- Email: [email protected]
Parametric studies of a greenhouse for summer conditions
Pergamon
PII: S0360-5442(98)00001-2
Energy Vol. 23, No. 9, pp. 733–740, 1998 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0360-5442/98 $19.00 + 0.00
PARAMETRIC STUDIES OF A GREENHOUSE FOR SUMMER CONDITIONS P. K. SHARMA,† G. N. TIWARI‡§ and V. P. S. SORAYAN† †
Centre of Rural Development & Technology and ‡Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi, India (Received 7 March 1997)
Abstract—We apply an analytical expression to the plants and enclosed air in a greenhouse for various design parameters and a given climatic condition. A numerical method has been used to validate an analytical expression for the plant temperature. Our analysis is based on energy-balance equations for different components of the greenhouse. Numerical computations have been carried out for a typical summer day in Delhi. The effects of parameters such as the rate and duration of ventilation, movable insulation, etc. have been studied. Our model may be used to standardize a greenhouse for any climatic conditions. 1998 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION
Greenhouses are available in various shapes and sizes for different climatic conditions. A greenhouse is an expensive option for rural farmers in India. A well designed greenhouse should maintain an optimum environment for healthy plant growth and maximum yield. Mathematical models have been developed to describe heat and mass transport processes in a greenhouse microclimate [1–4]. Previous models [5] have not considered the effect of evaporative and conductive losses from plant components and the ground. This is an important parameter for predicting the thermal behavior of a greenhouse. Albright et al. [6] have developed a mathematical model for a greenhouse. However, they have also not considered the effects of evaporation and conduction losses. Tiwari et al. [7] have presented a mathematical model with inclusion of these effects. Analytical expressions were derived for the plant temperature (Tp ), room air temperature (Tr ), instantaneous efficiency ( i ), etc. In this communication, the model developed by Tiwari et al. [7] has been used for parametric studies. The effects of ventilation and movable insulation are included in predicting the performance of the greenhouse. We conclude the following: (i) the greenhouse efficiency factor (F⬘), plant temperature (Tp ) and room air temperature (Tr ) are strongly dependent on the relative humidity ( ␥ ), duration and rate of ventilation and movable insulation; and (ii) the instantaneous efficiency of the greenhouse ( i ) is a strong function of the heat capacity of the plant (isothermal mass). 2. DESCRIPTION AND WORKING PRINCIPLE
The greenhouse used in the analysis has an area of 6 m × 4 m. Its maximum height at the center is 3 m. A door (0.94 m × 1.80 m) is provided on the east side. The greenhouse is covered with a single sheet of UV-stabilized polyethylene of 0.7 transmittivity. Radiation is transmitted to the greenhouse through the canopy cover. A part of the transmitted radiation is absorbed by the plant leaf and the rest by the uncovered floor area. All of the absorbed energy raises the plant temperature. To reduce the plant and room temperatures, forced air and movable insulation are used. An experiment was conducted to grow cucumbers in pots in the greenhouse. The plant and room air temperatures for a typical day in May are given in Fig. 2.
