Category Archives: BACKGROUND

Example: Double Facade Simulation with TRNFLOW

The development of TRNFLOW was finished in March 2003. Since that date it has already proved it’s strength in various projects like in the simulation of cross ventilation of offices, natural ventilation of double facades and atria’s, the pressure difference at doors of high-rise buildings or pollutant concentration in a building. The Figures 7 and 8 show a multi story building with double facade as an example.

TRNFLOW has demonstrated its suitability for large building models by an example with more than 60 thermal zones and lots of auxiliary nodes. No numerical or other difficulties have been obtained in those runs.

Fig. 5: Air flow network model of a multi story building with double facade

Screening testing/analysis for service life prediction

Screening testing is thereafter conducted with the purpose of qualitatively assessing the importance of the different degradation mechanisms and degradation factors identified in the initial risk analysis of potential life-limiting processes.

When selecting the most suitable test methods for screening testing, it is important to se­lect those with test conditions representing the most critical combination of degradation factors.

Using artificially aged samples from the screening testing, changes in the key functional properties or the selected degradation indicators are analysed with respect to associated material changes. This is made in order to identify the predominant degradation mecha­nisms of the materials in the component. When the predominant degradation mechanisms have been identified also the predominant degradation factors and the critical service con­ditions determining the service life will be known.

Screening testing and analysis of material change associated with deterioration in per­formance during ageing should therefore be performed in parallel. Suitable techniques for analysis of material changes due to ageing may vary considerably.

On the static solar materials of Task 27, a number of accelerated screening have been performed including simulation of possible degradation in performance under the influence of high temperature, high humidity/condensation, UV, and corrosion loads; either single or combined loads; see Table 5.

In Figure 3 the results from a series of screening tests on pure aluminium, used as refer­ence reflector material, are shown as an example of result from the Task 27 study. Degra­dation in optical performance is observed mainly, as expected, in the corrosion tests. In Figure 4 the result from the testing of a number of antireflective glazing materials at 80 °C and 95 %RH is given. The cause of degradation in optical performance is in this case not understood and the degradation therefore needs to further analysed. To identify degrada­tion mechanisms for the tested materials various analytical techniques are presently em­ployed.

Comparison between numerical and experimental values

To verify the mathematical model, the experimental results reported by [Flores and Alvarez, 2002] were used. The verification consisted in comparing interior air temperatures measured with the same ones calculated by the theoretical model. Table 2 presents twelve experimental temperatures, the numbers in the parenthesis are the coordinates of each measured point. Table 3 shows their corresponding theoretical air temperatures and Table 4 presents their corresponding percentage differences. From this table, we can see that the maximum percentage difference was 6.04% (30.34°C experimental, 28.51 °C calculated, maximum difference 1.83°C,) and the minimum percentage was 0.11%. The average percentage difference was 1.87%, which corresponds to an average difference of

0. 66°C. The uncertainty of the experiment was ±0.5°C, thus the theoretical model can represent very closely the experimental air measurements in the interior of the cavity.

Table 2. Experimental air temperatures and its x, y, z-coordinate

31.75 (0.2,9,5)

40.63 (2.5,9,5)

42.35 (7.5,9,5)

49.29 (9.8,9,5)

30.34 (0.2,5,5)

35.55 (2.5,5,5)

35.72 (7.5,5,5)

43.69 (9.8,5,5)

26.50 (0.2,1,5)

30.49 (2.5,1,5)

31.71 (7.5,1,5)

41.76 (9.8,1,5)

Table 3. Theoretical air temperatures calculated and its x, y, z-coordinate

31.14 (0.2,9,5)

40.59 (2.5,9,5)

41.81 (7.5,9,5)

49.01 (9.8,9,5)

28.51 (0.2,5,5)

34.71 (2.5,5,5)

34.77 (7.5,5,5)

44.71 (9.8,5,5)

26.42 (0.2,1,5)

30.04 (2.5,1,5)

