NUMERICAL STUDY OF MIXED CONVECTION IN THEPHOTOVOLTAIC TROMB WALL WINDOW FOR PASSIVE COOLING IN BIOCLIMATIC BUILDINGS. OF ADVANCED

A numerical study is conducted to investigate mixedconvectionwith the Boussinesq approximation in the Photovoltaic Trombwall window for passive cooling in the building.The small sized solar chimney, specially having a variable absorberplate height heated from thefronttop solar PV cells plate with a constant flux is integrated at the south façade of the building. Then three different values respectively for absorber height, chimney width, and inlet opening size are considered for different combinations of the governing parameters namely, Reynolds number(20 <Re<200) and the Grashof number (10 4 <Gr< 10 6 ).The results are presented in the form of streamline and isotherm plots, mass flow rate, outlet velocity,PV cells’ electrical efficiency, the variation of local Nusselt number on the

A numerical study is conducted to investigate mixedconvectionwith the Boussinesq approximation in the Photovoltaic Trombwall window for passive cooling in the building.The small sized solar chimney, specially having a variable absorberplate height heated from thefronttop solar PV cells plate with a constant flux is integrated at the south façade of the building. Then three different values respectively for absorber height, chimney width, and inlet opening size are considered for different combinations of the governing parameters namely, Reynolds number (20 <Re<200) and the Grashof number (10 4 <Gr< 10 6 ).The results are presented in the form of streamline and isotherm plots, mass flow rate, outlet velocity,PV cells' electrical efficiency, the variation of local Nusselt number on the heated plates Copy Right, IJAR, 2018,. All rights reserved.

…………………………………………………………………………………………………….... Introduction:-
Ventilation is one of the important options in providing thermal comfort in buildings. A solar chimney is one of several available options for achieving natural ventilation in a building through solar induced air movement. A solar chimney can be constructed in one of the components of a building, in which one or more walls of a vertical chimney are made transparent by providing glazed wall(s) for allowing solar radiation to accumulate enough heat to induce the chimney effect. Solar energy heats up the air inside the chimney. As a result of the temperature difference in the air, a density gradient between the inside and outside of the chimney is obtained that in turn induces a naturalupwardairmovement. The solar chimney is similar to the Tromb wall concept. The distinct difference between them is that while the Tromb wall has a massive thermal wall that absorbs solar energy and recirculates warm air for passive heating of the building, the solar chimney does not have a massive wall. Rather, storage of heat in the wall behind the absorber is undesirable. The Tromb wall has been used for decades as an efficient solar heating method. There is a massive thermal wall and a clear glazing cover with an air duct in between. As the surface of the thermal wall is painted black, it is hard to meet the aesthetic requirement of buildings. PV cells integrated on the cover glazing of theTromb wall are more appealing. Hence  in their study have proved that the PV Tromb wall converts solar radiation into electricity and heat simultaneously. In contrast to the application of the Tromb wall, the purpose of a solar chimney is to provide ventilation to the building during the day without recirculation of room air. The energy used for heating, cooling and air conditioning of buildings should be minimized with some design based precautions. Thus (Yilmaz et al., 2008) proposed that special systems like the Tromb wall system might be used to decrease energy consumption in buildings. (Zamora et al., 2009) indicated that theTromb wall system uses solar energy to heat, ventilate and provide thermal comfort in buildings. In fact (Aste et al., 2008) proved in their study that the PV/T collectors aim is to increase electrical efficiency of the PV