§
Author for correspondence. Fax: 91-11-6862037; e-mail: [email protected] 733
734
P. K. Sharma et al 3. THERMAL ANALYSIS
Energy-balance equations for different components of the proposed greenhouse have been written with the following assumptions: (i) the properties of the plant mass are considered to be equivalent to those of water; (ii) the relative humidity in the greenhouse does not vary with height; (iii) the analysis is based on quasi-steady-state conditions in the greenhouse; (iv) no stratification occurs in the temperatures of the plant, greenhouse enclosure, covers, etc.; (v) the air heat capacity in the greenhouse is neglected; and (vi) the heat loss from the floor to the ground occurs at the steady state. Energy-balance equations for different components of the greenhouse are given below. For greenhouse plants, ␣p( S) rate of solar flux absorbed by the plant surface
For the greenhouse floor, ␣G(1 − ␣P )( S) rate of solar flux received by the floor surface
= Mp Cp (dTp /dt) rate of thermal flux used to raise the plant temperature
+ hp Ap(Tp − TR ) + ho[p(TP ) − ␥p(TR )]. (1) rate of thermal energy convected and evaporated from the plant to the enclosed room
= − k(∂T/∂x)兩x = 0 AG + hGAG(T兩x = 0 − TR ). (2) rate of the thermal energy rate of thermal energy transferred to conducted into the ground at x the greenhouse enclosure due to =0 convection and evaporation
For the enclosed air in the greenhouse, (1 − ␣G )(1 − ␣P )( S) = Ma(dTP /dt) +[h(t)(TR−Ta )+hDAD(TR−Ta )]+ rate of solar flux received by rate of thermal energy used to rate of thermal energy convected out the greenhouse raise the temperature of the of the greenhouse through each wall enclosed air surface − AGhG(T兩x = 0 − TR ) − + V1Ac(TR − Ta ) rate of thermal energy carried rate of thermal energy transferred by away due to ventilation convection and evaporation from the floor to the greenhouse + h0AP[p(Tp ) − ␥p(TR )] (3) − hPAP(TP − TR ) rate of thermal energy rate of thermal energy transferred by transferred by convection from evaporation from the plant to the plant to the room enclosed room where h0 = 0.016 hP, S = AESE + ANSN + ASSS + AWSW, V1 = NV/3. The values of SN, SS, SE and SW have been determined by using the Liu and Jordan formula [8] for the beam and diffuse radiation as given in Fig. 1. In Eqs (1) and (3), the partial vapor pressures of the plants and the room air temperatures have been linearized in the form p(TP ) = R1 TP + R2, and p(TR ) = R1 TR + R2; these are equations of straight lines, with R1 the slope and R2 the intercept. Eqs (1)–(3), after neglecting the air heat capacity, may be combined into the following form: (dTP /dt) + a TP = f(t),
(4)
where a = {[(hPAP + h0APR1 )(1 − HPG/U1 )]/MPCP}, and f(t) = {[( ␣ )eff S + HPG (U2 + UbAG )TA /U1 + KK − (HPG V1Ac )/U1 ]/MPCP}. The solution of Eq. (4) may be written with the help of the initial condition TP兩x = 0 = Tp0, as TP = f(t)(1 − e−at )/a + Tp0e−at.
(5)
The room air temperature (Tr ) may now be determined by using the equation TR = [(heff1 + eff2 )S + (U2 + UbAG )Ta + (hpAp + h0ApR1 )Tp − K − V1Ac ]/U1.
(6)
Parametric studies of a greenhouse for summer conditions
735
Fig. 1. Curves of the solar intensity (total, beam and diffuse) and ambient temperature (Ta ) vs time of day (h).
The ambient temperature (Ta ) and other constants are given in Fig. 1 and Table 1, respectively. The instantaneous thermal efficiency ( i ) of a greenhouse is defined as the ratio of the thermal energy used to raise the temperature of the plant from Tpo to Tp to the input energy and may be expressed as:
i = MpCp(1 − e−at )/Uefft[( ␣ )effS − Ueff(Tp0 − Teff )] = F⬘[( ␣ )eff − Ueff(Tp0 − Teff )/S¯ ], Table 1. Constants used for the experimental study. Symbol AG AR AD Ap Mp hG hp t
Value 24.0 26.4 1.70 40.0 80.0 5.7 5.7 3600
Symbol
␣p ␣G ␥ hb hD CP Ca
Table 2. Design parameters for a greenhouse. ( ␣ )eff = ␣p. + (heff1 + eff2 ) HPG /U1 Teff = HH Ta + KK-HPGV1Ac /U1 )/Ueff1 HH = (U2 + UbAg ) HPG/U1 KK = -HPG K/U1-HoApR2(1 − ␥ ) HPG = Ap(hp + ho ␥R1 ) U1 = ⌺ Aihi(t) + hdAd + V1 Ac + hpAp + hoAp ␥ R1 + Ub Ag U2 = ⌺ Ai hi (t) + hd Ad + V1 Ac eff1 = ␣g (1 − ␣p ) eff2 = (1 − ␣g ) (1 − ␣p ) Ueff = (ho Ap R1 + hp Ap ) (1 − HPG/U1 ) K = − R2 (1 − ␥ ) ho Ap
Value 0.7 0.55 0.06 0.4–0.7 1.0 3.99 4190.0 1006.0
(7)
736
P. K. Sharma et al
Fig. 2. Curves of the theoretical and experimental values of Tp and Tr vs time of day (h).
