Category Archives: BACKGROUND

THERMAL PERFORMANCE OF HISTORICAL BUILDINGS: A CASE STUDY OF LUCKNOW

Dr. Anupama Sharma, Department of Architecture & Plng, Maulana Azad National Institute of Technology, Bhopal (INDIA)

Introduction

A building with a good thermal performance establishes an indoor environment which nearly approaches comfort conditions in a given climatic setting. In architectural term, this means that the planning and structure of a building should utilise natural possibilities to improve comfort conditions with out the aid of mechanical devices.

It is evident that any improvement exercised by the building itself will show up in the promotion of comfort, which is difficult to define exactly. In other words; any heat energy captured in the under heated periods will reduce heating costs; and any quantity of heat kept from reaching the interiors in overheated times will lesson the expenditure for cooling. There are many studies of thermal design in vernacular architecture (Bahadori, 1978;Watson, 1976;) but as Markus (1980) & Vinod Kumar in 1984 has pointed out it is not sufficient to have a qualitative understanding of such buildings. To develop confidence in the passive heating and cooling methods we need data to know the kind temperatures and thermal environment that prevails in vernacular buildings. Combined with the pattern of building usage, such data can be an indicator of the level of thermal comfort that was provided by the buildings in question.

In order to strengthen the above facts thermal performance study of the selected buildings were carried out. This was done through on site monitoring of the climatic parameters like Air temperature, Air velocity, Relative humidity etc.

Approach

The case studies, its critical appraisal are the major part of any Research to identify and simulate the findings for its practical use. The city of Lucknow has been selected for the case studies due to the follows main reasons.

1. India’s major population is in composite climate zone in which the city of Lucknow lies. Thus findings will be benefited to a large population.

2. Keeping with the tradition of learning from traditions, the major accent of research is on historical buildings. The Lucknow is India’s one of the famous historical city with its rich architectural heritage.

Software tools and modelling

To conduct the study on the natural lighting the software package ADELINE [10] has been used. This software package has been developed by a department being part of the Organisation for Economic Cooperation and Development (OECD): the International Energy Agency (IEA). One of the main IEA’s goals, within the programme "Solar Heating & Cooling” (Task 21), consists in the development of the natural lighting technology by favouring an innovative and self-conscious lighting design. ADELINE (acronym of Advanced Day and Electric Lighting Integrated New Environment) is a sophisticated integrated software tool for lighting design being able to work out, by the analysis of a wide range of inputs (geometric, photometric, climatic, optical data etc.), realistic simulations, graphic and numerical information [10].

Inside ADELINE, a CAD program, Scribe Modeller, allows modelling the room being studied and is connected with two very well known lighting calculation programs, Superlite and Radiance, by a conversion program, Plink, allowing to simplify the complex input deriving from Scribe. The tridimensional outline of the studied object could be also realized using other CAD systems, availing theirselves of a further conversion program included in the package, but the restrictions imposed by Superlite [10] generally do not allow to use the model such as it is worked out by the widespread CaD programs; from this it follows that the modeller Scribe, even though it is quite primitive compared to the commonly used design software tools, turns out to be much more easy to use.

The study module on which the lighting analysis has been performed is represented by one of the two side bays of the central body; this module consists of one of the four lecture halls, while, according to the state of the project, it consists of a side bay of the new reading room. The modelling performed with Scribe has met with most serious difficulties in the definition of the vaulted roof as Superlite does not import curved lines and surfaces. For this reason the vault straight arch has been schematized with a broken line, and the vault itself with inclined planes, the realization of which passes through a very complex process. The lantern has been simulated with a parallelepiped having glazed side faces and opaque upper face, while the lower face, leaned on the horizontal plane delimiting the top of the vault, is schematized with a glass having a transmission coefficient of 1.0, like an open space. For the simulation of the surroundings two obstructions have been introduced: the first, on the west side, simulates the presence of the pavilion “C”, situated at a distance of about 14 m, the second, on the east side, simulates the presence of the medieval walls being about 1.50 m far.

