Anales AFA - XVI Meeting on Recent Advances of Physics of Fluids and its Applications 46-51

IMPACT OF DESIGN PARAMETERS ON THE NATURAL VENTILATION OF A FAMILY

HOUSE ATTIC FROM SANTA FE (ARGENTINA)

M. Berli*1, A. Brondino1y J. Di Paolo 1

1Grupo de Investigación en Mecánica de Fluidos (GIMEF) – Universidad Tecnológica Nacional – Facultad Regional Santa Fe,

Lavaisse 610 – (3000) Santa Fe – Santa Fe – Argentina.

Recibido: 27/10/2021 ; Aceptado: 15/11/2021

The roof of a family home introduces important amounts of heat into the house. In Santa Fe city (Argentina), the attic

of social family houses is not designed with thermal optimization purposes. In this work, a low Reynolds number k-e

turbulent model is computationally implemented to show that a proper selection of constructive parameters of a vented

attic leads to a great reduction of the heat transferred from the roof to the ceiling. The main physical consequence of a

vented attic is the existence of a convective ﬂow barrier close to the roof that carries important amounts of heat from

the attic out to the environment. It is shown that the heat transferred through the ceiling to the interior of the house can

be reduced in more than 70% for summer conditions. Roof pitch and attic volume are also explored.

Keywords: vented attic, computer ﬂuid dynamic, buoyancy ﬂow.

https://doi.org/10.31527/analesafa.2022.ﬂuidos.46 ISSN 1850-1168 (online)

I. INTRODUCTION

A family home roof is usually the component that trans-

fers more heat than any other wall of the house. Conse-

quently, most design building codes suggest passive ventila-

tion as an alternative to produce important energy savings,

i.e., the International Residential Code [1] demands attics

ventilation unless local codes state the contrary, generally

due to atmospheric or climatic conditions.

Most attics of social family houses in Argentina are built

without connections to the exterior. In some cases, only

ventilation grills are used to allow pressure homogenization

with external environment and to evacuate moisture, but the

vent size, position, and orientation are not speciﬁcally de-

signed to generate an important ﬂow rate. Passive cooling

isn’t recommended by any national building code and is

rarely implemented in local government social houses pro-

grams. The advantages and disadvantages of the application

of attic ventilation compared to the traditional closed attic

need to be evaluated using local climate data bases before

recommending it as requirement in model house schemes

[2]. Therefore, the impact of natural convection airﬂow on

the heating load and its relationship with standard construc-

tion parameters (roof inclination angle, air gap cavity volu-

me, etc.) can offer helpful information for sustainable roof

design, especially in hot climate zones like Santa Fe city

(Argentina) with temperatures that can exceed 43ºC. In this

work, a trapezoidal-shaped cavity is used to describe the

geometry of a single pitch roof attic. This geometry allows

the possibility to study different roof pitches yet maintai-

ning the attic volume constant and vice versa [3].

Recent works [4] have proved Computer Fluid Dynamics

(CFD) as a valuable tool to estimate the impact of attic ven-

tilation in roof thermal performance. Wang et al. [5] studied

the natural convection effects on vented attics performan-

* marcelo.berli@uner.edu.ar

ce under winter conditions employing a two-dimensional

steady-state ﬁnite volume model on a triangular air cavity

by changing the vent size, ambient air temperature and cei-

ling insulation. On later papers, Wang and Shen [6,7] em-

ployed a 2D unsteady CFD model assuming a mid-plane

symmetry to study the impacts of ventilation ratio, vent ba-

lance and roof pitch on air ﬂow and heating load of both

sealed and vented attic for summer conditions. Recently, If-

fa and Tariku [8] studied the effects on temperature proﬁle

and airﬂow patterns inside the cavity by varying the gap size

between roof sheathing and ceiling insulation and the loca-

tion of the vent area under both summer and winter condi-

tion. The same authors used transient boundary conditions

[9] to study the dynamic response of the roof thermal per-

formance. All mentioned works showed the beneﬁts of a

vented attic in reducing the cooling loads, but they were

mostly based on strict building codes guidelines and focu-

sed mostly in the vent size inﬂuence on the thermal per-

formance, minimizing the importance of other constructive

parameters that could improve the thermal performance of

the attic of social homes of our zone.

