International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

Mathematical and Experimental study of Rooftop Solar Collector for Natural Ventilation in Baghdad City

Ahmed Abdulnabi Imran

was 2.25 m2, and found that the air induced through Abstract— A mathematical and experimental model for rooftop the chimney ranges (140 - 330 m3/h), and solar radiation (200 solar collector under different ambient conditions and different - 1000 W/m2). Mathure et al. [5] investigated the effect of the geometrical parameters. Steady state equations were set to calculate the temperatures at the absorbing wall, the inclination angle of the roof on the passive glass cover and the air between them. The model was converted ventilation. They found that the optimum inclination angle of to a FORTRAN computer program and solved by iteration absorber varies from 40° to 60° with latitude ranges from 20° matrix procedure. The experimental study of solar collector was built and set up on the roof of the to 30°. Jalal and Zinah [6] was studied a solar chimney at Department University of Technology in Baghdad city. The various angles and gap thicknesses. The results depicted that 3 results revealed that for 2 m height, 1 m width and different air the maximum volume of air flow rate is 306 m /h and the gap depths (0.1, 0.15, and 0.2 m). The air volume flow rate was maximum air temperature is 101.7°C for a solar radiation 500 (100 to 280) m3/h was obtained under solar intensity varies from W/m2 and chimney gap thickness of 0.2 m. Ong and Chow [7] 200 to 800 W/m2 and inclination angle 60°. The model developed suggested a mathematical model for a solar chimney under is general and it can be easily customized to describe different of different ambient conditions and geometrical shapes. The solar chimney arrangements. A good agreement showed between experimental model was conducted on a 2m high×0.45m wide, the mathematical and experimental results. and air gaps 0.1, 0.23 and 0.3 m. The result shows that the

velocities of air are between 0.25 m/s and 0.39 m/s for a Index Terms— Collector, solar radiation, , 2 heat transfer. radiation up to 650 W/m . Hussain et al. [8] studied the behavior of rooftop chimney during the day time is essential I. INTRODUCTION for the suitable designing. The analysis of mathematical model was carried out in different collector areas (15, 150, and 600 n Iraq, the gain of heat in the summer overheats the indoor m2) and various chimney heights (5, 10, and 15 m). The I environment of buildings and insufficiencies in electricity results demonstrated the performance of the system affected are the chief trouble. This advertised to use mechanical by the solar strength. Karima and Saif [9] investigated the cooling systems to restore relaxation, and require more thermal behavior of solar chimney numerically and consumption for electrical energy. Therefor to reduce the heat experimentally, with and without paraffin (phase change gain in the buildings, and drop in demand on the electrical material PCM). The results demonstrated that the solar energy by using passive ventilation systems represented by the chimney with PCM extended the period of ventilation after the solar chimney [1]. The solar chimneys are natural ventilation sunset. Xu and Liu [10] studied the operation of solar systems which can contribute to improve the energy efficiency chimneys. A model was prepared in the "Energy Plus in the buildings. Numerous studies in this field were included Program" for the implemented in the simulation of thermal in which numerical simulation, mathematical analysis and chimneys. They showed the maximum rate of ventilation experimentation. Ahmed et al. [2] proposed a numerical and increases with the increase of the ratio between the height of experimental model, for the solar chimney in order to absorber and a gab thickness of air. Nadia et al. [11] proposed recognize their performance for various different shapes under mathematical model and experimental study of the air flow in Iraqi weather conditions. Results have shown that, the the solar chimney. The tests indicate that the field velocities in maximum velocity of the air is 0.8 m/s under solar radiation the chimney are affected by the width of the channel and also 2 750 W/m and the thickness of the air gap was 50 mm. the angle of tilt of the chimney. Alex and Nyuk [12] Ramadan and Nader [3] numerical and analytical study for the investigated of the solar chimney system within the "zero solar chimney with dimensions of 1 m length and 1 m wide energy building in tropical Singapore" to define the effects of and 0.1 m thickness for the natural ventilation room. The ambient conditions and internal heat gain on the demeanor of results showed that, the width of the chimney weighty on the the solar chimney. They demonstrated that high ambient air shape of inside the chimney. Bansal et al. [4] velocity (greater than 2 m/s) improves the air velocity within numerical study for a solar chimney with the area of the the solar chimney. Ahmed and Chaichan [13] were studied solar chimney experimentally in Baghdad-Iraq’s autumn weather 2009, the results obtained that the solar chimneys if Lecturer/ Department of Mechanical Engineering / University of Technology, designed properly can maintain chimney air temperatures Baghdad – Iraq.E-mail address: [email protected] , [email protected] consistently above the external temperature, which would 169