The glazed surfaces (i. e. the two portals on the west facade, the lantern windows and the new large glass facade towards the medieval walls) have been schematized with a plain glass having a transmission coefficient of 0.90. The opaque enveloping surfaces are characterized by opportune reflection coefficients according to the material and to their scheduled dye: for the walls a reflection coefficient of 0.60, corresponding to mean-light dyeings has been considered, while a reflection of 0.30, corresponding to dark dyes, and a coefficient of 0.85, corresponding to very light colours, have been considered, respectively, for the floor and for the vault intrados. Finally, the two work planes have been intoduced according to which the values of illuminance and of daylight factor inside the study-module are calculated; they correspond to the new library reading desks: the first, placed at the height of +0,80 m and the second at the height of +4,20 m, coinciding with the reading work plane on the mezzanine floor.

Once the tridimensional model has been realized and imported, by Plink, into Superlite, it is possible to carry on the lighting simulations. This program requires as an input, in addition to the geometrical model, the definition of the site and of the sky models. Three possible ways exist for the site definition: assigning the position of the sun and the site radiance data, assigning the site geographical data as well as the atmospheric ones relating to the air turbidity and, finally, assigning the position of the sun and the data on the air turbidity. The first of the three options has been necessarily chosen, since systematical data on the air turbidity all over the national territory are not available [11-12]. The site identification (Pisa, Tuscany region) has, therefore, occurred by the definition of the sun position (altitude and azimuth angles, variable with the simulation day and hour), of the altitude compared to mean sea level of the site of interest (4 m, in the case investigated), of the ground reflection coefficient around the building (asphalt: reflection coefficient of 0.07) and of the data relating to the site radiance, in particular the values of the direct solar radiation as well as of that diffused by the sky onto a horizontal plane and, finally, the relative luminous efficacy, constant with the variation of the simulation day and hour, and assumed to be equal to 105 for the direct value and 140 for the diffused value [13-14].

The sky models contemplated within the package ADELINE coincide with the models standardized by the Commission International de l’Eclairage (CIE), that is the model: CIE Standard Overcast Sky (defined as a completely overcast sky in which the sun position cannot be seen, and producing, on a horizontal plane without obstructions, a illuminance of 21500 lux) and CIE Clear Sky with Sun (defined as a sky covered with clouds for less of the 30% of its apparent surface). It has to be remembered that such standardizations, occurred around the 50s, refer to two extremal meteorological conditions and recent studies have demonstrated their inadequacy especially in certain climatic regions [15]. In fact new models, representing intermediate conditions compared to those described in the models CIE (it is the case of the sky model “Mediterranean”, representative of the illuminance conditions at our latitudes), have been recently elaborated [16].

Once the required inputs have been introduced, Superlite calculates the illuminance on the work planes existing in the tridimensional model. The results are described numerically in terms of illuminance level or daylight mean factor and visualised with isolux curves.

Design methodology

1.1 Shape Analysis

Figure 1. SIEEB building shape

The SIEEB building shape, shown in figure 1, derives from the analysis of the site and of the specific climatic conditions of the Beijing. Located in a dense urban context, surrounded by some high-rise buildings, the building optimises the need for solar energy in winter and for solar protection in summer. The shape of the building evolves from a series of tests and simulations carried out earlier by present authors (Butera et al., 2003).

1.2 Advanced Technological Solutions and Control Strategies

The envelope characteristics derive from a series of simulations of the thermal behaviour of the building, optimising between energy and architectural factors. Building energy analysis, carried out by means of detailed computer simulations, showed that, in order to minimise CO2 emissions, the key issue was electricity consumption, mainly because of the highly polluting electric production and distribution system in China. The envelope characteristics were defined on the basis of the advanced technologies for energy savings.

From such an evidence the following design strategies were derived:

o Maximise natural lighting, for minimising the need of artificial lighting o Minimise the electricity demand of the HVAC system

o Cover as much as possible the electricity demand of the building by means of cleaner production systems.

Development of the Second Generation Prototype Module

The basic technical objective of the current project is to develop a modular second generation prototype of an advanced thermal storage system with high energy density based on sorption technology. To achieve this main objective, the existing first generation sorption heat storage unit was monitored and evaluated in the present installation. In order to meet the targets of straight forward installation and a reduction of costs, the main improvement is the integration of key components (evaporator/condenser and the reactor) into one single container as illustrated n figure 8. Then a vacuum connection between the different units is no longer needed, which makes the installation of the modules much easier. Due to the target of having a modular design and reducing the size and weight of the modules, the sorption units are designed much smaller than the first generation prototypes.

Evapwal/оп/ condensation area

Heatexchangei-

Firm heating

Inner surface

Figure 8: The second generation prototype module.

