The computational code was validated by reducing it to cases reported in the literature [7], obtaining a very good agreement. The maximum percentage temperature difference of 2 % was obtained considering an irradiance of 400 W/m2, an absorbing plate of 2.0 m high and of 0.145 m channel width.

3.3 Results

Parameters of Tables 1 are input to simulate the performance of the solar chimney. A length Lt=2.0 m, a width Wi =1.0, a depth di = 0.15 m, an irradiance Gi =200 W/m2 , and the ambient temperature Ta i=25 °C (298 K) were used. Curves of Glazing temperatures, metallic plate temperature and thermal efficiency are plotted as a function of the length of the solar chimney for both channels in Figure 3. It is observed that, all the temperatures increase as the length of the vertical plate increases, however, the efficiency decreases as length of the vertical plate increases. Because the optical properties of Table 1, symmetrical results were expected for both channels, (Figure 3, a-b).

60 50 40 30 o’ 20 ^ 10 0

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 Length (m) (a) Channel 1

Fig. 3. Temperature and efficiency vs. length for both channels of the solar chimney. Irradiance of 200
W/m2, ambient temperature of 25°C (298 K), channel depth of 0.15 m, channel width of 1.0 m, area rate of
A0/Ai=1.0, discharge coefficient of Cd=0.52, and wind velocity of 3.0 m/s.

Also, the figure shows that for 1.0 m length, a small step appears in the temperature curve of the metallic vertical plates Tw, as well as in the efficiency n curve. These fact is attributed to the change of Nusselt number correlation, from laminar to turbulent flow (Equations 6, 7), as was reported by Ong, 2003. The maximum temperatures were obtained at L=2.0 m, Tw=54 °C, Tf=40 °C, and Tg=32 °C. The efficiency n was from 35 % at L=0.25 m to 11 % at L=2.0 m.

The average thermal efficiency and mass flow rate leaving the solar chimney as a function of the incident solar radiation is presented in Figure 4. The same previous input parameters of Table 1 and 2 were used except for G=60-500 W/m2. As we can see, the thermal efficiency increases from 11 % to 28 %, and the mass flow rate increases from0.01 kg/s to 0.03 kg/s.

0 100 200 300 400 500 600 700 Irradiance (W/m2) Fig. 4. Efficiency and mass flow rate vs irradiance for one channel of the solar chimney. Irradiance of 60-500 W/m2, ambient temperature of 25°C, channel depth of 0.15 m, channel with of W=1.0 m, area rate of A0/A1=1.0, discharge coefficient of Cd=0.52, and wind velocity of 3.0 m/s.

2. Conclusions

Natural ventilation systems like solar chimneys have become important devices lately. Its theoretical study has been intensified since the last three decades, which has helped to understand its performance. The performance of a two flow solar chimney was theoretical studied, the results showed that, temperature of the metallic plate Tw, the fluid temperature Tf, and the glass temperature Tg, increase, and the efficiency decreases as the plate length increases. The average maximum flow rate through the two flow chimney was 0.06 kg/s, when incident solar radiation was 500 W/m2. A very low efficiency (r <30 %) was obtained when natural convection is used for this device.

Further theoretical and experimental study is in progress to predict more accurately its thermal performance.

Acknowledgments

The authors acknowledge CONACYT, DGEST-SEP, AECI, and DGET-UNAM, for their support to this project.

Nomenclature

A, Inlet area, (m2).

A0i, Outlet area, (m2).

A і Area aspect ratio.

Cd, Discharge coefficient of 0.52. c/; Air specific heat, (kJ/kg. K) d. Channel depth, (0.15 m). g Gravitational constant, (9.81 m/s2).

G Irradiance, (W/m2).