32.01 (7.5,1,5)

41.08 (9.8,1,5)

Table 4. Percentage differences between the experimental and theoretical interior air ________________________________ temperatures in the cavity._______________________________













Knowing the air temperatures distribution from the numerical solution of the governing equations, the interior convective, radiative and total Nusselt numbers were calculated for an irradiation of 1000 W/m2. From the results, assuming that the absorption of energy of the glass is zero, the absorbed thermal energy by the solar control coating was 500 W/m2, in which, 81.1 W/m2 is transferred to the interior by thermal radiation; 72.4 W/m2 is by convection to the interior. Thus the energy that is transferred to the interior is 653.5 W/m2 and 346.5 W/m2 is going to the exterior. Therefore, we can see that percentage of radiative energy that goes to the interior is 12.41% and the percentage convective energy is 11.01%.

Using equations (17) and (18) the convective and radiative numbers were calculated. The convective Nusselt number was 11.48 and the radiative one was 12.8. Thus, the order of magnitude of the contribution of the radiative energy is almost the same as the convective one, meaning that the radiative exchange between surfaces plays and important role in the heat transfer process for this cavity. The solar heat gain coefficient calculated by using equation (19) was 0.65 and imply that 65% of the energy goes into the interior.

Electrochromic Devices: Improving the Performance and Color Properties

E. Avendano, A. Azens, J. Backholm, G. Gustavsson*, R. Karmhag*, G. A. Niklasson and C. G. Granqvist

Department of Engineering Sciences, The Angstrom Laboratory, Uppsala University,

P. O. Box 534, SE-75121 Uppsala, Sweden

*Also at Chromogenics Sweden AB, Uppsala University Holding, SE-75183 Uppsala, Sweden

This paper presents a detailed study of the optical properties of a number of electrochromic nickel-oxide-based and iridium-oxide-based films. Chromaticity is analyzed with regard to a set of illuminants pertinent to different natural and artificial lighting conditions. In particular, it is shown that additions of Mg, Al, Si, Zr, Nb, and Ta can improve the transmittance of nickel-oxide-based films, and that Mg, Al, and Ta can have the same effect for iridium-oxide-based films.


Electrochromic materials are able to reversibly change their optical properties upon charge insertion-extraction induced by an external voltage [1-3]. The materials can be integrated in electrochromic devices of several different types and can be all-solid — state constructions as well as polymer laminated ones, with or without self-powering by solar cells [4]. These devices open a number of technologically interesting possibilities to modulate optical transmittance, reflectance, absorptance, and emittance. Recently, special attention has been devoted to designs incorporating electrochromic hydrated nickel oxide films operating in conjunction with electrochromic tungsten oxide; this combination of materials makes it possible to attain a neutral gray color in the dark state. Optical scattering can be essentially nil

[5] . Rigid (usually glass-based) devices [2,3] as well as flexible, polyester-based foil devices [6,7] have been investigated during the last decade.

Among the numerous applications of electrochromism, we note architectural “smart windows”, which are able to combine improved indoor comfort (less glare and thermal stress) with good energy efficiency (especially lowered air conditioning loads in cooled buildings) as apparent from order-of magnitude estimations [6] as well as buildings simulations [8]. The use of “smart windows” has been discussed in detail in literature on innovative architecture [9,10]. Other applications concern non-emissive displays, variable-reflectance mirrors, variable-transmittance eyewear of different kinds, and variable-emittance surfaces for temperature stabilization of space vehicles. For these and other uses, however, there is a long-standing problem with hydrated nickel oxide, which tends to show residual optical absorption in the 400 < A < 500 nm wavelength interval, thereby precluding a fully transparent state.

This paper contains an investigation of the optical properties of hydrated nickel oxide with several different additives introduced with the objective of reducing the

absorption in the visible range without compromising the electrochromic properties. This investigation is complemented by a study of iridium-oxide-based electrochromic materials. The films were made by reactive magnetron sputtering, which is an industrially viable technology with proven upscaling capability.