The heat exchanger design and production of the adsorbers play a dominant role for the system. In the new system the adsorber/desorber heat exchanger will be completely redesigned. For better a heat exchange, U-shaped finned tubes will be used. The silica gel area is surrounded by the evaporation/condensation area. In doing so, the ratio area to volume is greater than it was in the first generation prototype. Since more water vapour per time is able to come in contact with the silica gel, the physico-chemical reaction is faster. The compartments (silica gel area, evaporation/condensation area) are separated from each other by a water vapour permeable membrane and a metal inner surface. The whole weight of the silica gel is supported by a perforated slab.

One goal of this project is to monitor the system under real operation conditions. For this reason, the second generation thermal sorption storage system will be installed in a single-family house with a solar heating system and low temperature heat distribution. The energetic characteristics of the system and the relevant temperatures will be measured for at least one year. The monitoring will give information about the optimum control strategy of the different energy sources, the energy distribution and the general reliability of the system. After the monitoring, the data and information of the field test will be analysed, compared with the simulation and reported.

Results and Discussions

Fig.2 shows the evaporation temperatures and COP obtained by using only the panels or the panels together with the heat exchanger arranged in parallel. The solar radiation intensity, I, was zero. The inlet water temperature at the condenser, tw1, was 20 °С, the ambient air temperature, ta, was about 8 °С, the wind velocity, V, was about 0.2 m/s

COP = 1 + —

H

(8)

Solving eqs.1,2 and 8 simultaneously, te and COP can be obtained similarly to the case that only the panels are used as the evaporator.

Time

during the measurements. The evaporation temperature at the exit of the expansion valve, te, was -13 °C ~-8 °C and COP was 2.3~3.5 for the case of using only the panels, but te was -8.5 °C ~-7 °C and COP was 3~3.6 when both evaporators were used.

Similar experiments were done in cloudy days as shown in Fig.3. The solar radiation intensity was about 120 W/m2 when the data were taken. The plots Fig.4 Relation between tW:1-te andCOp.

Fig. 5 Comparison between the experimental and analytical results of COP (single use of panels).

Fig. 6 Comparison between the experimental results for the heat pump using panels together with air-refrigerant heat exchanger and analytical results for the heat pump using only panels.

show the average values in 30 minutes. The use of the two evaporators gave higher COP in these cases also.

Fig.4 shows the variation of COP with the evaporation temperature. The best fitted curve was given by the following equation.

COP = 0.0019(tw l — te )2

— 0.231(tw, i — te) + 8.40

From experimental results, the power consumption of the compressor was given by the following equation.

H = 3.44tw1 +107 [W] (10)

Fig.5 shows the comparison between the experimental and analytical results of COP for single use of panels. F’ was assumed to be 0.9 in the analysis. The analytical results for tw, i=20 °C are specially agreed well with the experimental results. The present analysis assumed that there was no heat loss from the system. The heat loss from the condenser and compressor to the air in the room increases with increases of the water temperature. This may case a little smaller COP in the experimental

results.

Fig.7 Comparison between experimental and analytical results for heat pump using panels and air-refrigerant heat exchanger in parallel (2003 / 2 / 3).

Fig.8 Comparison between experimental and analytical results for heat pump using panels and air-refrigerant heat exchanger in parallel ( 2002 /12 / 26).

Fig.6 shows comparison of COP and te between the experimental results for the heat pump using panels together with the heat exchanger and analytical results for the heat pump using only panels. The water temperature was 30 °С. The agreement between the experimental and analytical results was good until about 3 p. m.. The solar radiation intensity, I, was larger than 400 W/m2 until that time. Since the evaporation temperature was about equal to the ambient temperature or higher than that until 15:00, it was expected that only the panels were used for evaporation. After about 15:30, the heat exchanger seemed to be used for evaporation also so that the evaporation temperature and COP become higher than the analytical results for the case of single use of the panels.

The value of K was obtained from the experiments by using only the air-refrigerant heat exchanger as the evaporator. Introducing the average evaporation temperature and COP obtained by experiments into eq.7, K=18.7 (W/K) was obtained. This value was used in the analysis. The same experimental results as shown in Fig.6 are shown in Fig.7. The analytical results in this figure were obtained by assuming that heat was absorbed by both evaporators when the evaporation temperature became less than the ambient air temperature. The agreement between the experimental and analytical results was good.