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

produce the desired buoyancy induced air flow through the 퐼 퐴푔 훼푔 + ℎ푟푤−푔 퐴푊 (푇푤 − 푇푔) = hcg−air 퐴푔 (푇푔 − 푇푓) + chimney. Based on reviewed literature, the present study 푈푡 퐴푔 (푇푔 − 푇푎푚푏) (1) attempts to simulate the ventilated rooftop solar collector used Equation (1) can be arranged equally: for breathing room under Iraqi weather condition. (푈 퐴 + ℎ 퐴 + ℎ 퐴 ) 푇 − ℎ 퐴 푇 − 푡 푔 푟푤−푔 푊 푐푔−푎푖푟 푔 푔 푟푤−푔 푃 푤 ( ) ℎ푐푔−푎푖푟 퐴푔 푇푓 = 훼푔 퐴푔I + 푈푡 퐴푔 푇푎푚푏 2 Air outlet II. MATHEMATICAL MODELLING

A mathematical model describes the heat transport phenomena hwind in the scheme. Fig.1 shows the schematic diagram of the collector and Fig.2 shows the physical model for it, the following assumptions are used: hw T 1. Steady state heat transfer through the collector g T conditions. a Ig T 2. All heat transfer in one direction through the w hg ha

absorber wall, glass cover and air gap. Tamb. 3. Absorber wall and glass cover are parallel. Glass

4. The temperature of the air at the inlet is equal to the Iw

ambient temperature. Absorber plate 5. Current of Air in the chimney is turbulent for Ra >

109.

6. The properties of air were evaluated at an average L Insulation temperature. Air inlet Air outlet Room air

Fig.2. Schematic diagram of heat transfers in the collector.

Depth

U 푡 = ℎ 푤푖푛푑 + ℎ푟푔−푠푘푦 (3)

L=2m The heat transfer coefficient due to the , ℎ푤, is calculated as suggested by Duffie and Beckmann [13] as:

W=1m ℎ푤푖푛푑 = 2.8 + 3.0 푉푤 (4) The heat transfer coefficient by radiation from the outer glass

surface to the sky, ℎ is obtained by, Bansal et al. [3]. 푟푔−푠푘푦 σε(푇 +푇 )(푇2−푇2)(푇 −푇 ) ℎ = 푔 푠 푔 푠 푔 푠 (5) 푟푔−푠푘푦 (푇 −푇 ) 푔 푎푚푏 푇 is given by [4] as follow: 푠 푇 = 0.0552 푇1.5 (6) 푠 푎푚푏 hrw−g is calculated as suggested by Bansal et al. [3] as follow: 2 2 σ(푇푤 + 푇푔 )(푇푤 + 푇푔) h = (7) rw−g 1 1 Air inlet ( ) + ( ) − 1 휀푤 휀푔 Fig.1. Schematic diagram of the collector. A thermal model for free convection inside the chimney, can be used the equations proposed by the Incropera [14], within A) Energy Balance the range of (0° − 70°). Heat balance of the physical model was shown in the Figure 3. 퐾푓@푇푔 hcg−air = 푁푢푔−푎 ( ) (8) Written the governing equations by a thermal equilibrium to 푑푤−푔 1708 sin(1.8휃)1.6) 1708 + points as follows: 푁푢 = 1 + 1.44 [1 − ] [1 − ] + 푔−푎 푅푎 cos 훽 푅푎 cos 휃 + 푅푎 cos 휃 1 B) Energy Balance for Cover (glass) [( )3 − 1] (9) [Incident solar radiation] + [Heat gained by radiation from the 5830 Where: absorber wall to the glass] = [transfer of heat by convection (+): exponent means that positive values in the square bracket for the flowing air in the chimney] + [heat loss from glass to were considered only, and zero is used for the negative values. ambient] Mathematically, can be expressed as:

170

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

3 𝑔훽(푇푔 − 푇푓)푑푤−푔 Similar to the energy balance in previous paragraph. The 푅푎 = 퐺푟 푝푟 = (10) 휗 energy balance for the absorber wall is: 1 [Solar radiation] = [convection of air in flow channel] + [long 훽 = 푇 wave re-radiation glass] + [conduction from the absorber plate 푓 to insulation back] C) Energy balance for air 휏푔훼푤 퐼 = [ℎ푐푤−푎푖푟 퐴푤(푇푊 − 푇푓) + ℎ푟푤−푔 퐴푤(푇푤 − 푇푔) + The energy balance of the air flow between the glass cover 푈푏 퐴푤(푇푤 − 푇푎푚푏)] (19 ) and absorber plate is: The convective heat transfer coefficient between the absorber [Convection from absorber]+ [convection from glass] = plate and air hcw-air using equations (8), (9), and (10). But the [useful heat gain by the air] glass temperature 푇푔 is to be replaced by the absorber plate temperature 푇푤. In the event of using good insulation with the I τ I optimum calculated thickness, the back conduction losses can αw q αg u be ignored. The average air temperature in the collector 푇푓

1/U depicted in equations (2), (11), (14), and (19) is compensated b T T 1/hcw-a 1/hcg g 1/hw be 0.5 (푇푓,표 + 푇푓,푖), when 푇푓,푖 = 푇푟. The energy balance

w equations can be redeveloped into a matrix form as presented T amb ∆xins/kin T Tamb under:

s 푎11 푎12 푎13 푇푔 푏1 1/hrg-sky |푎21 푎22 푎23| |푇 | = |푏 | (20) 푓 2 Ts 푎31 푎32 푎33 푏 1/hrw-g 푇푤 3 Fig.3. Thermal network for collector When, the matrix coefficients are defined as follows: For the short length of the absorber wall, the useful heat gain 푎11 = (푈푡 + ℎ푟푤−푔 + ℎ푐푔−푎푖푟)퐴 by the air can be calculated through the following equation. 푎12 = −ℎ푐푔−푎푖푟 퐴 Taking up the temperature on the cover, 푇푔 , and the absorber 푎13 = −ℎ푟푤−푔퐴 plate, 푇푤, to be constant over the entire areas of the cover and 푎21 = ℎ푐푔−푎푖푟 퐴 the absorber plate, respectively. This energy balance is written 푐푝 푎 = − (ℎ 퐴 + ℎ 퐴 + 푚∙ ) equally: 22 푐푤−푎푖푟 푐푔−푎푖푟 훾 푞푢 = ℎ푐푤−푎푖푟 퐴푤(푇푤 − 푇푓) + ℎ푐푔−푎푖푟 퐴푔(푇푔 − 푇푓) (11) 푎23 = ℎ푐푤−푎푖푟 퐴 They gained useful energy carried out is by air: 푎31 = −ℎ푟푤−푔 퐴 ∙ 푞푢 = 푚 푐푝 (푇푓,표 − 푇푓,푖) (12) a32 = −hcw−g A The average air temperature could be approximated using 푎33 = (ℎ푐푤−푎푖푟 + ℎ푟푤−푔 + 푈푏) 퐴 equation proposed by Bansal et al. [3] as: 푏1 = 훼푔퐴 퐼 + 푈푡 퐴 푇푎푚푏 푇푓 = 훾푇푓,표 + (1 − 훾)푇푓,푖 (13) 푇 푏 = −푚∙ 푐푝 푟 The mass flow rate is calculated by using the formula 2 훾 proposed by Bansal et al. [3] 푏3 = 휏푔훼푔 퐼 퐴 + 푈푏 퐴 푇푎푚푏 ∙ 휌푎,표퐴표 2푔퐿푆푖푛휃(푇푓−푇푟) 퐴 = 퐴 = 퐴 푚 = 퐶푑 √ (14) 푔 푤 √1+퐴푟2 푇푟 퐴표 퐴푟 = (15) 퐴푖 III. MATHEMATICAL SOLUTION The velocity of the air flow in the chimney was found using the continuity equation as follow: The above matrix is iteratively solved using a Gauss- 푚. 푣표 = (16) Elimination Methods Fig.4 shows a flow chart representation 휌푎퐴표 of the solution procedure. A FORTRAN computer program is The value of the coefficient of discharge C is taken 0.57 as d built up for solving the set of linear equations (eq. 20); Start suggested by Andersen [15]. with an initial guess for the unknown temperature,푇 , 푇 and The volume flow rate of air can be given by equation 푔 푓 • 푇푤 then, the matrix is solved to obtain the converged 푉 = 퐴 × 푣표 (17) The number of air change per hour is calculated as follow temperatures. The physical properties of air are assumed to [16]: change linearly with air temperature because of the low ACH = (V• × 3600) /volume of the room (18) temperature range encountered. The following empirical In this equation, the volume of an actual size room (e.g. relationships are projected, based on tabulated data from Typical room of 27 m3) stand by ASHRAE [16], the air Incropera and DeWitt [14] for air properties between 300 and change obtained would indicate that the rate of ventilation in a 350 K: real life situation. Dynamic viscosity: −5 휇푎 = [1.846 + 0.00472(푇푓 − 300)] × 10 (21) D) Energy balance for absorber plate : 휌푎 = [1.1614 − 0.00353(푇푓 − 300)] (22)

171

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

Thermal conductivity: - Air openings; Air enters to chimney from the bottom and 푘푎 = [0.0263 + 0.000074(푇푓 − 300)] (23) exits from the top. The dimensions of the openings were Specific heat: 15cm×1m. −3 The temperatures measured by using a (7) thermocouples type 푐푝푎 = [1.007 + 0.00004(푇푓 − 300)] × 10 (24) "K" distributed at selected locations on absorber plate, air in, IV. MODEL VALIDATION air out from the chimney and glass cover were shown in Fig. 6. Good contact between the thermocouple junctions with An experimental model describes the solar collector. This plate and glass was guaranteed to prevent the error readings. solar collector was built and installed on the roof of the The absorber plate temperature was measured at three selected Mechanical Engineering Department University of different positions plate mid lines. The glass cover Technology in Baghdad city as shown in Fig.5. The prototype temperature was measured by two thermocouples located at a is summarizing its main parts as follows:

W

W

W

Fig.5. Photographic picture of the experimental rig

Fig.4. Flow chart of the iterative procedure to solve the system matrix

- Absorber plate; A thin absorber plate was built of galvanized steel with a surface area of (2×1) m2, and thickness of 0.5 mm. It was tinted with mat black for much absorption and to reduce emission. - Glass cover; A commercial glass sheet of 4 mm thickness fitted in iron frame was used to cover the absorber. The glass cover was located at one side of the solar chimney, the area of 2 glass covering the chimney was 2×1 m . The aim of utilizing a All dimensions in meter glass cover was to decrease convection heat losses from the absorber plate end. Fig.6. shows the locations of thermocouples for the plate

- Insulation; Back surface of the absorbed plate was insulated and the glass respectively. with a glass wool layer of (5 cm) thickness to thin out the heat losses at minimum.