Gr Grashof number.

g ,w, i

hgConvection heat transfer coefficient for glass cover, (W/m2.K).

hw. Convection heat transfer coefficient for the metallic plate at both sides, (W/m2.K).

h Wind heat transfer coefficient, (W/m2.K).

hng., Radiation heat transfer coefficient, from the metallic plate to the glass covers, (W/m2.K). hrsi Radiation heat transfer coefficient from the glass cover to the sky, (W/m2.K).

(і = 1, channel one, and і = 2, channel two. kf, is the thermal conductivity of air, (W/m. K),

Lc is a short length of the chimney, Lc = Lt /10, (m),

L is the total length of the chimney, (m),

M, Theoretical parameter.

ml Mass flow rate through each channel, (kg/s).

Nui Nusselt number.

Ra t Rayleigh number.

sg. Solar irradiance covering the glazing at both sides, (W/m2),

SwJ, Transmitted solar irradiance covering the metallic plate, at both sides, (W/m2). T Ambient temperature, K.

Ta. Air temperature at the inlet, (K).

Tmi Mean temperature, (K).

T = Tai, Room temperature, (K).

Ts Sky temperature, (K).

Ut. Top loss coefficient, (W/m2.K).

V, Wind velocity, (m/s).

W is the width of the channel, (1.0 m),

Greeks ag. Glass absortivity.

awi Metallic plate absortivity.

PfJ Volumetric coefficient of expansion, (1/K).

у Experimental constant (0.75), Hirunlabh, [12].

Gg, i Glass emissivity.

£wi Metallic plate emissivity.

Dynamic viscosity of the fluid, (kg/s. m).

vfi Kinematic viscosity, (m2/s).

pot Air density, (kg/m3).

c Stefan-Boltzmann constant, c = 5.67x10s W/(m2K4)

Tgit Glass transmissivity.

^ Efficiency, (%).

References

[1] Mathur J., Bansal N., Mathur S., Jain M., Anupma “Experimental investigation on solar chimney for room ventilation”, Solar Energy, Vol. 80, pags. 927-935, 2006.

[2] Bouchair A., “Solar chimney for promoting cooling ventilation in southern Algeria”, Building Serv. Eng. Res. Technol. 15 (2): 81-93, 1994.

[3] Gan G. “A parametric study of Trombe walls for passive cooling of buildings” Energy and Buildings, 27: 37-43, 1998.

[4] Gan G. y Riffat S.,“A numerical study of solar chimney for natural ventilation of buildings with heat recovery”, Applied Thermal Engineering, Vol. 18, Pags. 1171-1187, 1998.

[5] Marti H., Jaime “Analisis de la chimenea solar del LECE para su caracterizacion energetica como sistema de ventilation natural en la edification”, Proyecto Energia Solar en la Edification. Departamento de Energias Renovables. Ciemat. Avd. Complutense 22, Madrid 28040. Septiembre de 2003.

[6] Marti H., J. y M. R., Heras C. “Dynamic physical model for a solar chimney”, Energetic Efficiency in Building. Renewable Energy Department. Ciemat. Avd. Complutense 22, Madrid 28040, Solar Energy, 2006.

[7] Ong K., “A mathematical model of a solar chimney”, Renewable Energy, Vol. 28, Pags. 1047­1060,2003.

[8] Duffie J. A., Beckman W. A., “Solar Engineering of Thermal Processes”, 2nd Ed. John Willey & Sons, Inc. 1991.

[9] Modest M. F., “Radiative Heat Transfer”, McGraw-Hill, Inc., 1993.

[10] Incropera F. P., De WITT D. P., “Fundamentals of Heat and Mass Transfer”, 5th Ed., John Willey & Sons, 2002.

[11] .Bansal N., Mathur R., y Bhandari M., “Solar chimney for enhanced stack ventilation”, Building and Environment. Vol. 28, Pags. 373-377,1993.

[12] .Hirunlabh J., Kongduang W., Namprakai P., y Khedari J., “Study of natural ventilation of houses by a metallic solar wall under tropical climate”, Renewable Energy, Vol. 18, Pags. 109­119, 1999.