Performance and cost analysis of a modified built-in-passive condenser and semitransparent photovoltaic module integrated passive solar distillation system

Journal of Energy Storage 24 (2019) 100809

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Performance and cost analysis of a modified built-in-passive condenser and semitransparent photovoltaic module integrated passive solar distillation system

T

Vineet Sainia, Lovedeep Sahotab, , V.K Jainb, G.N. Tiwaric ⁎

a

Amity University, Sector-125, Noida, UP, 201303, India Gargi College, University of Delhi, Sri Fort Road, New Delhi, 110049, India c Research and Development cell Shri Ramswaroop Memorial University, Lucknow-Dewa Road, (UP) India b

ARTICLE INFO

ABSTRACT

Keywords: Solar still Photovoltaic module Condenser Solar cell

In present paper, the performance of single slope solar still integrated with SPV module and passive condenser has been studied for the hot climatic conditions of New Delhi, India. The analysis has been carried out by developing a thermal model of the system. The effect of packing factor (βc = 0, 0.25, 0.45, 0.65 and 0.85) of the solar cell of different PV technologies (c-Si, p-Si, a-Si, CIGS, CdTe etc.) has been investigated. The overall energy efficiency of the system is analytically found to be maximum- 57.5%, 55.2%, 53.4%, 53.1%, and 41.4% for βc = 0.85, 0.65,0.45,0.25 and 0 respectively for c-Si SPV module. Moreover, the productivity of the system is calculated and found to be 1.78 kg, 2.83 kg, 3.66 kg, 4.12 kg and 4.92 kg per day for βc = 0.85, 0.65, 0.45, 0.25 and 0 respectively for c-Si SPV module. It is self-sustained system and economical in rural sector; and the electrical, thermal and overall energy efficiency of the system can be controlled or limited by changing the packing factors of the SPV module according to our requirement. It not only fulfills the electricity requirement (maximum value of thermal and electrical energy gain is 3.98 kW h and 0.38 kW h (βc = 0.85) respectively for cSi SPV module) but also enhance the system productivity as compared to the conventional solar distillation systems. Cost analysis have also been performed to get the cost per liter of potable water produced by the system.

1. Introduction

water vapors in solar still lowers the overall temperature difference between the water (evaporative) and inner surface of the condensing cover. This temperature difference can be improved by separating the condensing surfaces from the solar still chamber. The water vapor get transferred from the solar still cavity to integrated condensing chamber and condensed there on the side wall of the condenser. Consequently, very little condensation occurs on the slopped surface. Since utmost condensation takes place in the condensing chamber, the temperature difference between the evaporative and condensing surface enhances which causes rapid evaporation and produce more distillate output [16–25]. Fath and Elsherbiny [16] theoretically and experimentally studied the effect of coupled passive condenser on the performance of passive solar still. They analytically studied the system for three different solar still - condenser mass transfer modes viz. (i) diffusion, (ii) purging, and (iii) natural circulation. They performed the experiment for the diffusion-purging modes and found good agreement with the theoretical results. They reported

Demand of potable water is rising rapidly and its availability is diminishing insufficiently with time; this situation creates water crisis in many regions worldwide. These water crisis are primarily due to unequal sharing of available water resources, rapid growth in population, and water pollution due to industrial progress in recent past [1,2]. With advances in science and technology, various conventional sources of energy dependent high and medium technologies have been developed for water purification. But, “solar distillation” relies on a renewable (or non-conventional source) of energy dependent simplest, environment friendly and cost effective technique to produce potable water [1]. “Solar stills” -a small device that converts salt water or contaminated water into drinking/potable water through vaporization and condensation process utilizing solar energy. In order to improve the efficiency of the solar stills, researchers have proposed and investigated different designs of the passive solar stills in detail [3–10]. From literature [11–15], it has been concluded that condensation of

⁎

Corresponding author. E-mail address: [email protected] (L. Sahota).

https://doi.org/10.1016/j.est.2019.100809 Received 28 November 2018; Received in revised form 21 May 2019; Accepted 18 June 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

Nomenclature g

b w

c 0

0

c m

Ag Ab Am Acond Cw w cond

hba I (t ) Kg Lg L Mbf

mw Nu t Tcond Ta Tv Tw Tc

TgiE

Fraction of solar energy absorbed by condensing cover Fraction of solar energy absorbed by basin surface Fraction of solar energy absorbed by basin water Packing factor of solar cell Packing factor at standard test condition Efficiency of PV module at standard test condition Efficiency of solar cell Efficiency of PV module Surface area of condensing cover, (m2) Basin area of solar still, (m2) Area of the module, (m2) Area of the passive condenser, (m2) Specific heat of water, (J/kg K) Emissivity of water surface Emissivity of condenser surface Heat transfer coefficient between basin liner and ambient air, (W/m2 ) Total solar intensity on cover, (W/m2) Thermal conductivity of condensing cover, (W/m ) Thickness of condensing cover, (m) Latent heat of vaporization, (J/kg) Mass of water in the basin of solar still Hourly yield (kg) Mass flow rate of water vapor (kg) Nusselt number Time interval (second) Condenser temperature, ( ) Ambient temperature, ( ) Vapor temperature, ( ) Basin water temperature, ( ) Solar cell temperature, ( )