172

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509 distance of 50 cm from the inlet and the second one at 150 cm Fig.8 shows the variance of temperature at different solar from the inlet. Two thermocouples were connected to the inlet radiation intensities for an inclination angle of 45o and and outlet of the chimney. All thermocouples were connected chimney air gap thickness of 0.1 m. As the figure indicates, all to a digital thermometer model YK-2001TM manufactured by temperatures generally increase as the solar intensity increases LUTRON Company. Air velocity was measured by using Hot- and reach a nearly asymptotic behavior. It can be also wire anemometer at exit. Solar radiation was assessed by understood that the absorber possesses a high temperature utilizing solar power meter of model TES 13334R from value compared to the glass and air temperatures. This LUTRON. Table 1 represents the mathematical model with increase in absorber temperature is due to getting more experimental results for different combinations of solar radiation as a solution of its black surface nature and storing radiation. high thermal energy. In accession, its reflectivity and trasmissivity are all most zero. Fig.9 illustrates a variation of Table 1: Experimental and mathematical results for collector the absorber wall temperature at different solar radiation. induced air volume. Solar Inlet Length of Inclination Ambient Air volume Errors 3 radiation chimney Collector angle temp. (K) (m /h) % (W/m2) dim. (m) Exp. Num. (m×m) 450 0.2×1 2 45o 302 118 131 9.9 600 0.2×1 2 45o 305 137 153 10.5 790 0.2×1 2 45o 307 164 177 7.4

V. RESULTS AND DISCUSSION

The ability of the system to supply the demand indoor conditions depends on several parameters such as the ambient conditions (temperature and solar radiation) and the dimension of the solar chimney. This study was carried out to find the effects of geometrical dimensions of the solar chimney on the performance of the system with different outdoor conditions. The following dimensions and specification are used in the Fig.8. Variation of temperature with solar computation: The location of chimney in Iraq-Baghdad, radiation intensity at inclination angle 45o, having 33.3°N latitude position, the solar chimney with a and gap air thickness 0.1 m. length of 2m facing south, 1m width, and depth of air gap was variable (0.1, 0.15, 0.2m). The inclination angle of the chimney is 45°, 60° to capture more radiation [4]. The model have gone over 24 runs for chimney thicknesses (0.1m, 0.15m, and 0.2m), inclination angles (45° and 60°), and heat fluxes between (200 to 800W/m²). The chimney dimensions were taken as (2m) and (1m) in length and width respectively. Fig.7 shows the variations of solar radiations with time at different angles of the solar chimney. The figure shows that the values of solar radiation for inclination angle 60o are greater than the values taken from the angle 45o.

Fig.9. Variation of absorber wall temperature with

solar radiation intensity at various gap air

thicknesses, and inclination angle 45o.

intensity for different chimney air gap thicknesses and inclination angles of 45o. The wall temperature decreases at an increase in the air gap thickness; this is due to when increasing the air gap thickness, an increasing in the air volume flow rate thus, more cooling occurred in absorber wall. Larger air gaps resulted in higher airflow through the solar chimney, causing greater cooling effect on heat absorbing walls and glass which Fig.7. Variations of solar radiations with time then tend to be lower. at different angles.

173

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

Fig.10. Variation of exit velocity with solar Fig.12. Variation of mass flow rate with solar radiation intensity at various gap air radiation intensity at various gap air thicknesses, and inclination angle 45o. thicknesses, and inclination angle 45o.

Figs.10 and 11 appraised in the variation of exit speed at Figs. 14 and 15 reveal the variation of the volume of air flow different solar radiation intensities, at various chimney air gap rate with solar radiation intensity at various air gap thicknesses thicknesses with inclination angle 45o and 60o. The velocity of with inclination angle 45o and 60o. It can be seen that the the air increased with an increase in the solar radiation and volume of air flow rate increases with the increase of cavity inclination angle, while it decreased with the increase in the width up to 200 mm. The maximum charge per unit of air flow chimney thickness. is 290 m3/h at solar radiation intensity 800 W/m2, an air gap thickness 200 mm and an inclination angle 60o. The minimum value of air flow rate is 85 m3/h at solar radiation intensity 200 W/m2, with air gap thickness 200 mm and an inclination angle 60o. Fig. 16 shows an air change per hour with solar radiation.