The results obtained for the water temperature of 40 °С are shown in Fig.8. The evaporation temperatures obtained by the analysis were 3 °C~4 °С higher than the ones obtained experimentally. The COP obtained by analysis was 0.2 higher approximately than the ones obtained in experiment. The heat loss from the condenser and the compressor might cause a little smaller evaporation temperature and COP in the experimental results.

5. Conclusions

The flat-plate collectors used as the evaporator of the heat pump was not fit for absorbing heat from the ambient air. Therefore, the evaporation temperature and COP became low when there was no or small solar radiation. The thermal performance of the heat pump was improved by adopting the air-refrigerant heat exchanger arranged in parallel to the flat-plate collectors. The predicted results of the evaporation temperature and COP for the heat pump with dual heat sources of solar heat and the ambient air agreed with these obtained experimentally.

Input variable selection

One of the key features in neural network modeling is the selection of the input variables. In general, for the non-linear ANN models there is no systematic approach, which can be followed. Thus, many approaches were conducted in order to identify the ANN architecture that gives the best results. Finally, a three-layer architecture was selected. It has 12 input neurons, 18 hidden neurons and 24 output neurons. Table 2 defines the inputs and outputs of the neural network.

Inputs

Description

1-4

Q(d-1,h)

h=1,4

5-7

Q(d-1,h), Q( d-2,h)

h=24

8

AQ(d-1,h)

h=1

9-11

T(d-1,h), Tmax(d-1),Tmin(d-1)

h=1

12

hour of the day

Outputs

Description

1-24

Q(d, h)

h=1,24

Table 2.: Definition of ANN inputs and outputs d=day index; h=hour of the day; Q=cooling load, AQ=cooling load gradient Q =cooling load forecast. T=temperature, Tmn=minimum temperature and Tmax= maximum temperature.

The performances of a solar collector are defined by the equation: „ (0 m — 0 a) „ (0 m “ Є a)2 IT 2 I 2 (6) . Solar Collector Function

where a0 represents the optical efficiency at normal incidence and a1, a2, the thermal losses of the collector.

We will show here the specificities of the glass collector in its function of solar collector, namely the evolution of the efficiency according to the angle of incidence (IAM) and the expression of the thermal losses.

a) Optical efficiency — evolution according to the angle of incidence

The results given here come mainly from the tests carried out by the ITW of Stuttgart [3], in accordance with the EN 12975-2 standard.

The optical efficiency, related to the entering surface, for the current version of the glass collector is estimated at 0.595. This value is logically lower than the optical efficiency of a flat plate solar collector (0.8) while the surface of absorber accounts only for approximately 65% of entering surface.

The incident angular modifier factors (IAM) according to the angle of incidence are represented on the figure 7:

Contrary to the flat plate solar collectors, the corrective coefficient relating to the transversal component of the solar radiation is higher than the unit. This is due to the effect of the inner glass reflectors, position 3.

b) Glass collector efficiency

a„ — a, .

0 1-ext

(9 m — 9 a)
I.

— a,

(7)

(9m — 9i) „ (Єm — 9a)2

I

■ — a

2

I2T

A specificity of the glass collector, in its solar collector function, is to have one of its sides in contact with the inner of the building. The losses in this case, cannot be expressed any more as in the equation (6). It is proposed then to represent the efficiency of the glass collector under its solar collector function, by the following equation:

Here one distinguishes the losses to the interior which are gains for the room presented in the equation 5 and losses to the exterior. Frame losses are here not taking into account. This model was implemented in TRNSYS like an alternative of type 1 [5]. From this implementation we carried out various simulations in order to quantify the energetic benefits of the glass collector.

2) Example.

In this paragraph we present a dynamic simulation of the energy efficiency of the glass collector [5].

First of all we considered a reference case in a low energy house of 120 m2 including a southern zone (zone 1) equipped with 10 m2 windows surface (Ug = 1.1 W/m2K).

From this reference, we simulated the replacement of 12.4 m2 opaque walls (Ug = 0.2 W/m2K) on the southern facade, by 4 modules of glass collector (height: 2.059 m, width: 1.51 m). The results obtained are summarized in the table 1, for a climate of the North­East of France.