The aim of this work is to obtain basic guidelines for se-

lecting a few construction parameters that can optimize the

attic thermal performance, i.e. vent openings size, attic vo-

lume and roof pitch. The turbulent air ﬂow and natural con-

vection heat transfer inside the attic are modeled in terms

of the low Reynolds number k−εturbulent model which is

validated using both experimental and numerical works.

II. MATHEMATICAL MODEL AND NUMERICAL

TECHNIQUE

Fig. 1sketches the typical parts of a single pitch roof that

usually cover a low-cost family house, where thermal loads

and the proposed vent openings on the front and back walls

are shown. The air cavity is bounded by the inclined roof,

the ceiling and the walls. The high temperatures of air and

FIG. 1: Low-cost family house vented shed roof (attic), with ther-

mals loads scheme.

solar radiation that impact on the roof, are transmitted to

the house indoor passing through this cavity. The received

thermal load will be considered as the combined effect of

both solar radiation and heat exchange by natural convec-

tion between the roof and the environment. The front and

back walls are assumed adiabatic (we neglect the heat ﬂow

through these walls). The ceiling consists of a thin cove-

ring material with negligible thermal resistance; therefore,

we assume that it has the same temperature as that inside

the house. The attic is located on a square room of 4 m long

each side. The set of governing equations for natural con-

vection turbulent ﬂow is given by the Reynolds-averaged

Navier-Stokes (RANS) equations of continuity (1), momen-

tum (2) and thermal energy (3):

∇·(ρu) = 0 (1)

(u·∇)u=∇·[−PI + (µ+µT)(∇u+ (∇u)T)

−

3(µ+µT)(∇·u)I−

3ρkI]+(ρ−ρ0)g(2)

ρCpu·∇T=∇·(λ∇T)(3)

where uis the velocity ﬁeld vector, ρthe temperature

dependent air density, ρ0the air density evaluated at a re-

ference temperature (ambient), Pthe pressure, gthe gravity

acceleration ﬁeld, µthe air dynamic viscosity, µTthe eddy

viscosity, kthe turbulent kinetic energy, Cpthe air heat va-

lue, λthe air thermal conductivity and Tthe temperature

ﬁeld.

The low Reynolds number k−εturbulence model em-

ployed in this work is a modiﬁcation of the well-known

k−εmodel, widely used in analyzing ventilation ﬂow in-

side houses and buildings [10]. The model introduces two

additional transport equations and two dependent variables:

the turbulent kinetic energy, k, and the turbulent dissipa-

tion rate εto the above RANS equations [11]. In order to

describe the ﬂow in the wall region, where viscous effects

dominate, the employed low Reynolds number k−εmo-

del adapts the turbulence transport equations with the AKN

(initials of its developers: Abe, Kondoh and Nagano) model

[12] by introducing damping functions.

The equations system was solved using the Non-

Isothermal Turbulent Flow module of the commercial ﬁni-

te element software COMSOL Multiphysics 4.4. To have a

good convergence scheme, the solutions were obtained by

following two steps: in the ﬁrst step, the viscosity was set

to a value approximately 10 times higher than the expected

physical viscosity inside the attic, in the second step, the ac-

tual physical viscosity is calculated using the ﬁrst step result

as initial guess.

The nonlinearity introduced by the Navier-Stokes

(RANS) and turbulence transport equations were solved

using a segregated approach [13]: Navier-Stokes equations

in one group and the turbulence transport equations in

another. For each iteration of the Navier-Stokes group, three

iterations for the turbulence transport equations were nee-

ded. A pseudo-time stepping approach was used to obtain

steady state solutions.

III. RESULTS AND DISCUSSION

Model validation

The Numerical model was validated with Ampofo and

Karaviannis [14] experimental measurements, who studied

the low turbulence air ﬂux driven by natural convection insi-

de a closed cavity of square cross section (0.75 m each side),

under a temperature gradient of 40 K between the lateral

walls (323 K on the left wall and 283 K on the right one),

with insulated top and bottom walls. The cavity was deep

enough (1.5 m) to assure a 2D ﬂux at any cross section far

from anterior and posterior walls. Velocity and temperature

proﬁles of moving air were measured at different positions

in a cross section placed at the middle distance between an-

terior and posterior walls. Our numerical results show good

agreement with experimental measurements (see Fig. 2).