INTERNATIONAL JOURNAL OF ADVANCED RESEARCH (IJAR)
912 cells by cooling the PV module surface. Hence the BIPV Tromb wall is a novel version in which glazing in the classic Tromb wall is replaced by a PV module.
In other words, the BIPV Tromb wall is a combination of these two systems used both for producing electricity and heat simultaneously for energy saving. In the BIPV Tromb wall, the cool air in the room enters the inter-space through the lower vent, absorbs the waste heat behind the PV panels, becomes hot and enters the room through the upper vent. (Chow et al., 2005) indicated that the absorption of PV heat results in an increase in PV efficiency as the PV panels function better when they are cool. Furthermore, (Hegazy et al., 2000)have proved that free air convective cooling is a simple and low cost method of keeping electrical efficiency at an acceptable level. It is an energy efficient system that is easy to apply on the south facing facades of both existing and new buildings. Nowadays, Bioclimatic Integrated Photovoltaic-Thermal (BIPV/T) systems have turned out to be an attractive technology. Either semi-transparent or opaque type photovoltaic modules can be used in BIPV/T systems. (Agrawal et al., 2010)showed that the semi-transparent type systems are integrated with the walls, roofs and windows of buildings using day lighting, while the opaque type systems and the semi-transparent type systems without lighting can be integrated with the walls and roofs of buildings. (Cheng et al., 2009) developed a correlation between the optimal angle of the BIPV system and the latitude of the site of the system. The system is supposed to be integrated on thesouth oriented tilted roof at 20 different locations in the Northern Hemisphere. Therefore, it was concluded that to get maximum solar radiation in thenorthern hemisphere, the system should face south and the angle of the panel should be equal to the latitude of the terrain. Then    (Li et al., 2009)showed that visual discomfort; solar heat gain, lighting energy consumption and HVAC equipment size can be reduced by replacingthe south west-facing tinted glass windows with semi-transparent a-Si PV panels and applying lighting controls in a typical office building in Hong Kong. (Lu and Law, 2013) also pointed out that using semi-transparent c-Si BIPV windows may enhance building energy performance. They suggested the following optimal office orientations for annual electricity savings in the following order for Hong Kong: south-east, south, east, south-west and west. (Olivieri et al., 2014)concluded that for intermediate and large openings covering more than 33% of the façade area, BIPV windows account for 18-59% energy savings compared to glass when applied to a typical middle-size office building in Spain. (Miyazaki et al., 2005) showed that primary energy consumption of a buildingcan be reduced by installing this type of BIPV window and adopting lighting controls. They suggested optimal transmittances of the PV module in accordance with different window to wall ratios of the building. A low emissivity coating was further shown by (Han et al., 2010)to reduce radiative heat transfer and the U-value of this BIPV window configuration. Hence (Chae et al., 2014)showed that up to 30% of the annual HVAC energy consumption can be saved by installing double-pane semi-transparent BIPV windows as opposed to double-pane clear glass windows, in the low and medium latitude US cities. Semitransparent PVs with different optical properties were recommended for maximum utility cost savings for these cities. The experiments conducted by  indicated that the indoor heat gain of the ventilated doublepane BIPV window was reduced to less than half of that of the single pane BIPV window. The thermal comfort level of the work space was also improved due to the lower inner surface temperature of the ventilated double-pane BIPV window. (Chow et al., 2007a)showed that a PV transmittance of 0.45-0.55 in the ventilated BIPV window resulted in the greatest electricity saving when taking into account air-conditioning load, artificial light consumption and PV electrical generation. Annually the BIPV window can cut down air conditioning power consumption by 28% for a typical Hong Kong office, compared to the conventional single absorptive glass window; (Chow et al., 2009). The authors also stated that high efficiency thin-film solar cells could facilitate the uptake of PV double-pane windows.