Passive Cooling

The ambitious limit for the primary energy demand does not allow active cooling for most of the floor space. Therefore various passive cooling strategies have been ap­plied in the demonstration buildings. Common features are moderate glazing propor­tions in the facades, exterior shading systems (total energy transmission < 15%) and low internal loads of less than 190 Wh m-2d-1. Uncovered concrete ceilings serve as mass storage for heat loads during the days, with different elements attached to the ceilings or the walls to compensate unsuitable reverberation properties of the rooms. The heat removal from the ceilings is realised either by night ventilation or by an inte­grated piping system run with ground water (five projects).

Night ventilation can be achieved with a mechanical ventilation system. This guaran­tees a good control of the air mass flow but requires additional electric energy. A low pressure drop along the air path and high temperature differences are advantageous for high cooling efficiencies which lay between 8 (warm nights) and 24 (cold nights) in the Pollmeier building. In the FhG-ISE building the mean temperature level could be lowered by approx. 1.2 K with mechanical night ventilation only during the second half of the night until the early morning.

The mass flow in natural ventilation concepts is determined by the temperature dif­ferences between indoor and outdoor, the difference in elevation of the air inlet and outlet and wind induced pressure differences on the building surface. In the Wagner building an air change rate up to 1.2 h-1 was monitored during the night. Cross venti­lation increases the air change rate; up to 8 h-1 have been measured in hot periods in the FH Bonn-Rhein-Sieg building.

Another component of passive cooling concepts are earth-to-air heat exchangers which take advantage of the heat storage potential of the ground. While playing only a minor role for preheating air in combination with a heat recovery system, the pre­cooling can be essential for achieving comfortable indoor air temperatures. Different types (concrete or plastic tubes) with different diameters and lengths have been used either with mechanical or natural ventilation.

Figure 4 gives an evaluation of the passive cooling strategies of three projects. From the great number of measurements it can be concluded that discomfort can be avoided if the limit of 25 °C is not exceeded by more than 10% of the attendance time. Rooms with two differently oriented glazed facades have to be treated very carefully.


Based on a total primary energy demand of 100 kWh m-2a-1 the electricity demand for lighting accounts to approx. 30%. The monitored projects covered a range between

3.7 and 18 kWh m-2a-1; the differences mainly result from the daylighting supply in the buildings, the applied glare protection/shading system, the electric power of the artifi­cial lighting, the control strategy and the user behaviour. In buildings with a high day­light autonomy the electric power demand shows a clear dependence on the global radiation: in the Lamparter building the daily mean electric power demand decreases below 1 W/m2 (installed power: 12 W/m2) with a global radiation of more than 100 W/m2. Here, sophisticated control systems show only little energy savings. In some of the buildings a rather high consumption (in correspondence with high cooling loads) was measured in corridors.


The funding programme with its realised demonstration buildings is an important step towards an environmental sound and resource-related evaluation of the (total) energy consumption of buildings. A corresponding EC directive on the total energy efficiency of buildings has to be incorporated in national codes within the next two years. The results of the programme show that a primary energy consumption of less than 100 kWh m-2a-1 can be achieved with investment costs that are comparable to con­ventional projects.

While the low energy and passive building standards seem to be transferable to commercial buildings without major problems, the extension of the scope to the sec­tor of electric energy is a real challenge for the planning of HVAC and lighting sys­tems. Passive cooling strategies showed promising results in terms of energy con­sumption and comfort. However the robustness of the concepts has to be improved because no back-up is available when disturbances occur. A better quality assess­ment of the planning and building process as well as of the operation of the building has to be achieved to keep up a maximum of workspace quality. New simulation tools incorporating models of the user behaviour in terms of ventilation, operation of shading systems etc. could improve the quality of decisions.