Moreover, the agreement between the temperature proﬁles

is very precise in the boundary layer region where heat ﬂu-

xes need to be computed in this work.

The model was also validated with the numerical work

by Wang et al. [5], who developed a V2f turbulent model

to analyze the buoyancy-driven air ﬂux inside a vented attic

of triangular shape, under a temperature gradient of 20 K

between the base and the inclined top side, for winter con-

ditions. The geometry of the 2D triangular cross section of

the attic was 8 m long in the base and had a roof inclination

ratio of 5/11. The streamlines and isotherms predictions ob-

tained with our model reproduce the same behavior, espe-

cially for the case of a vented attic with 2 cm openings width

and a R-20 insulation type for a 267 K ambient temperatu-

re. But the best agreement is observed when comparing two

variables relevant for our study at summer conditions: heat

transferred through the ceiling (HTTC) and mass ﬂow. The

HTTC predicted by Wang et al. [6] is 48.5 W/m while ours

is 46.8 W/m, computing a percentage difference of about

3.5%, while the mass ﬂow difference between both models

is about 1% (0.0236 kg/s for Wang’s model and 0.0238 kg/s

for our model).

Summer boundary condition: Roof constant temperatu-

re vs solar radiation.

The inﬂuence of geometric dimensions on the attic ther-

mal performance is very dependent on the thermal boun-

dary conditions. A 295.15 K temperature is desired to have

a comfortable indoor environment, being this the prescribed

temperature on the ceiling. But it is not fully understood

what types of thermal conditions can mimic the real roof

conditions for any situation.

For winter conditions and snowfall zones, constant roof

Berli et al. / Anales AFA - XVI Meeting on Recent Advances of Physics of Fluids and its Applications 46-51 47

FIG. 2: Comparison of the present model results and experimental

measurements made by Ampofo and Karaviannis14. Red: Vertical

velocity. Orange: Temperature.

temperature is an appropriate condition since snow accumu-

lation imposes its temperature and insulates the roof from

outside atmosphere. For summer conditions, the roof is ex-

posed to sun radiation, different ambient air temperature

and convective dissipation, so it is not clear which roof tem-

perature should be used as a boundary condition. For this

reason, we compared two cases: a) a prescribed constant

roof temperature (CRT), used widely in the literature [5-8]

and b) a prescribed constant solar radiation (CSR) coupled

to convective heat exchange with external environment. For

both cases, a closed cavity without conection with exterior

is used.

The value of 345.15 K was used for the CRT, as a ty-

pical summer roof temperature [6]. For the CSR case both

solar radiation (heat ﬂux) of 1000 W/m2and a convective

heat ﬂux from the Non-Isothermal Turbulent Flow module

of COMSOL was used under different summer air tempera-

tures.

Table 1compares the HTTC between CRT and CSR for

a varying ambient temperature and summarizes the abso-

lute percentage differences (APD) between them. It can be

noted that the APD minimum difference is computed for

305.15 K, and can be as greater as 22.5%. This means that

TABLE 1: Constant roof temperature and constant solar radiation

results comparison for summer conditions.

Ambient Tempe-

rature (K)

Roof

Average

Tempera-

ture (K)

Heat

transfer

to the

ceiling

(MW/m)

Absolute

percen-

tage

difference

(APD)

(%)

CRT Case 345.15 65.6 -

CSR

300.15 340.75 55.3 15.8

305.15 345.47 64.6 1.5

310.15 350.99 72.0 9.7

315.15 355.51 80.3 22.5

prescribing a constant roof temperature with a single value

could not be an appropriate boundary condition for diffe-

rent ambient scenarios. The roof temperature will be hardly

constant during summer for a wide ambient temperature va-

riation and it is expected that the attic thermal performance

will depend on the heat dissipation due to atmosphere con-

ditions changes.