Fig.11. Variation of exit velocity with solar radiation intensity at various gap air o thicknesses, and inclination angle 60 . Fig.13. Variation of mass flow rate with solar

radiation intensity at various gap air

thicknesses, and inclination angle 60o. Figs.12 and 13 exhibit the variation of bulk flow rate with the solar radiation intensity at various chimney air gap thicknesses with inclination angle 45o and 60o, respectively. The outcomes intensity at various air gap thicknesses with different angles of indicate that the stack flow rate increasing gradually by inclination. The rate of induced air change depends mainly on increasing the air gap thickness and inclination angles from the strength of the solar radiation. The corresponding induced 45o to 60o. ACH by chimney was quite high during the day, varying between 3 to 11 ACH, this high air change rate induced by solar chimney is due to the fact that more heat radiation is taken through the see-through glass screen. To satisfy resident comfort for different activities and non-air conditional spaces, 174

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

a higher ACH is required; therefore a chimney with 200 mm air gap thickness at an inclination angle 60o could induce a natural ventilation rate of (180 - 290) m3/h depending on the intensity of solar radiation. With a volume chamber of 27 m3, the corresponding air change varies between 7 to 11 ACH.

VI. CONCLUSION

The induced natural ventilation has been studied mathematically and validated experimentally; the model successfully predicted the flow velocity and mass flow rate in an inclined rooftop solar chimney. The study was carried out to determine the effects of size of the air gap, environmental condition on ACH. The results showed that there is an optimum size of 0.2 m air gap at which maximum ACH is resulted. The outcomes indicate that the most influencing parameter on the rooftop solar chimney performance Fig.14. Variation of air volume flow rate with is the solar radiation. It is also found that the chimney with a solar radiation intensity at various gap air proper plan can offer the natural ventilation in moderate climes. thicknesses, and inclination angle 45o.

NOMENCLATURE 2 Ag, surface area of glass sheet and absorber wall [m ] Aw Ao, cross sectional areas of outlet and inlet to air flow 2 Ai channel [m ] Ar ratio of Ao/Ai Cd coefficient of discharge of air channel [=0.57] cp specific heat of air [J/kg K] dw-g distance between wall and glass [m] g gravitational constant [=9.81 m/s2] I total solar radiation incident on surface [W/m2] Ig solar radiation heat flux absorbed by glass cover [W/m2] 2 Iw solar radiation heat flux absorbed by wall [W/m ] Fig.15. Variation of air volume flow rate with hcg- convective heat transfer coeff. between wall and air 2 solar radiation intensity at various gap air air [W/m K] thicknesses, and inclination angle 60o. hg convective heat transfer coefficient between glass cover and air gap [W/m2 K] hcw- convective heat transfer coefficient between absorber 2 air wall and air gap [W/m K] ha convective heat transfer coefficient between outer wall and outside air [W/m2 K] hrg- radiative heat transfer coefficient between glass cover 2 sky and sky [W/m K] hrw- radiative heat transfer coefficient between absorber 2 g wall and glass cover [W/m K] 2 hwin convective wind heat loss coefficient [W/m K] d kf thermal conductivity of air [W/m K] kins thermal conductivity of wall insulation [=0.067W/m K] L length of collector [m] m° mass flow rate [kg/s] 2 qu heat gain by air [W/m ] Tam ambient temperature [K] b Fig.16. Variation of air change per hour with T mean temperature of air in gap [K] f solar radiation intensity at various gap air Tf,i inlet air temperature [K] thicknesses, and different inclination angles. Tf,o outlet air temperature [K] Tg mean glass cover temperature [K] 175

International Journal of Computation and Applied Sciences IJOCAAS, Volume3, Issue 1, August 2017, ISSN: 2399-4509