On the other hand comfort regulations and codes have probably to be revised in or­der to meet the new dynamic indoor climate situations due to passive cooling. Finally,

a number of prices and acknowledgements show that ambitious energy targets can go hand in hand very well with high quality architecture.


The work is funded within the project SolarBau:Monitor by the German Ministry of Economy and Labour (BMWA) under the reference number of 0335007C since 1995 and will end in December 2005. The authors also appreciate the support from the ministry’s project co-ordinator PTJ in Julich.


1. Voss, K.; Lohnert, G.; Wagner, A.: Energieeinsatz in Burogebauden, Bauphysik, part 1: Heft 2, S. 65 72, 2003; part 2: to be published in Heft 5, 2003

2. http://www. solarbau. de

3. Energy and Buildings — Special Issue on Thermal Comfort, volume 34, nr. 6, 2002

Characterization techniques

The normal reflectance of prepared and aged samples was measured in the wavelength interval 0.3 to 20 pm. A Perkin-Elmer Lambda 900 spectrophotometer equipped with an integrating sphere of diameter 150 mm, circular beam entrance and sample ports of 19 and 25 mm, respectively was used in the wavelength interval 0.3 to 2.5 pm. The infrared wavelength interval, 2.5 to 20 pm, was covered with a Bomen Michelson 110 FTIR spectrophotometer with an integrating sphere of diameter 4 inches (102.4 mm) and a circular beam entrance and sample port of 11/8 inches (28.8 mm). An evaporated gold mirror was used as a reference mirror for the measurements done with the infrared spectrophotometer. The measurements were combined to create one spectrum and the normal asol and stherm values were calculated using the equations below [8]. Normal solar absorptance, asol, is theoretically defined as a weighted fraction between absorbed radiation and incoming solar radiation. The solar spectrum, Isoi, used here is defined according to the ISO standard 9845-1 (1992) with an air mass of 1.5. Normal thermal emittance, stherm, is as well a weighted fraction but between emitted radiation and the Planck black body distribution, Ip, at 100°C.


J Isol (A)( 1 — R(A))dA



J Iso, W dA



J Ip (A)(1 — R(X))dA

_ 2.5_______________________________


JIp (A)dA



Absorbing layer

Samples heat treated with 5, 30 and 60 0Cmin-1 up to 580°C were tested for 150 hours. Two samples of each type were subjected to the condensation test. Tests showed that the higher temperature increase rate a sample had been subjected to the better did it perform in the accelerated ageing test. Samples were tested for 150 hours and the samples made with the lowest temperature increase rate showed strong absorption in the infrared wavelength range after the condensation test and consequently failed the performance criterion. The specific bands have not been analyzed but the locations of them indicate that hydroxide compounds are involved. It is most probable that surface alumina had reacted with water and formed some sort of aluminum hydroxide or oxo-hydroxide. The reflectance curve of samples treated with a higher temperature increase rate was not as largely affected. The surface appearance became slightly rough causing the impinging light to scatter more and hence the absorption in the visible wavelength range increased. The transition from low to high reflectance was also shifted towards shorter wavelengths. Samples made with a higher temperature increase rate than 30 0min-1 all passed the PC limit of 0.05.

The absorbing base layer typically attains a normal solar absorptance of 0.80 and a normal thermal emittance of 0.03.

Figure 1a and b. Comparison of absorber samples without an AR layer, before and after 150 hours of an accelerated ageing test. (a) heated with 5 °min1 up to 580°C (b) heated with 60 min1 up to 580oC.

Anti reflection layer

A base layer made of 65 volume percent nickel, heat treated with 50 °min’1 up to 550°C, has been coated onto all samples before the AR coating was applied. The only exception is the base layer for the alumina coated sample which has a 70 % nickel base layer heat treated with 30 °min’1 up to 580°C. The parameters stherm, asoiand PC for the aged samples can be found in table 1. Two samples of each type of coating were subjected to the condensation test. The five different AR materials were: A = alumina, S = silica, HS = hybrid silica (80 mol% TEOS and 20 mol% MTES), ST73 = silica-titania (70 mol% TEOS and 30 mol% TBOT).