Radiation values are known from daily weather reports

and convective coefﬁcient can be easily obtained from bi-

bliography, but roof temperature is not always known. Mo-

reover, for vented conﬁgurations, the air exchange between

the attic and the atmosphere could affect the average roof

temperature due to an increased heat exchange by convec-

tion. Thus, the following results were obtained using radia-

tion and convective exchange as the roof thermal boundary

conditions.

Open vs closed cavity

In this section, we compare the HTTC between open

(vented, see Fig. 1) and closed attic. For a 2D analysis, it

is assumed that the openings go through the entire thick-

ness of the walls. In this section, a constant height (vent

size, see Fig. 1) of 5 cm is selected for the openings. Com-

parison is made for a proposed ambient temperature ran-

ge corresponding to a hot summer day. As Fig. 3shows,

a constant HTTC difference between open and closed attic

can be observed for the full ambient temperature range (Ta-

ble 2). This difference is about 43 W/m for the selected ope-

ning height and is an important reduction of heat that does

not enter the house. It can be noted that the HTTC increa-

ses with the ambient temperature for any case. However, for

the highest ambient temperature (315.15 K), the computed

HTTC for the vented attic is 50% lower than that for the

closed attic. The lower the heat transferred through the cei-

ling, the lower the energy needed to maintain a comfortable

indoor temperature.

Air ﬂow streamlines inside the cavity for the open cavity

with h=5 cm can be observed in the second attic from

above in Fig. 4, where an air ﬂow near to the roof running

from inlet to outlet vents can be observed. This ﬂow creates

a convective barrier that carries important amounts of heat

from the attic out to the external ambient, thus reducing the

heat transferred to the ceiling. This socalled ﬂow barrier is

a buoyancy-driven convective ﬂux created by the inlet air in

contact with the roof, being the ﬁrst cooler than the second.

Berli et al. / Anales AFA - XVI Meeting on Recent Advances of Physics of Fluids and its Applications 46-51 48

FIG. 3: Heat transferred through the ceiling for both closed and

open cavity. Mass ﬂow through the attic is plotted for the open

cavity.

TABLE 2: Impact of ambient temperature.

Ambient

Tempera-

ture (K)

Closed Attic Open Attic

Heat transfer to

the ceiling (MW/m)

Mass ﬂow

(kg/ms)

300.15 55.3 13.4 86.4

305.15 64.6 21.4 82.5

310.15 72.0 30.0 78.0

315.15 80.3 37.3 72.9

Inﬂuence of vent (openings) size.

In the previous section, it was shown that the cavity with

openings greatly improves the thermal performance of the

attic. It is expected that the wider the openings, the higher

the air ﬂow rate through the attic, thus optimizing the con-

vective heat exchange with the external environment. In this

section, the attic thermal performance is explored for the fo-

llowing openings heights: 2 cm, 5 cm, 8 cm and 11 cm (see

Fig. 4). The ambient air temperature was set to 305.15 K.

The wider the openings, the greater the convective barrier

near the ceiling and therefore the greater the heat dissipated

convectively to the outside of the cavity, as can be seen in

Fig. 4.

Fig. 5shows that even for a small opening height of 2 cm,

the HTTC is reduced up to 58% respect to the closed cavity,

while for the widest vents (h=11 cm) the reduction exceeds

73%, meaning that the wider the openings the better the

attic thermal performance. This great reduction in HTTC

is generated by the existence of a ﬂow barrier close to the

roof that gets thicker as openings size is increased (see Fig.

4), which transports convective heat to the outside of the

attic, as was explained in the previous section. However, the

HTTC reduction seems to be kept under 80% for h>11 cm,

being this the maximum opening size we recommend.

Inﬂuence of roof pitch.

The roof pitch not only involves the possibility of thermal

optimization, but also implies different material costs and

water drainage performances. The minimum recommended

pitch is 7º and this value should not exceed 20º. In this sec-

tion, the thermal performance will be explored for a roof

pitch ranging from 7º to 17.5º. For this purpose, the attic

height at the center of the base (parameter Am in Fig. 1) will

be kept constant at 0.8 m, to keep the attic volume constant.

