Consideration of permeable and semi-transparent
shading devices into the modeling of the exchanges
between the building and its environment: proposition of
a simple and flexible model
Antoine Duguéa, Denis Bruneaub, Alain Sommierb
aNobatek, bINSTITUT de MECANIQUE et d’INGENIERIE (I2M),
Esplanade des Arts et Métiers33405 TALENCE CEDEX
This investigation aims at providing an efficient description of solar shading devices
behaviour which can be integrated into modelling platforms currently on the market.
A 1D model is developed by considering precisely the radiative exchanges in short
and long wavelengths, and integrating ascending laminar flow which takes place
between the shading device and the wall (structural skin). The model describes the
heat and mass flows through the solar textile screen by considering it permeable and
Two different types of correlation which explicit the characteristics of the mass flow in
the cavity are presented. The first one is based on the driving force as a difference of
pressure between the air in the cavity and the air outside. The second one relies on
experimental and numerical studies that propose correlations between the Nusselt,
Rayleigh and Reynolds numbers. Their pertinences are discussed based on the first
measurements realized on the experimental protocol which has been built and
Study is still currently underway to refine the chosen correlations and to validate the
model for natural convection with a permeable shading device.
Keywords: shading devices, natural convection, heat transfer coefficient, air flow
Convective heat exchange coefficient
Mass air flow
Relative to the shading device
Relative to the wall
Solar incident radiation flux
The increasing development of highly glazed buildings subject exposed to high solar
gain induces a greater use of solar protection solutions such as textile screens or
outside climbing plants which allow passive solar gain in winter. However current
thermal simulation platforms do not accurately integrate those architectural solutions,
especially the induced air flow between the wall and the shading device.
The study presents a model of heat transfers which are observable at the scale of a
wall. A system composed of a shading device placed in front of a wall is instrumented
by flux and temperature sensors. Part of the measurements is used for model settings
definition and others for model validation. We propose here an analysis of different
flow patterns and an interpretation of preliminary results which justifies the choice of
models and their settings.
2. Experimental protocol
In order to quantify the heat flows which take place in the studied configuration, an
experimental platform has been built and instrumented. 5cm thick glass wool was
fixed on an existing wall with two 13mm thick plaster boards; the studied shading
device is placed in front of it, delimiting a ventilated cavity.
The instrumentation is made of 18 thermocouples placed at three different heights and
at different depths, a pyranometer operating on the spectral range 400 to 1100nm
measuring the incident solar flux on the wall, a cup anemometer for the external wind
speed and a hot-wire anemometer placed in the middle of the air gap at a median
height (see scheme).
Measurements were carried out in June for two opaque wooden claddings (see photo)
with a 6cm air gap, and others in the month of September 2011 with solar screens.
Figure 1: Photograph of the
Figure 2: Representation of sensors location
3. Description of the model
The wall is discretized into a set of volumes for which the flux balance is written in a
dynamic regime. The temperature in the cavity is considered uniform temperature and
corresponds to an average temperature.
3.1 General model
3.1.1 Radiative fluxes
The short wave and long wave radiative fluxes are differentiated, and we consider the
multi-reflexion phenomenon as presented by Rodriguez .
Figure 3: Scheme illustrating the infinite reflexion phenomenon
The total short wave flux absorbed by the wall can be written in a fully developed form:
Recognizing a geometric series, we can write the total:
3.1.2 Convective fluxes
For the external convection heat transfer coefficient, we consider a “medium smooth”
surface according to Ashrae 1989 manual to write:
And the heat loss in the cavity due to the advection can be written as:
Figure 4: Thermal network for the external part of the studied experimental platform
The heat balance on every node gives a linear differential equation (E5):
(E5) can be written in a matrix form distinguishing internal and external loads,
respectively the matrices F and G, and the vector of temperatures in the wall T and U
which consists of the incident solar flux and the outside temperature.
The numerical solution of this differential equation is obtained with the implicit Euler
method with a time step of 1 minute using Matlab, where matrix F must be
recalculated at every step.
3.2 Air flow model, determination of the air speed and the heat transfer
Different models of natural convection between two plates exist - mostly established
for a steady state- which fall into two types. The first comes from the writing of the
driving pressure gradient in the air gap as the difference between the temperature in
the cavity and the outside temperature. It is found in the ASHRAE Handbook and
European standards EN13363. Ong  provides the following form for a solar
The latter type considers the flow (possibly asymmetric) in the walls adjacent to the
cavity to establish correlations between Nusselt and Rayleigh numbers. These
numerical models were first established experimentally and next using CFD. Aung 
wrote in 1972 the correlations between the numbers of Nusselt, Rayleigh and flow. In
2011 Gan  sets those more generally for a set of configurations in the form of two
relations to explicit the heat transfer coefficient and the mass flow in the cavity.
4. First results
To study the respective relevance of these two models, we draw the driving terms
depending on air speed in the cavity: the one integrating the temperature difference
and the term including the solar radiative flux.
Figure 5 shows that the distribution of pairs corresponding to the Aung’s model  is
irregular while the identity function would be expected. On the opposite, the terms
which correspond to relationships based on heat flows from the walls to the air gap
reflect a strong correlation whose shape can be explained by the inertia of the layer of
We can conclude that the predictions of the second type correlation are more in
adequation with the measurements, and thus such type of correlation should be used
in the model.
Figure 5: Analysis of the correlations of two types of models calculating the air flow
The model has been validated for a non-permeable shading device and considering a
forced air flow in the cavity. Current work aims at refining the existing correlations for a
better integration which takes into account the natural convection in the cavity.
Meanwhile, measurements are underway for solar screens, for which the mass flow
prediction must be adjusted taking into account the charge losses associated to the
 Aung, W., LS Fletcher, and V. Sernas. “Developing laminar free convection
between vertical flat plates with asymmetric heating.” International Journal of
Heat and Mass Transfer 15, no. 11 (1972): 2293–2304.
 Ong, K. “A mathematical model of a solar chimney.” Renewable Energy 28, no.
7 (June 2003): 1047-1060.
 Gan, Guohui. “General expressions for the calculation of air flow and heat
transfer rates in tall ventilation cavities.” Building and Environment 46, no. 10
(April 2011): 2069-2080.
 Rodriguez, Julio (2006) “Déshydratation par effet de serre d'un produit emballé
dans un film polymère perméable aux molécules d'eau: approche
expérimentale et de modélisation ». Doctorat Génie energétique, Paristech >
 Cole, R. J., and N. S. Sturrock. 1977. The Convective Heat Exchange at the
External Surface of Buildings. Building and Environment, Vol. 12, p. 207.