thermal

amb a cav

D in NPL

amb

T T

CA gH T

− & = Δ (8) 

 (if and baffle is vertical). T T amb a cav > ,

 is the effectiveness of the openings and 

depends on opening geometry and the orientation with 

respect to the wind. ASHRAE HoF (2001) indicates 

values of 0.25−0.6. This value is user input. 

Cv

 is the discharge coefficient for the 

opening and depends on opening geometry. This value 

is user input. 

CD

Mass continuity arguments lead to modeling the area of 

the openings as one-half the total area of the openings, 

so we have: 

2

vent openings

in

A

A =

g is the gravitational constant taken as 9.81 

[m/s2

]. 

 is the height from midpoint of lower 

opening to the neutral pressure level. This value is user 

input. 

ΔHNPL

If the cavity is horizontal and , then T T amb a cav > ,

V = thermal

& 0 because this is a stable situation. 

SAMPLE RESULTS AND DISCUSSION

The model was implemented in EnergyPlus. In this 

implementation, the Heat Balance Model with 

conduction transfer functions was used to model the 

underlying heat transfer surface. The exterior cavity 

model provides a method of updating the boundary 

conditions that are exposed to the outside plane of the 

underlying heat transfer surfaces. The interdependence 

of Eqs. 2 and 4 is handled with sequential substitution. 

An example of using the model is presented for the case 

of photovoltaic roof paver systems. One common 

configuration for membrane roofs involves mounting 

the photovoltaic modules to interlocking foam boards 

with standoffs that raise the modules away from the 

underlying foam. This allows outside air to naturally 

ventilate the cavity under the modules. To demonstrate 

the model and its implementation, we present results for 

the two configurations diagrammed in Figure 4. The 

vented cavity configuration is compared to a similar 

configuration, but without the standoffs that raise the 

module. In both cases, the photovoltaic modeling is 

thermally coupled so that the electrical energy 

converted by the photovoltaics is exported from the 

system and the module operating temperatures are 

obtained from the heat transfer modeling. 

The model was run for Chicago with TMY2 weather, 

and results are presented for a single representative 

sunny day of July 8. The exterior cavity model used the 

following input data: vent area fraction of 0.03, thermal 

emissivity of 0.84, solar absorptivity of 0.92, cavity 

thickness of 0.05 m, Cv of 0.25, and CD of 0.5, and a 

length scale of 0.05 m for buoyancy. The two roof 

assemblies cover the same interior thermal zone. The 

empirical model from Sandia National Laboratories 

(King et. al. 2004) was used to model photovoltaic 

module performance. The panels are BP Solar model 

BP275. 

Figure 4 Photovoltaic roof configurations, (a) with 

ventilated cavity and (b) with integrated surface 

mounting. 

Figure 5 shows the results for dry bulb temperatures on 

July 8, including the outdoor air, the cavity air, the 

baffle surface, the underlying surface, and the integrated 

surface for comparison. In the beginning of the day, the 

baffle heats more quickly than the integrated roof 

assembly and then cools more quickly. The underlying 

surface’s outside temperature is lower than the 

unventilated integrated surface during the daytime, but 

is slightly warmer during the night as it cools more 

slowly. For this day, the thermal protection of the 

vented configuration makes the inside surface (facing 

the interior) under the roof deck below the ventilated 

configuration about 1.6oC cooler than below the 

integrated collector, shown in Figure 6. This indicates 

the importance of including an exterior cavity model 

when modeling the thermal impacts of ventilated roofs. 

5
The photovoltaic panel efficiencies are also affected by 

the module temperatures (see Figure 7). 

The model results for the underlying surface 

temperature are much higher than the cavity air 

temperatures. This indicates that radiation heat transfer 

is the dominant heat flow mechanism. Figure 8 explains 

this result by showing the calculated heat transfer 

coefficients. The correlations from ISO (2003) 

standard 15099 appear to produce relative low values 

for convection coefficients, which limits the rate of 

ventilation-driven cooling. Most results for convection 

coefficients (for this rooftop paver configuration) are 

being capped at a lower threshold of 0.534 W/m2

-K. 

This indicates that the ISO 15099 convection 

correlations are not very dynamic for horizontal cavities 

in these operating ranges and further investigation on 

convection correlations is warranted. 

0

10

20

30

40

50

60

70

80

90

0:00 12:00 0:00

Time of day 

Temperature [Deg. C]

O utdoor air Baffle surface

Cavity air Underlying surface

Integrated surface

Figure 5 Exterior temperature results 

20

22

24

26

0:00 12:00 0:00

Time of day 

Temperature [Deg. C]

Below integrated PV

Below vented PV

Figure 6 Interior temperature results 

0%

2%

4%

6%

8%

10%

12%

0:00 12:00 0:00

Time of day 

PV efficiency [%]

Integrated roof PV efficiency

Vented roof paver PV efficiency

Figure 7 Photovoltaic efficiency results 

6
0

1

2

3

4

5

6

7

8

0:00 12:00 0:00

Time of day 

Heat transfer Coef. [W/m2-K]

Cavity convection coefficient

Cavity radiation coefficient

Figure 8 Heat transfer coefficient results 

CONCLUSION AND FUTURE WORK

A model was presented for use in building simulation 

programs for the special case where opaque envelope 

surfaces have ventilated cavities on their exterior. The 

model forms separate heat balances on a baffle and a 

cavity that are used to determine boundary conditions 

for modeling heat transfer in a more massive underlying 

surface. 

The model is suggested as an appropriate mathematical 

framework for subsequent research to derive input data 

from empirical measurements. The model developed is 

based on engineering first principles and has not been 

experimentally validated. There are currently very few 

appropriate input data to use with the model. 

Experimental and field research efforts are needed to 

characterize appropriate input values for the ventilation 

opening areas and discharge coefficients for various 

types of systems. Cavity convection coefficients were 

modeled with accepted correlations for window 

glazings; however, this needs to be revisited because the 

correlations may not be performing well for some 

configurations. 

ACKNOWLEDGMENT

This work was supported by the Building Technologies 

Program within the Office of Energy Efficiency and 

Renewable Energy at the U.S. Department of Energy. 

REFERENCES

ASHRAE HOF 2001. 2001 ASHRAE Fundamentals 

Handbook. American Society of Heating 

Refrigeration and Air-Conditioning Engineers. 

Atlanta GA. 

Ciampi, M., Leccese, F., and Tuoni, G 2003. 

Ventilated facades energy performance in summer 

cooling of buildings. Solar Energy 75 (2003) pp 

491-502. Elsevier. 

DOE. 2006. EnergyPlus Engineering Reference. U.S. 

Department of Energy. 

http://www.eere.energy.gov/buildings/energyplus/p

dfs/engineeringreference.pdf 

ISO. 2003. ISO 15099:2003. Thermal performance of 

windows, doors, and shading devices – Detailed 

calculations. International Organization for 

Standardization. 

King, D.L., Boyson, W.E., Kratochvil, J.A. 2004. 

Photovoltaic Array Performance Model. Sandia 

National Laboratories. Albuquerque, NM. 

SAND2004-3535 

7
F1147-E(12/2004) 

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A Model for Naturally Ventilated Cavities on the Exteriors of Opaque 

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14. ABSTRACT (Maximum 200 Words)

This paper describes a model for naturally ventilated cavities on the exterior of opaque building thermal envelopes 

that are formed by the presence of a lightweight baffle. The model can be used for building components that are 

slightly detached from the main envelope (but do not connect to the interior). 

15. SUBJECT TERMS

opaque; thermal envelope; commercial buildings; energy performance; zeb; zero energy building 

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