TgiW

(UA)SL Utc, a Ubc, w Utcond, a

Uba Y

Inner condensing cover temperature of east side of solar still, ( ) Inner condensing cover temperature of west side solar still, ( ) Overall heat transfer coefficient from the sides, (W/m2 ) Overall heat transfer coefficient between solar cell (top side) and ambient, (W/m2 ) Overall heat transfer coefficient between solar cell (backside) and water, (W/m2 ) Overall heat transfer coefficient between condenser and ambient air, (W/m2 ) Overall heat transfer coefficient between basin liner and ambient air, (W/m2 ) Annual of productivity/yield (l)

Subscripts a El b Th v Ovr,th

Ambient Electrical Basin surface Thermal Vapor Overall thermal

Abbreviation SPV HTC c-Si a-Si p-Si CIGS CdTe

Semitransparent Photovoltaic Heat Transfer Coefficient Crystalline Silicon Amorphous Silicon Polycrystalline Silicon Copper Indium Gallium Selenide Cadmium Telluride

productivity for midday solar intensity of 700 W/m2. Also, they found that productivity increases from 5.8 kg/m2-d to 7.7 kg/m2-dfor the rise in ambient temperature from 10 0C to 30 0C. Rabhi et al. [29] experimentally investigated the performance of a modified single-basin single-slope solar still with pin fins absorber and condenser. They showed that the use of solar still with external condenser is more effective than the use of absorber fins (on the basin liner). They reported a gain of water productivity around 32.18% by incorporating external condenser as compared to the conventional solar still; and it is around 14.53% for the soar still with simple pin fins absorber. Balhadj et al. [30] performed the numerical analysis of a doubleslope solar still coupled with capillary film condenser in south Algeria. Their proposed prototype perfectly functioned system produces daily yield about 7.15 kg/m2. Also, the condenser plate contribute around 39% of the total distillate yield. Kumar et al. [31] reported the performance enhancement of a single basin single slope solar still using agitation effect and external condenser. They used a shaft coupled with a dc motor and exhaust fan for agitating of water and transferring vapor to external condenser side. The productivity enhanced by 39.49% as compared to the output of conventional solar still. Bhardwaj et al. [32] experimentally investigated the performance of inflatable plastic solar still with passive condenser household use. Their system produced around 0.75 l/h potable water. Furthermore, they observed enhancement more than 0.95 l/hr with use of air flow over the passive condenser to mimic wind or with use of wet tissue on the passive condenser to mimic evaporation cooling. Later, Hassana and Abo-Elfadlb [33] studied the effect of the condenser type and the medium of the saline water on the performance of the solar still in hot climatic conditions. They tested four different types

around 70% enhancement (purging mode) in the productivity using the passive condenser. Later Fath et al. [17] investigated the built-in-passive condenser based naturally circulated humidifying/dehumidifying solar still. They reported 5.1 kg/m2-d per day productivity of the solar still. Madhlopa and Johnstone [18] analytically studied the passive solar still with separate condenser; and reported that purging is a significant approach of vapor transfer from the solar still cavity or evaporator into the condenser chamber. They reported 62% enhancement in the solar still productivity as compared to the conventional solar still. Also, it has been observed that first (single basin in evaporator), second (one additional basin in condenser) and third effects (two additional basins in evaporator) contribute 60%, 22% and 18% of the total distillate output respectively. Monowe et al. [26] investigated a portable thermo-electric single basin solar still with external condenser and reflecting booster. They reported that the solar still efficiency increases up to 77% (5-8 l/ m2-d) using the preheated saline water for domestic purposes. Also, the productivity further enhances up to 85% (6-10 l/m2-d) on using this preheated saline water during night times. In recent times, advances in nano-science and engineering gives hope to find the smart and promising solutions of the various current problems including water purification. Kabeel et al. [27] investigated the performance of modified solar still coupled with external condenser and using Al2O3-water based nanofluid. They reported 53.2% enhancement in solar still productivity with external condenser only; whereas incorporation of nanofluid together with external condenser gives the enhancement in output around 116%. Al-Nimr and Al-Ammari [28] studied the performance of passive solar still with the modification of photovoltaic thermal solar cell immersed at the bottom of the basin and integrating with external fin-condenser. They reported 7.9 kg/m2-d 2