Fig. 3. Curve of the instantaneous efficiency ( i ) vs (Tpo –Teff )/S.
where F⬘ is the greenhouse efficiency factor which is a measure of the greenhouse thermal efficiency and S¯ = (⌺AS)/Ap. Eq. (7) is similar to the characteristic equation of a flat-plate collector [8]. The expressions for ( ␣ )eff, Ueff and Teff etc. are given in Table 2.
Parametric studies of a greenhouse for summer conditions
737
Fig. 4. Curve of F⬘ vs the isothermal mass (Mp ).
Fig. 5. Curves of Tp and Tr and F⬘ vs time of day (h) for different numbers of air changes per hour (N). 4. RESULTS AND DISCUSSION
The theoretical and experimental values of the plant and room air temperature (TP and Tr ) are shown in Fig. 2. It is observed from Fig. 2 that the theoretical values are close to the experimental values of Tp and Tr. The characteristics curve (Fig. 3) shows that the behavior of a greenhouse is similar to that of a flat-plate collector [8]. Figure 4 shows the effect of the heat capacity of the plants or isothermal mass (Mp ) on F⬘. F⬘ increases with the isothermal mass (Mp ) due to a storage effect.
738
P. K. Sharma et al
Fig. 6. Curves of Tp and Tr and F⬘ vs time of day (h) for M.I. and N (the duration extends from 11 a.m. to 5 p.m.).
Fig. 7. Curves of Tp and F⬘ vs time of day (h) for different ␥.
The effect of the number of air changes per hour (N) on the plant, the room air temperature and F⬘ are shown in Fig. 5. The temperatures Tp and Tr and F⬘ decrease with an increase in the rate of ventilation. However, the rates of increase of Tp and Tr decrease for N ⱖ 324. The effects of movable insulation (M.I.) and duration of ventilation on Tp and Tr and F⬘ are shown in Fig. 6. There is a greater
Parametric studies of a greenhouse for summer conditions
739
Fig. 8. Curves of Tp and ( ␣)eff vs time of day for different ␣p.
reduction in Tp than in Tr for movable insulation (Fig. 6). This effect may be due to reduced evaporation from the plants. There is no effect of the movable insulation on F⬘. The hourly variations of Tp and F⬘ for different relative humidities ( ␥ ) are shown in Fig. 7. Tp increases with ␥ due to a reduced rate of evaporation. F⬘ decreases with an increase in ␥. There is optimal level of ␥ to achieve desirable values of Tp and F⬘. Beyond a certain level, ␥ has a detrimental effect on growth of plant. The hourly variation of Tp and ( ␣ )eff for different ␣p are shown in Fig. 8, which indicates an increase in Tp, particularly during sunshine hours, with an increase in ␣p. This result may be due to increased utilization of solar radiation during sunshine hours. The ( ␣ )eff also increase with ␣p. Acknowledgements—The authors are thankful to the Indian Council of Agricultural Research (Govt of India) and the Council of Scientific and Industrial Research (Govt of India) for partial financial support.
REFERENCES
1. 2. 3. 4. 5. 6.