January

February

March

April

Mav

June

Julv

August

September

October

November

December

Total

Heating load of zone 1 reference building [kWh]

1016

725

432

292

49

0

0

0

14

291

753

1001

4572

Heating and hot water load for reference building [kWh]

1268

952

684

536

301

244

252

252

258

543

997

1252

7538

Heating demand for zone 1 of glass collector building [kWh]

993

699

408

302

60

0

0

0

13

256

739

985

4453

Load variation for zone 1 [%]

-2

-4

-6

3

22

0

0

0

-12

-12

-2

-2

-3

Fsave_therm compared to the reference building [%]

13

30

48

54

85

100

100

100

96

60

19

10

39

Table 1 : Simulation results

The replacement of the walls by glass collectors gives nearly the same thermal behavior in zone 1. The heating load is slightly weaker during the winter months because of the passive gains. The passive gains are lower in the middle season, due to the shading effect of the glass collector, and tend to increase the heating load.

In regard to the summer comfort, simulations showed that the cumulated curves of the ambient temperatures of the zone 1 are similar in the reference case and the alternative with glass collector. Thus, the replacement of walls by glass collectors does not affect the summer comfort.

The efficiency of the solar collector function is illustrated by the values of the fsave factor, for each month of the year. This relative ratio compares the energy saved by the solar collectors with the heating and domestic hot water load. The installation of 12.4 m2 of glass collectors in facades leads to a fsave annual value of 39%, so completely equivalent to one obtained with a similar area of a facade flat plate solar collectors [6].

Architectural integration

The basic idea of the project is quite clear. However, it is not so clear how to integrate this vegetal layer in the building architecture. There are several problems: supporting elements, accesibility for easy maintenance, irrigation and draining pipes, avoiding direct contact be­tween the plant and the facade, etc. The designs by Biosca & Botey (Fig. 1) are a quite natural solution for these questions. However, it is important to ensure if for the majority of the building users it is acceptable to loose totally or partially the outdoor vision. To some users, the presence of the creeping plants may be uncomfortable or even claustrophobic, if

Figure 2: Definition of the green areas and vegetation densities to allow a good architectural integration (by Juhling GBR).

Figure 3: Definition of the green areas and vegetation densities to allow a good architectural integration (by Jardineria Bordas).

they are too dense. A high density of creeping plants covering all the transparent areas of all the building wont be acceptable except in special situations.

Part of the experiments that are being carried out are aimed to observe the reactions of different users and thus to estimate the maximum vegetation densities that are acceptable. The solutions proposed in Fig. 2 and also in Fig. 3 are based in covering only a part of the facade and/or using vegetation with controlled leaf density. A different approach is used in Fig. 4-left, where a set of vertical shadowing elements orthogonal to the facade are proposed and in Fig. 4-right, where the shadowing elements are hortizontal. The numerical simulations to be carried out after the validation of the numerical model will allow to evaluate the energy to be saved using each of these approaches.

Switchable mirrors

incident

hem. trans.

hem. trans.

angle

(mirror-state)

(transparent-state)

0.656

0.721

0

О

CM

0.519

0.579

0

о

■M-

0.182

0.186

50°

0.108

0.266

0

О

CD

0.077

0.430

Tab. 1: measured values of the hemispherical transmittance of a structure equal to that shown in figure 4 with a face selective attached switchable mirror in its reflecting-state and its transparent-state

One type of switchable mirrors as they are researched at the Fraunhofer ISE consist of a layer of a Mg and Ni mixture5, where both elements are evaporated or sputtered at the same time. A second layer of Palladium (Pl) is needed as a catalyst for the hydrogen — activated switching process. This multiple layer is obviously much more complex than a single layer. Therefore, it has to be proved that it is also possible to attach a switchable mirror face selectively. Already showed above in figure 7 and figure 8, is a SEM image of an applied switchable mirror coating. The edges of the coating are sharp and the geometry is as expected, but in this way it is not possible to distinguish whether the structure of the layer itself is suitable for optical switching. In Table 1, the results of some measurements of the hemispherical transmission of the structure shown in figure 7 for several incidence angles in both states of the switchable mirror are presented. The effect of switching from the reflecting to the clear state reaches a maximum for high incidence angles, while for small angles the effect is small. This is the result one would expect when using this arrangement. Unfortunately, on high incident angles the measurement error was increasing due to the small available sample size and the available measurement setup itself. Therefore, this measurements can only give a qualitative idea of the possible results, but they are still suitable to demonstrate the feasibility of the concept. As mentioned above, the use of switchable mirrors need a new structure. The optical properties of the switchable mirrors, e. g. the minimisation of the absorptance in its clear state, are still subject for further research, and they are changing for different samples. So we had to work with varying parameters for the simulation of the coating. Figure 11 shows a first concept of a controllable light shading structure using switchable mirrors. The parabolic design was chosen because this should be easy to realise on a large scale with the existing technology of interference lithography. The coating is attached to the area marked with bold lines. The function of the structure is shown schematically. Light of low incident angles will pass through the structure in both states of the coating. For large incident angles in the reflective-state the light will be reflected, while for the transparent state most light will pass through. Therefore one can