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From a monetary point of view, (Ng and Mithraratne, 2014) showed that with government subsidies certain PV modules with high efficiencies are cheaper to install than conventional double-glazed windows.
However on the basis of litterature review, it appears that no work in surveyed papers was reported on mixed convection in the PV windows integrated on the facade of buildings. None of the surveyed papers however showed the interrelated influence of the thermal efficiency or the electrical efficiency of the solar PV cells in the ventilation process in the room. Thereafter, due to the practical importance of this problem in a wide variety of engineering applications of passive cooling, thermal comfort. Hence the subject needs further effort to improve our knowledge in this field. The aim of this study is to explore the possibility of using the small sized window openings as solar chimneys for passive cooling in buildings.
The object of the present paper is to study numerically a mixed convection problem in a small-sized solar chimney, specially having a variable absorber height(PV window) heated from the front top solar PV cells plate with a constant flux. In this analysis, the air flow enters the PVwindow through an inside opening size in the room andleaves from the outlet opening size. Then it is very important to know the air movement or temperature distribution inside the PV Tromb wall windowand the PV cells' electrical efficiency.

Fig.1:-Physical model
The geometrical configuration deals with a simple room with length Land height hmounted on the left side of the vertical parallel plates of the chimney. The chimney is designed as a solar collector with plate separation dand height h. The PV/T collector is composed of four elements: the front glass cover, the semi-transparent photovoltaic cells (PV), the air flow, the absorber plate. The collector acts as an exhaust fan by sucking room air and venting it out during sunshine hours. In the system, the PV panel absorbed the incident solar radiation and transfers heat to air in the gap by convection and radiation phenomena. The temperature of the absorber plate with variable height (h 1 ), rises and in turn, together with the PV module, heats up the air in the gap. The right side cold wall is maintained at the ambient temperature, the upper horizontal wall and the floor of the room are assumed perfectly insulated and adiabatic. The physical system is sketched in fig1.
The non dimensional set of the governing equations (continuity, momentum and energy equations) for a twodimensional, incompressible laminar flow are the following: Heat Transfer:-From the engineering viewpoint, the most important concern is heat transfer through the PV cells modules, the heated walls. These are best represented by Nusselt number. The local Nusselt number on the front side plate and the inner absorber plate of the chimney are given by: The electrical efficiency of the solar PV cells is given as follows: The mass flow rate in the channel is expressed: Where is the average absolute temperature of the PV plate