Tr [K] [9] Karima E. A., Saif W. M., “Experimental and numerical studies of T sky temperature [K] solar chimney for natural ventilation in Iraq”, Energy and Buildings, s 47, 450-457, 2012. Tw mean absorber wall temperature [K] [10] Xu J., Liu W., “Study on solar chimney used for room natural Ub overall heat transfer coefficient between back side wall ventilation in Nabjing”, Energy and Building, 66, 467-469, 2013. and air [W/m2 K] [11] Nadia S., Noureddine S., Boubekeur D., Belkhir N., Nasreddine C., “ Experimental study and simulation of air flow in solar chimneys”, Ut overall heat transfer coefficient from top of glass cover 2 Energy Procedia, 18, 1289-1298, 2012. [W/m K] [12] Alex Y., Nyuk H., Influences of ambient air speed and internal heat Vw wind velocity [=1m/s] load on the performance of solar chimney in the tropics, Solar vo exit air velocity [m/s] Energy, 102, 116-125, 2014. [13] Sabah T. A. and Miqdam T. C., A study of Free Convection in A solar Chimney Model, Eng. & Tech. Journal, Vol.29,No.14. 2986- Greek symbols 2997,2011. αg absorptivity of glass [=0.06] [14] Duffie, J. A. and Beckmann W. A., Solar Engineering of Thermal αw absorptivity of wall [=0.95] Processes, Wiley Interscience, New York, 1980. β coefficient of expansion of air [1/K] [15] Incropera, F. P. and Dewitt D. P., Fundamentals of Heat and Mass ɛ emissivity of glass [=0.9] Transfer, John Wiley 1996. g [16] Andersen K. T., “Theoretical consideration on natural ventilation by ɛw emissivity of absorber wall [=0.95] thermal buoyancy”, Trans. ASHRAE, 101(2), 1103-1117, 1995. γ constant in mean temperature approximation [=0.74] [17] ASHRAE HANDBOOK FUNDAMENTALS, 2009. μ dynamic viscosity of air [kg/m s2] ν kinematic viscosity of air [m2/s] τg glass transmissivity [= 0.84] ρ [kg/m3] 3 ρa,o density of air exit [kg/m ] σ Stefan-Boltzmann constant [= 5.67×10-8 W/m2 K4] θ inclination angle of collector

Dimensionless terms

Nu Nusselts number [h L/k] Pr Prandtl number [μ cp/k] Gr Grashof number [g β(Tw-Tf) d3/ν3] Ra Rayleigh number [Gr Pr]

REFERENCES [1] Chaichan M. T. & Kazem H. A., "Thermal storage comparison for variable basement kinds of a solar chimney prototype in Baghdad - Iraq weathers," International journal of Applied Science (IJAS), 2(2): 12-20, 2011. [2] Ahmed A. I., Jalal M. J., Sabah T. A.,|” Induced flow for ventilation and cooling by a solar chimney”. Renewable Energy, 78, 236-244, 2015. [3] Ramadan B., Nader S., “An analytical and numerical study of solar chimney use for room natural ventilation”, Energy and Buildings, 40, 865-873, 2008. [4] Bansal, N. K., Mathur, R., Bhandari, M. S., “Solar chimney for enhanced stack ventilation”, Building and Environment, 28(3), 373- 377, 1993. [5] Mathur, J., Mathur, S., Anupma, “Sumer performance inclined roof solar chimney for natural ventilation”, Energy and Building, 38, 1156-1163, 2006. [6] Jalal M. J., Zinah J. K., “Induced buoyancy in inclined solar chimney for natural ventilation”, J. of Eng. Tech., 29(2), 183-194, 2011. [7] Ong K. S., Chow C. C., “Performance of a solar chimney”, Solar Energy, 74: 1-17, 2003. [8] Hussain H. A., Srcejaya K. V., Syed I. U., “Mathematical analysis of the influence of the chimney height and collector area on the performance of a roof top solar chimney”, Energy and Buildings, 68, 305-311, 2014.

176