Soribe, F. I. and Curry, R. B., Journal of Agricultural Engineering Research, 1973, 18, 133. Chandra, P., Albright, L. D. and Scott, N. R., Transactions of ASAE, 1981, 24(2), 442. Chandra, P., Singh, J. K., Dogra, A. K. and Majumdar, G., Energy—The International Journal, 1989, 4, 21. Yang, X., Short, T. H., Fox, R. D. and Bauerle, W. L., Transactions of ASAE, 1990, 33(5), 1701. Maher, M. J. and Flaherty, T. O., Journal of Agricultural Engineering Research, 1973, 18, 197. Albright, L. D., Sieginer, I., Marsh, L. S. and Oko, A., Journal of Agricultural Engineering Research, 1985, 31, 265. 7. Tiwari, G. N., Sharma, P. K., Goyal, R. K. and Sutar, R. F., Energy and Buildings, 1998, in press. 8. Duffie, J. A. and Beckman, W. A., Solar Engineering of Thermal Processes, 2nd edn. Wiley, New York, 1991. NOMENCLATURE
A = Area (m2 ) Ac = Area of the cooling pad (m2 ) AD = Area of door (m2 ) AG = Greenhouse floor area (m2 ) Ap = Area of foliage (m2 )
AR = Area of roof (m2 ) F⬘ = Greenhouse efficiency factor ho = Heat transfer coefficient between room air and ambient air through walls (W/m2-°C)
740
P. K. Sharma et al
hp = Heat transfer coefficient between the plant and the enclosure air (W/m2-°C) h(t) = Overall heat transfer coefficient from the inside of the room to the ambient through the walls, floor and canopy cover (W/m2-°C) Mp = Mass of the plant (kg) Cp = Heat capacity of plants (J/kg-°C) Ma = Heat capacity of the enclosed air = mass of air × specific heat (J/°C) N = Number of air changes/h p(T) = Partial vapour pressure at temperature T (N/m2 ) S = Hourly average of the intensity of solar radiation at time t (W/m2 ) T兩x = 0 = Temperature of the floor (ground) at x = 0 (°C) Ta = Ambient temperature (°C) Tp = Plant temperature at time t (°C) Tpo = Plant temperature at time t = 0 (°C) TR = Room air temperature of the greenhouse (°C) t = Time (s) V1 = Rate of exchange due to ventilation and infiltration (W)
V = Volume of the greenhouse (m3 ) x = Depth position coordinate inside the ground (m) Greek letters
␣g = Absorptivity of the greenhouse cover (canopy cover) ␣p = Absorptivity of the plant = Transmissivity of the canopy cover ␥ = Relative humidity i = Instantaneous thermal efficiency ( ␣ )eff = Effective absorptance–transmittance product Suffix D = Door E = East G = Floor N = North P = Plant R = Room S = South W = West
PII: S0360-5442(98)00001-2
Energy Vol. 23, No. 9, pp. 733–740, 1998 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0360-5442/98 $19.00 + 0.00
PARAMETRIC STUDIES OF A GREENHOUSE FOR SUMMER CONDITIONS P. K. SHARMA,† G. N. TIWARI‡§ and V. P. S. SORAYAN† †
Centre of Rural Development & Technology and ‡Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi, India (Received 7 March 1997)
Abstract—We apply an analytical expression to the plants and enclosed air in a greenhouse for various design parameters and a given climatic condition. A numerical method has been used to validate an analytical expression for the plant temperature. Our analysis is based on energy-balance equations for different components of the greenhouse. Numerical computations have been carried out for a typical summer day in Delhi. The effects of parameters such as the rate and duration of ventilation, movable insulation, etc. have been studied. Our model may be used to standardize a greenhouse for any climatic conditions. 1998 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION
Greenhouses are available in various shapes and sizes for different climatic conditions. A greenhouse is an expensive option for rural farmers in India. A well designed greenhouse should maintain an optimum environment for healthy plant growth and maximum yield. Mathematical models have been developed to describe heat and mass transport processes in a greenhouse microclimate [1–4]. Previous models [5] have not considered the effect of evaporative and conductive losses from plant components and the ground. This is an important parameter for predicting the thermal behavior of a greenhouse. Albright et al. [6] have developed a mathematical model for a greenhouse. However, they have also not considered the effects of evaporation and conduction losses. Tiwari et al. [7] have presented a mathematical model with inclusion of these effects. Analytical expressions were derived for the plant temperature (Tp ), room air temperature (Tr ), instantaneous efficiency ( i ), etc. In this communication, the model developed by Tiwari et al. [7] has been used for parametric studies. The effects of ventilation and movable insulation are included in predicting the performance of the greenhouse. We conclude the following: (i) the greenhouse efficiency factor (F⬘), plant temperature (Tp ) and room air temperature (Tr ) are strongly dependent on the relative humidity ( ␥ ), duration and rate of ventilation and movable insulation; and (ii) the instantaneous efficiency of the greenhouse ( i ) is a strong function of the heat capacity of the plant (isothermal mass). 2. DESCRIPTION AND WORKING PRINCIPLE
The greenhouse used in the analysis has an area of 6 m × 4 m. Its maximum height at the center is 3 m. A door (0.94 m × 1.80 m) is provided on the east side. The greenhouse is covered with a single sheet of UV-stabilized polyethylene of 0.7 transmittivity. Radiation is transmitted to the greenhouse through the canopy cover. A part of the transmitted radiation is absorbed by the plant leaf and the rest by the uncovered floor area. All of the absorbed energy raises the plant temperature. To reduce the plant and room temperatures, forced air and movable insulation are used. An experiment was conducted to grow cucumbers in pots in the greenhouse. The plant and room air temperatures for a typical day in May are given in Fig. 2.