FIG. 4: Streamlines (black lines) and temperature ﬁeld for an open

cavity. Legends on the right show temperatures in K.

FIG. 5: Dashed curve: HTTC for every explored opening height.

Solid curve: Percentage reduction of computed HTTC for the open

attics with respect to that of the closed one.

The opening height was set to 5 cm.

Table 3shows that the HTTC increases with roof inclina-

tion. One could expect that the higher the roof inclination

the enhanced buoyancy effect and the greater the mass ﬂow

that carries convective heat out of the attic, but the reason

for HTTC to be increased is that the higher the roof incli-

nation the wider the roof area that is exposed to solar radia-

tion. Although the mass ﬂow increases, the proportion of

heat transferred to the ceiling also increases. In this sense,

a pitch of 7º seems to be the better choice from a thermal

viewpoint, and it is the cheaper choice too. It can also be

noted that for any roof inclination, the vented attic shows a

very high reduction of the HTTC compared to a closed one,

being this reduction about 63% for a pitch of 7º and 67 %

for 17.5º.

Inﬂuence of Attic volume.

Attic volume was also explored keeping both the roof

pitch and the opening height constants, with values of θ=

Berli et al. / Anales AFA - XVI Meeting on Recent Advances of Physics of Fluids and its Applications 46-51 49

TABLE 3: Impact of roof pitch.

Roof

Pitch

(º)

Closed Attic Open Attic

Heat transfer to

the ceiling (MW/m)

Mass ﬂow

(kg/ms)

7 40.6 16.2 64.8

10.5 52.6 17.8 69.6

14 64.6 21.4 82.5

17.5 77.0 25.0 92.1

14◦and h=5 cm, respectively and varying the middle

height of the attic (Am). The inclination was selected by

considering the abundant rains in summer days of our zone.

In this sense, roof drainage is critical.

Table 4shows that the HTTC is reduced as Am increa-

ses, an expected trend because the taller the attic the greater

the air volume that generates a natural insulation between

the roof and the ceiling. For a vented attic, the HTTC re-

duction between the extreme volume sizes is 32 %, while

this reduction is about 23% for a closed one. Even though

these reductions are important, the attic cannot be as tall as

desired due to construction costs. Even for the lowest ven-

ted attic (Am = 0.7 m) the HTTC is 56% lower than that for

the tallest closed one (Am = 1.0 m). When comparing these

results with the ones observed for different vent sizes, we

can conclude that a vented attic needs an optimization of

its openings instead of the roof height to greatly reduce the

HTTC without requiring higher construction costs. Due to

the lack of ventilation, the attic volume is more important

to be higher for a closed cavity.

TABLE 4: Impact of attic middle height.

Attic Middle

Height (m)

Heat transfer to the ceiling (MW/m)

Closed Attic Open Attic

0.7 73.6 23.9

0.8 64.6 21.5

0.9 59.3 19.2

1.0 55.2 17.0

IV. CONCLUSIONS

A low Reynolds number k−εturbulent model was nu-

merically solved to analyze the natural ventilation inﬂuence

on an open cavity which resembles the attic of a low-cost

family house. The model was validated with experimental

and numerical models, showing good agreements in both

cases. The analysis was focused on studying how simple

construction parameters can reduce the heat transferred to

the interior of the house, i.e., openings sizes, roof pitch and

attic volume. By exploring these parameters, we found that:

The wider the openings (inlet and outlet), the better the

attic thermal performance.

The lower the roof pitch, the lower the HTTC due to a

lower surface exposed to solar radiation.

For a closed attic, the greater its inner volume the bet-

ter the thermal performance. For a vented attic, the vo-

lume is not as important as the openings size to have

an important reduction of the HTTC.

Opening’s existence is the most important feature that

can enhance the attic thermal performance. It was shown

that a vented attic can reduce the HTTC in more than 70%

with respect to a closed one for summer conditions of Santa

Fe (Argentina). As limitations, we can mention that winds,

winter conditions, ceiling insulations and possible 3D ef-

fects of different internal attic geometries were not conside-

red in this work.

FUNDING

This work was supported by Universidad Tecnológica

Nacional through Project AMUTIFE 3457.

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