The reflectance curve of the alumina coated absorber, sample 1, tested for 80 hours show strong absorption bands in the infrared, see Figure 2a, and consequently the normal thermal emittance value drastically increased. Since the sample already after 80 hours of testing exceeded the limit of the performance criterion, no further testing was needed.

All other AR materials proved to be very resilient, minor or no changes at all to the optical performance were seen, even after 600 hours of testing, see the figures below and Table 1. No difference in reflectance after 300 and 600 hours of testing for the S and HS samples heated to 350°C was observed. Consequently it was concluded that it was enough to test the remaining samples for 300 hours in order to see any trend if there was one.

Samples coated with silica and heated to 350°C showed a small decrease in normal solar absorptance and a small increase in normal thermal emittance. Silica and hybrid silica coated samples heated to 550°C showed an increase in thermal emittance. In general both S and HS samples proved to be very durable and the difference in performance between samples heated to 350 or 550°C was small. However one evident trend was that hybrid silica samples were more resilient than the corresponding silica samples. Samples treated with ST73

revealed as slight increase in normal thermal emittance while the normal solar absorptance value remained constant.

The best selective properties were obtained for samples coated with alumina or silica-titania 70/30 molar %. The normal solar absorptance and the normal thermal emittance values for ST73 were typically 0.91 and 0.03. Alumina coated samples attain the same values but are not that interesting since this material did not withstand the condensation test.

Figure 2a and b. Comparison of samples before and after an accelerated ageing test. (a) coated with alumina, heated to 580°C and tested for 80 hours (b) coated with silica, heated to 350°C and tested for 600 hours.

Figure 3a and b. Comparison of samples before and after an accelerated ageing test. (a) coated with silica, heated to 550°C and tested for 300 hours (b) coated with hybrid silica, heated to 350°C and tested for 600 hours.

Figure 4a and b. Comparison of samples before and after an accelerated ageing test. (a) coated with hybrid silica, heated to 550°C and tested for 300 hours (b) coated with silica(70%)-titania(30%), heated to 500°C and tested for 300 hours.


The durability of the absorbing base layer revealed to be very dependent upon the temperature increase rate at which the samples were treated with. It seems like the absorbing layer becomes more durable when it was treated with a high temperature increase rate. Antireflection treated samples coated with silica, hybrid silica, or silica-titania proved to be very resilient. The absolute best test results were found for samples coated with hybrid silica. Hybrid silica seems to be more flexible and less prone to crack, in accordance with the expectations, which make it an excellent protecting layer. The only two layer absorbers which did not pass the condensation test were samples coated with alumina working as the AR layer.

The solution-chemical method investigated has proved to produce coatings with good selective optical properties. The study has however shown that it seems virtually impossible to achieve a durable two layer absorber with more than 0.91 in normal solar absorptance. To be able to compete with commercially available selective absorbers which have a as0i value of about 0.95, a third layer is most probably needed.

Other important factors for the creation of a successful solar selective coating are scratch resistance and adhesion. All samples produced in this study had, after the heat-treatment, excellent adhesion properties and were reasonably tolerable towards scratching. The adhesion ability of the coating solution on the aluminum substrate is very important for the quality of the film. The coating solution will not homogenously stick to a greasy aluminum surface, instead small droplets are formed on the surface and the resulting heat-treated film will appear stained. The pretreatments of substrates in this work were fully adequate. In conclusion the process is simple, utilizes readily available chemicals and does not demand sophisticated equipment, which makes it accessible for not only the industrialized world but also developing countries.