Numerical Method:-
The non linear partial differential governing equations, (1-3), were discretized using a finite difference technique. The first and second derivatives of the diffusive terms were approached by central differences while a second order upwind scheme was used for the convective terms to avoid possible instabilities frequently encountered in mixed convection problems. The integration of equations (2-3) was assured by theThomas algorithm. At each time step, the Poisson equation, Eq. (4), was treated by using the Point Successive Under-Relaxation method (PSUR) with an optimum under-relaxation coefficient equal to 0.8 for the uniform grid (101×101) adopted in the present study. Convergence of iteration for stream function solution is obtained at each time step .The following criterion is employed to check for a steady-state solution. Convergence of solutions is assumed when the relative error for each variable between consecutive iterations is recorded below the convergence criterion ε such that    the room is maintained at ambient temperature and cold due to passive cooling. Consequently, fig.5 (a-b) showed that the mean temperature of the PV cells and the absorber heated plates are both decreasing functions of Reynolds number. Fig.4 indicates that the outlet velocity is an increasing function of Reynolds number. Then, the outlet airflow velocity increases and overtakes a maximal value in the middle of the width of the chimney before decreasing to attain the minimal value near the insulated absorber plate as shown in fig.4.    At the low value of the Grashof number, such as Gr=10 3 , the forced convection due to the driven force dominates the flow structure in the integrated solar chimney, fig. 9(a). At this order of Grashof number, the inertia force of the fluid is dominant compared to the buoyancy force. As shown by streamlines in Fig. 9(a-c), air circulation inside the chimney is very weak at lowGrashof number and increases with the Grashof number. A high insolation effect increases the air circulation inside the chimney and .the isotherms become more distorted. As the Grashof number increases to Gr = 10 4 , the Richardson number Ri=1 ,the inertia and buoyancy forces balance each other, which then results in a mixed convection, fig.3 (c). When the Grashof number further increases to Gr = 10 6 , (Ri=100) the buoyancy force becomes the dominant mechanism driving the convection of the air, and the flow is in the regime of natural convection in the room and chimney. The closed cells appear in the chimney and the back flow phenomenon is observed, Fig. 9(c). The isotherms plotted for increasing Grashof number are represented in fig.9 (a-c). One can observe that the isotherms are greatly distorted near the solar PV cells andthe absorber plates. This tendency indicates the effect of the increase intheGrashof number on the heat transfer process. Fig.10 (a-b) shows the variation of the mean dimensionless temperature along the active plates versus the heated flux. The dimensionless temperature increases and reaches the maximum value for the low value of the heated flux before decreasing for the high intensity of incident solar radiation at the fixed Reynolds number. Hence in fig.11 (a-b), the local Nusselt number along the PV cells and the absorber plates is an increasing function of Grashof number. In fig.12 (a), the mass flow rate is decreasing, when the incident solar radiation is increasing. This situation indicates that for increasing grashof number or incident heated flux, the back flow phenomenon appears in the chimney. The same results are obtained by (S.L. Sinha et al.2000) in the numerical simulation of a two-dimensional room air flow with and without buoyancy that the intensity of the recirculation zone in the cavity increases as Grashof number Gr increases to 10 8 .In fig.12 (a) the vertical component of the velocity decreases at the outlet of the chimney, when the Grashof number increases. This variation is illustrated by the back flow phenomenonestablishmentforincreasingGrashof number. Consequently, the mass flow rate is decreasing when the Grashof number related to the incident solarradiation is increasing, fig.12 (b). absorber plate height H 1 is increasing. Fig.14, indicates that the outlet velocity is decreasing in the first middle of the width of the chimney when the absorber plate height is increasing, before increasing in the second middle of the width of the chimney to reach the maximal value and then decreasing along the upper part of the absorber plate to attain the minimal value. This tendency shows that the no sleep boundary condition along the absorber plate is verified. In fig.15 (a), the local Nusselt number along the PV cells plate, increases when the height of the absorber plate increases and then decreases to attain the minimal value, before increasing again to reach the high value at the top. This heat transfer phenomenon illustrates the main interest of the variable absorber height in the PV Tromb wall window. The variation of the absorber plate height induces the variation of the solar chimney entry opening (e W ). The fig.15 (b) shows that theair temperature in the chimney is stratified along the width of the chimney. Fig.16 (a-c) shows the chimney width (d) effect on streamline and the isothermal line distribution. One can observe that for the low value of the chimney width (d), the big closed cells between the absorber plate and the cold wall of the room appears. There is a presence of the parallel open lines in the chimney. The small closed cells located at the entry of the chimney, increases progressively and prevents the open lines from exiting through the chimney. Fig.17(a-b) and the fig.18 (a-b) show respectively that the variation of the local Nusselt number along the PV cells and absorber plates is significantly affected by the chimney width (d) and the inlet opening size (e) effects.

Conclusion:-
The numerical investigation in this study allowed the authors to know that the air flow in the hybrid photovoltaicthermal chimney integrated with the south façade of the building for the lowest value of Reynolds number is natural convection while it is forced convection for the highest value of Reynolds number.The air flow role is to extract the excess heat along the solar PV cells and absorber plates in thechimney. The flow analysis in the solar chimney has given severalpossibilitiesforutilizingPVTrombwallwindow as solar chimney for the low values of inlet velocity or Reynolds number. This device gives possibilities to reduce the energy charge for air conditioning andprovides passive cooling in the room. Within the investigated parameter ranges, the following conclusions can be drawn:  For the low value of the chimney width, the solar PV cells are more heated, hence the electrical efficiency decreases.  For the low value of the absorber plate height, there is no circulation closed cells in the room  The solar chimney is able to provide ventilation to the building during daylightwithout recirculation of room air.  PV Tromb wallwindowgives the possibility to decrease energy consumption in buildings and provides passive cooling.  PV Tromb wall window uses solar energy to ventilate and provide thermal comfort in buildings.