Fig. 11: Schematic drawing of the structure used for the simulation shown in figure 12. The arrows are representing the lightshading effect in the reflecting-state. For large incident angles the light is reflected, while for low incident angles the light is transmitted

incidence angle /°

Fig. 12: simulated hemispherical transmittance of the structure shown in figure 11. The solid line shows the angle dependend behaviour for the reflecting-state, where the dotted lines show maximum and minimum values for the limited reachable transmittance in the transparent state.

control the intensity of the direct sun, with this system while diffuse light will still be transmitted. Figure 12 shows the result of a raytracing simulation of this design. The calculated hemispherical transmission as a function of the incidence angle is plotted. The solid line represents the structure with the coating in its mirror-state. For this first analysis, a constant reflectance of 0.9 and an absorptance of 0.1 has been assumed. Further work will include the exact optical properties, but these values proved to be a good estimation. By changing the structure parameters like the aspect ratio as well as the ratio of the coated area to the non-coated area, the angle of incidence, where the transmittance reaches its minimum can be adjusted. The dotted lines are the upper and lower limits for the transparent state, depending on the coating parameters that are to be expected. The upper line represents the transmission of the non-coated structure, i. e. zero absorptance of the mirror in the clear state, whereas the lower line was calculated with a coating of 50% transmittance in the clear state. It is estimated that a transmittance of more than 60% is reachable. The shown structure still has big potential for optimising e. g. to increase the transmission in the clear state. Not only the coating itself can reach a higher transmittance, but it should be also possible to increase the transmittance of the non-coated structure e. g. by changing the index of refraction and optimisation of the geometry. For this purpose detailed parameter studies will be carried out in future works. Beside the optimisation of the transmittance also several applications with different cut-off angles will be studied

Test Facility

An outdoor test facility (Fig. 1) has been developed for research on double fagades with integrated photovoltaic modules. The test facility has two test-sections on the south-facing fagade so that two different systems may be tested under the same conditions.

Vision section with motorized blind in i

Outlet damper (similar on room interior)

Two double facade test

sections

A double fagade — airflow window with integrated photovoltaic (PV) panels is the concept tested in the new facility. In this fagade air flows from the outdoors through inlets and across a cavity behind the PV panels, cooling them, and then enters the heated space or HVAC system as preheated fresh air (in summer the air flows out). The airflow window also includes a motorized blind to control daylight transmission. The project involves both experiments in an outdoor test-room as well as formulation of a numerical model and simulations to optimize the system. The project is focused on optimization of the heat and fluid flow processes, as well as of the resulting electricity generation. The simulation model developed as a result of the project will serve as a design tool for optimization of the system and for identification of potential problems such as local overheating.

Spheral solar panels

iwatt pam

Inlet damper

irash. air intake

Figure 1. Photograph of Concordia building-integrated PV test facility.

The fagade concept developed consists of two sections, the PV and vision sections, as shown above. An indoor exhaust fan is operated to draw air through the fresh air intakes into the room. Winter operation for fresh air preheating is studied in this paper with focus on the PV section. The above facility is currently utilized to study the performance of two test sections — one with photowatt panels (PWX 500 — 47.5 W typical output) exposed to the outside and another section with spheral solar panels in the middle of a glazed cavity with air flowing on both sides. This paper reports results mainly for the cavity with the photowatt panels.

Three models are being developed to optimize the system as follows:

1. A one-dimensional model that assumes isothermal surfaces but determines the exponential rise of the air temperature with height [4].

2. A two-dimensional transient model that divides the cavity into control volumes and also models the radiation exchange between all control volume surfaces.

3. A CFD model that includes also radiation and which is intended to study and optimize the airflows.

This paper presents some predictions from a 1D analytical model and compares them with experimental results.