Spin-coating processes are very easy to handle but there is one considerable disadvantage. This technique cannot handle large surfaces. Instead two other wet coating methods could be of practical interest for industrial use, spray — or dip-coating. Spray-coating techniques are quick, easily adaptable to different coating solutions, complex shapes can be coated, suitable for the establishment of an in-line process and there is a minimum of material waste. One shortcoming is that one nozzle can coat only one surface at a time. Dip-coating processes are simpler and coat two sides at the same time but they are slow and the material waste is larger. The number of advantages with a spray-coating method suggests that this is the technique to prefer when up scaling the process.


First of all I would like to thank my supervisor Dr. Eva Wackelgard, who came up with the idea that led to this study, for her invaluable support and excellent counseling.

Dr. Gunnar Westin deserves a lot of credit for his guidance and for letting me use his technique even though it has not been patented yet. Further I would like to express my gratitude to Dr. Annika Pohl and Dr. Asa Ekstrand for providing me with help and their never — ending patience. Finally I would like to thank all members of the Solid State Physics group for their backing and encouragement.

The work has been carried out under the auspices of The Energy Systems Program which is financed by the Swedish Energy Agency.

Novel Material for Electrochemical Solar Cell

Akos Nemcsics, College of Engineering Budapest, Tavaszmezo str. 17, H-1084 Budapest, Hungary and Research Institute for Technical Physics and Materials Science, P. O.Box 49, H-1525 Budapest, Hungary, e-mail: nemcsics. akos@kvk. bmf. hu

The problem of electrical energy storage possible can be solved with the help of electrochemical solar cell, which is suitable to generate either electrical energy or hydrogen under special condition. The greatest problem of the electrochemical solar cell technology is the find for novel materials with appropriate properties for electrochemical energy conversion. In this work will be presented Cd4GeSe6 which is a novel material for purpose of electrochemical solar cell.

Some Aspects to Electrochemical Solar Cell

Solar cell technology is a very developed area of the microelectronics where are still some researched problems. One of the greatest problems in the solar cell application is the storage of electrical enegy. This problem can possiby be solved with the help of electrochemical solar cells, which are suitable to generate either electrical energy or hydrogen under special conditions [1]. The technology of electrochemical solar cells have some technical and scientific problems. One such problem is the solution of the photo corrosion, which occurs at the electrolyte — semiconductor interface. The photo corrosion ruins the semiconductor electrode during the working of the solar cell. The possible direction of this research is the search for novel materials of appropriate properties for electrochemical applications. One of the important groups of such semiconductor compounds is the chalcogenides such as Cd4GeSe6.

In this work will be presented Cd4GeSe6 which is a novel material for purpose of electrochemical solar cell. The properties of this material are investigated, which has been a scarcely studied material whose properties are not known in detail. Cd4GeSe6 belongs to the agryrodite family where lattice parameters are determined [2]. The band gap and type of band transition was deterimined by absorption and also from — V characteristics determined by photoelectrochemical method [3]. Furthermore were found that this material shows very good resistivity against photocorrosion [4]. The electrical parameters of the Cd4GeSe6- electrolyte junction are very important to know for solar cell application which are also determined in this work. The properties of the Cd4GeSe6 crystal — electrolyte junction are investigated with impedance analysis. The evaluation of the measured data was carried out with the help of a computer program developed by us in pascal language. We used an equalent circuit with physical meaning which is appropriate for the calculation [5].

New Features for Building simulation in TRNSYS16

The multi-zone building model in TRNSYS is known as Type 56. Building input data is defined using a visual interface, TRNBuild. TRNBuild is the next generation of the well — known Prebid interface.

Integration of a 2-band model for solar radiation

Many modern glazing systems have properties depending on the wave-length of the solar radiation. For example, a sun protection glazing might have a transmittance for the entire solar spectrum of Tsol = 38 % whereas the transmittance in the visible band of the spectrum is Tvis = 66 %. Because of those selective properties, a 1-band model can give incorrect results if two or more selective glazing systems are in series, as shown in the following example:

The amount of energy entering the sunspace is 38 % for both models, but differences occur for the room adjacent to the sunspace. The amount of energy entering the room is 14.4 % for the 1-band model. The correct value of 22.3 % is only derived by the 2-band model with a visible and invisible band. The new 2-band model assumes that the solar energy in the undisturbed spectrum is split equally between the visible and invisible. The required glazing properties can be read from the existing window library.