§
Author for correspondence. Fax: 91-11-6862037; e-mail: [email protected] 733
734
P. K. Sharma et al 3. THERMAL ANALYSIS
Energy-balance equations for different components of the proposed greenhouse have been written with the following assumptions: (i) the properties of the plant mass are considered to be equivalent to those of water; (ii) the relative humidity in the greenhouse does not vary with height; (iii) the analysis is based on quasi-steady-state conditions in the greenhouse; (iv) no stratification occurs in the temperatures of the plant, greenhouse enclosure, covers, etc.; (v) the air heat capacity in the greenhouse is neglected; and (vi) the heat loss from the floor to the ground occurs at the steady state. Energy-balance equations for different components of the greenhouse are given below. For greenhouse plants, ␣p( S) rate of solar flux absorbed by the plant surface
For the greenhouse floor, ␣G(1 − ␣P )( S) rate of solar flux received by the floor surface
= Mp Cp (dTp /dt) rate of thermal flux used to raise the plant temperature
+ hp Ap(Tp − TR ) + ho[p(TP ) − ␥p(TR )]. (1) rate of thermal energy convected and evaporated from the plant to the enclosed room
= − k(∂T/∂x)兩x = 0 AG + hGAG(T兩x = 0 − TR ). (2) rate of the thermal energy rate of thermal energy transferred to conducted into the ground at x the greenhouse enclosure due to =0 convection and evaporation
For the enclosed air in the greenhouse, (1 − ␣G )(1 − ␣P )( S) = Ma(dTP /dt) +[h(t)(TR−Ta )+hDAD(TR−Ta )]+ rate of solar flux received by rate of thermal energy used to rate of thermal energy convected out the greenhouse raise the temperature of the of the greenhouse through each wall enclosed air surface − AGhG(T兩x = 0 − TR ) − + V1Ac(TR − Ta ) rate of thermal energy carried rate of thermal energy transferred by away due to ventilation convection and evaporation from the floor to the greenhouse + h0AP[p(Tp ) − ␥p(TR )] (3) − hPAP(TP − TR ) rate of thermal energy rate of thermal energy transferred by transferred by convection from evaporation from the plant to the plant to the room enclosed room where h0 = 0.016 hP, S = AESE + ANSN + ASSS + AWSW, V1 = NV/3. The values of SN, SS, SE and SW have been determined by using the Liu and Jordan formula [8] for the beam and diffuse radiation as given in Fig. 1. In Eqs (1) and (3), the partial vapor pressures of the plants and the room air temperatures have been linearized in the form p(TP ) = R1 TP + R2, and p(TR ) = R1 TR + R2; these are equations of straight lines, with R1 the slope and R2 the intercept. Eqs (1)–(3), after neglecting the air heat capacity, may be combined into the following form: (dTP /dt) + a TP = f(t),
(4)
where a = {[(hPAP + h0APR1 )(1 − HPG/U1 )]/MPCP}, and f(t) = {[( ␣ )eff S + HPG (U2 + UbAG )TA /U1 + KK − (HPG V1Ac )/U1 ]/MPCP}. The solution of Eq. (4) may be written with the help of the initial condition TP兩x = 0 = Tp0, as TP = f(t)(1 − e−at )/a + Tp0e−at.