Microclimate characterization

In order to be able to predict expected service life of the component and its materials from the results of accelerated ageing tests, the degradation factors under service conditions need to be assessed by measurements. If only the dose of a particular environmental stress is important then the distribution or frequency function of a degradation factor is of interest.

For measurement of microclimatic variables relevant in the assessment of durability of the static solar materials studied in Task 27, various kinds of climatic data during outdoor ex­posure at different test sites are monitored such as global solar irradiation, UV-radiation, surface temperatures, air humidity, precipitation, time of wetness, wind conditions, and atmospheric corrosivity. Such data will be used to predict expected deterioration in per­formance over time by making use of degradation models developed from results of accel­erated tests. Some results from the measurement of microclimatic data are shown in Table 6 and Figure 5.

Table 6 Atmospheric corrosivity measured at three test sites for outdoor exposure of

Exposure Site of the metal refer­ence specimens

Orientation South/90° — South/45°

First year metallic mass loss




Carbon steel

ISE, Freiburg, Germany

7.2 — 9.5

2.8 — 4.7

73 — 83

SP, Boras, Sweden




SPF, Rapperswil, Switzerland

4.0 — 5.2

2.6 — 7.9

71 — 81

Figure 5 Microclimatic data measured during outdoor exposure of solar fagade absorbers at ISE in the IEA Task 27 study. Left diagram: Surface temperature frequency histograms for a black painted and a black chrome absorber; Right diagram: UVA and UVB light doses versus exposure time

Comparison between numerical and reported values for 2-D and 3-D

To perform the comparison between the numerical Nusselt numbers and the reported ones, we consider a cavity with differentially heated walls; two opposite vertical walls heated at different temperatures and the others were adiabatic. The Rayleigh number of 2.3×106 was considered, which is the same as in the experiment.

Table 5 presents the comparison between the present work and the theoretical and experimental convective, radiative and total Nussetl numbers of Ramesh et al. in 1999 (experimental) and Balaji and Venkateshan en 1994 (numerical). From these results, we can see that for Rayleigh of 2.3×106 the differences between the convective Nusselt number of Ramesh and the present work was 13.2%, meanwhile for the Balaji was 11.45%. For the radiative Nusselt number, the highest difference was for Balaji, but for the experimental one, the difference decreases until 14.61%. That is due to the fact that Balaji considers 2-D model and we considered 3-D model. Nevertheless, the differences between the total Nusselt number and the present work was 1.6% for Ramesh and 5.58% for Balaji.

Table 5. Comparison between the Nusselt numbers reported and the present work for

Ra=2.3 x 106



Balaji, 1994 2-D theoretical

Present work 3-D theoretical


10.14 (13.2%)

10.30 (11.45%)



14.61 (11.9%)

15.49 (16.9%)



24.75 (1.6%)

25.79 (5.58%)


3. Conclusions

This paper presented the influence of the radiative heat transfer of a three dimensional cavity with a semitransparent wall with solar control coating, considering that the temperature distribution of the test glass is function of the thermal interaction between the interior and the exterior of the cavity. The results indicated that the model can represent very closely the experimental air measurements in the interior of the cavity, thus the model can be considered verified experimentally. From the absorbed thermal energy in the solar control coating, 12.4% was for radiative energy and 11.0% was for convective energy, meaning that the radiative exchange between surfaces plays and important role in the heat transfer process for this cavity.

Additional results were the comparison with reported work. The results indicated that the theoretical model can reproduce the theoretical and experimental total Nusselt number with an approximation less than 6%. However, there is a difference, high 16.9% and

lowest 10.14% when individual convective and radiative Nusselt numbers were