(5)
The room air temperature (Tr ) may now be determined by using the equation TR = [(heff1 + eff2 )S + (U2 + UbAG )Ta + (hpAp + h0ApR1 )Tp − K − V1Ac ]/U1.
(6)
Parametric studies of a greenhouse for summer conditions
735
Fig. 1. Curves of the solar intensity (total, beam and diffuse) and ambient temperature (Ta ) vs time of day (h).
The ambient temperature (Ta ) and other constants are given in Fig. 1 and Table 1, respectively. The instantaneous thermal efficiency ( i ) of a greenhouse is defined as the ratio of the thermal energy used to raise the temperature of the plant from Tpo to Tp to the input energy and may be expressed as:
i = MpCp(1 − e−at )/Uefft[( ␣ )effS − Ueff(Tp0 − Teff )] = F⬘[( ␣ )eff − Ueff(Tp0 − Teff )/S¯ ], Table 1. Constants used for the experimental study. Symbol AG AR AD Ap Mp hG hp t
Value 24.0 26.4 1.70 40.0 80.0 5.7 5.7 3600
Symbol
␣p ␣G ␥ hb hD CP Ca
Table 2. Design parameters for a greenhouse. ( ␣ )eff = ␣p. + (heff1 + eff2 ) HPG /U1 Teff = HH Ta + KK-HPGV1Ac /U1 )/Ueff1 HH = (U2 + UbAg ) HPG/U1 KK = -HPG K/U1-HoApR2(1 − ␥ ) HPG = Ap(hp + ho ␥R1 ) U1 = ⌺ Aihi(t) + hdAd + V1 Ac + hpAp + hoAp ␥ R1 + Ub Ag U2 = ⌺ Ai hi (t) + hd Ad + V1 Ac eff1 = ␣g (1 − ␣p ) eff2 = (1 − ␣g ) (1 − ␣p ) Ueff = (ho Ap R1 + hp Ap ) (1 − HPG/U1 ) K = − R2 (1 − ␥ ) ho Ap
Value 0.7 0.55 0.06 0.4–0.7 1.0 3.99 4190.0 1006.0
(7)
736
P. K. Sharma et al
Fig. 2. Curves of the theoretical and experimental values of Tp and Tr vs time of day (h).
Fig. 3. Curve of the instantaneous efficiency ( i ) vs (Tpo –Teff )/S.
where F⬘ is the greenhouse efficiency factor which is a measure of the greenhouse thermal efficiency and S¯ = (⌺AS)/Ap. Eq. (7) is similar to the characteristic equation of a flat-plate collector [8]. The expressions for ( ␣ )eff, Ueff and Teff etc. are given in Table 2.
Parametric studies of a greenhouse for summer conditions
737
Fig. 4. Curve of F⬘ vs the isothermal mass (Mp ).
Fig. 5. Curves of Tp and Tr and F⬘ vs time of day (h) for different numbers of air changes per hour (N). 4. RESULTS AND DISCUSSION
The theoretical and experimental values of the plant and room air temperature (TP and Tr ) are shown in Fig. 2. It is observed from Fig. 2 that the theoretical values are close to the experimental values of Tp and Tr. The characteristics curve (Fig. 3) shows that the behavior of a greenhouse is similar to that of a flat-plate collector [8]. Figure 4 shows the effect of the heat capacity of the plants or isothermal mass (Mp ) on F⬘. F⬘ increases with the isothermal mass (Mp ) due to a storage effect.
738
P. K. Sharma et al
Fig. 6. Curves of Tp and Tr and F⬘ vs time of day (h) for M.I. and N (the duration extends from 11 a.m. to 5 p.m.).
Fig. 7. Curves of Tp and F⬘ vs time of day (h) for different ␥.
The effect of the number of air changes per hour (N) on the plant, the room air temperature and F⬘ are shown in Fig. 5. The temperatures Tp and Tr and F⬘ decrease with an increase in the rate of ventilation. However, the rates of increase of Tp and Tr decrease for N ⱖ 324. The effects of movable insulation (M.I.) and duration of ventilation on Tp and Tr and F⬘ are shown in Fig. 6. There is a greater
Parametric studies of a greenhouse for summer conditions
739
Fig. 8. Curves of Tp and ( ␣)eff vs time of day for different ␣p.
reduction in Tp than in Tr for movable insulation (Fig. 6). This effect may be due to reduced evaporation from the plants. There is no effect of the movable insulation on F⬘. The hourly variations of Tp and F⬘ for different relative humidities ( ␥ ) are shown in Fig. 7. Tp increases with ␥ due to a reduced rate of evaporation. F⬘ decreases with an increase in ␥. There is optimal level of ␥ to achieve desirable values of Tp and F⬘. Beyond a certain level, ␥ has a detrimental effect on growth of plant. The hourly variation of Tp and ( ␣ )eff for different ␣p are shown in Fig. 8, which indicates an increase in Tp, particularly during sunshine hours, with an increase in ␣p. This result may be due to increased utilization of solar radiation during sunshine hours. The ( ␣ )eff also increase with ␣p. Acknowledgements—The authors are thankful to the Indian Council of Agricultural Research (Govt of India) and the Council of Scientific and Industrial Research (Govt of India) for partial financial support.
REFERENCES
1. 2. 3. 4. 5. 6.
Soribe, F. I. and Curry, R. B., Journal of Agricultural Engineering Research, 1973, 18, 133. Chandra, P., Albright, L. D. and Scott, N. R., Transactions of ASAE, 1981, 24(2), 442. Chandra, P., Singh, J. K., Dogra, A. K. and Majumdar, G., Energy—The International Journal, 1989, 4, 21. Yang, X., Short, T. H., Fox, R. D. and Bauerle, W. L., Transactions of ASAE, 1990, 33(5), 1701. Maher, M. J. and Flaherty, T. O., Journal of Agricultural Engineering Research, 1973, 18, 197. Albright, L. D., Sieginer, I., Marsh, L. S. and Oko, A., Journal of Agricultural Engineering Research, 1985, 31, 265. 7. Tiwari, G. N., Sharma, P. K., Goyal, R. K. and Sutar, R. F., Energy and Buildings, 1998, in press. 8. Duffie, J. A. and Beckman, W. A., Solar Engineering of Thermal Processes, 2nd edn. Wiley, New York, 1991. NOMENCLATURE
A = Area (m2 ) Ac = Area of the cooling pad (m2 ) AD = Area of door (m2 ) AG = Greenhouse floor area (m2 ) Ap = Area of foliage (m2 )
AR = Area of roof (m2 ) F⬘ = Greenhouse efficiency factor ho = Heat transfer coefficient between room air and ambient air through walls (W/m2-°C)
740
P. K. Sharma et al
hp = Heat transfer coefficient between the plant and the enclosure air (W/m2-°C) h(t) = Overall heat transfer coefficient from the inside of the room to the ambient through the walls, floor and canopy cover (W/m2-°C) Mp = Mass of the plant (kg) Cp = Heat capacity of plants (J/kg-°C) Ma = Heat capacity of the enclosed air = mass of air × specific heat (J/°C) N = Number of air changes/h p(T) = Partial vapour pressure at temperature T (N/m2 ) S = Hourly average of the intensity of solar radiation at time t (W/m2 ) T兩x = 0 = Temperature of the floor (ground) at x = 0 (°C) Ta = Ambient temperature (°C) Tp = Plant temperature at time t (°C) Tpo = Plant temperature at time t = 0 (°C) TR = Room air temperature of the greenhouse (°C) t = Time (s) V1 = Rate of exchange due to ventilation and infiltration (W)
V = Volume of the greenhouse (m3 ) x = Depth position coordinate inside the ground (m) Greek letters
␣g = Absorptivity of the greenhouse cover (canopy cover) ␣p = Absorptivity of the plant = Transmissivity of the canopy cover ␥ = Relative humidity i = Instantaneous thermal efficiency ( ␣ )eff = Effective absorptance–transmittance product Suffix D = Door E = East G = Floor N = North P = Plant R = Room S = South W = West