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

of the condenser (glass, aluminum plate, aluminum heat sink with pin fins, and aluminum plate covered with an umbrella); and four mediums of the saline water inside the basin (only saline water, layers of black steel fibres, saturated sand with saline water, and mixture of sand and black steel fibres saturated with saline water). They reported that maximum daily productivity around 31% have been obtained using the case of heat sink condenser with only saline water to 52% in the case of using black steel fibres in the basin. Rahmani and Boutriaa [34] reported the numerical and experimental study of a passive solar still integrated with an external condenser for natural circulation loop (NCL) for hot and cold weather conditions. They found that the maximum daily output is 4.73 kg/m2 and 2.71 kg/m2 for summer and winter conditions respectively. Later, Kabeel et al. [35] presented a detailed review on different solar stills coupled with condenser. They discussed solar stills with built-in-condenser, internal condenser, and passive condenser in detail. They conclude that on providing an additional area for condensation increases the condensation rate and ultimately increases the evaporation rate in the basin; and ultimately, the efficiency of the condensation process depends mainly on the temperature difference between the evaporating and condensing zone. In all above studies (Table 1), researchers have reported the solar still with built-in condenser and some other additional modifications i.e. multi-basin surfaces; integrating reflectors, fins; and addition of metallic nanoparticles etc. An “external condenser” provides a larger surface and with the help of a fan, can impinge the walls more rapidly reducing pressure in the solar still. Therefore, in all condenser based modified solar stills, the “condenser” acts as a heat and mass sink. Its main function is to continuously remove the water vapor from the solar

still cavity, condenses it and maintains the solar still at low pressure. On the other hand, a solar cell or photovoltaic (PV) cell is a device that converts solar energy into electricity by the photovoltaic effect. The electrical output of the PV module depends on the size and number of cells, their electrical interconnection, and, of course, on the environmental conditions to which the module is exposed [36,37]. Consequently, in the proposed system, we replaced the top transparent glass cover by the semitransparent PV module coupled with built-inpassive condenser (discussed above) of single slope solar still. A DC fan (2 V, 1A) is mounted at the top edge of the semitransparent PV module inside the solar still. The running DC fan enhances the vapor transfer rate from the solar still cavity into the condenser chamber. Eventually, it is self-sustained system; and this two-in-one controlled output (electrical power generation and potable water production) option is not studied so far in any passive solar distillation system in literature; the passive systems with external condenser only have been studied so far (Table 1). The overall electrical and thermal energy; and overall energy efficiency of the system can be controlled or limited by changing the packing factors of the SPV module according to the requirement. Moreover, the effect of packing factor of the solar cell of different PV technologies (c-Si, p-Si, a-Si, CIGS, CdTe etc.) has been investigated to study the performance of proposed system. The schematic view of single slope solar still integrated with semitransparent photovoltaic c-Si module (ISC = 8.5Amp; VOC = 620 mV; IMax = 7.8Amp; VMax = 510 Mv; PMax = 4.0 W; FF = 74% at Standard test conditions (solar intensity-1000 W/m2, temperature- 25 °C and air mass-1.5)) and passive condenser (purging mode) is presented in Fig. 1(a). The performance of single slope solar still coupled with semitransparent PV module (top cover) and passive condenser has been

Table 1 Reported modified models of solar still integrated with passive condenser. Reference

Modification

Results

Fath et al. [16]

Passive condenser integrated to single slope solar still. Studied mass transfer modes viz. (a) diffusion, (b) purging and (c) natural circulation. Natural-circulated humidifying/dehumidifying solar still with built-in condenser. Passive solar still with separate condenser. Studied three different effects of additional basin surfaces viz. (a) single basin in evaporator (b) one additional basin in condenser and (c) two additional basins in evaporator. Portable thermo-electric single basin solar still with external condenser and reflecting booster. Solar still integrated with external condenser and using Al2O3 water based nanofluid. Single slope basin solar still with PV/T cell immersed at the bottom of its basin and coupled with outside finned condenser

70% enhancement in productivity.

Fath et al. [17] Madhlopa and Johnstone [18] Monowe et al. [26] Kabeel et al. [27] Al-Nimr and Al-Ammari [28] Rabhi et al. [[29] Belhadj et al. [30] Kumar et al. [31] Bhardwaj et al. [32] Hassana and Abo-Elfadlb [33]

Rahmani and Boutriaa [34] Present work

Solar still with pin fins absorber and condenser Numerical study of a double-slope solar still coupled with capillary film condenser in south Algeria Single basin single slope solar still using agitation effect and external condenser. Experimentally investigated the performance of inflatable plastic solar still with passive condenser household use. Effect of the condenser type and the medium of the saline water on the performance of the solar still in hot climate conditions. Tested four different types of the condenser: glass, aluminum plate, aluminum heat sink with pin fins, and aluminum plate covered with an umbrella; and Four mediums of the saline water inside the basin: only saline water, layers of black steel fibers, saturated sand with saline water, and mixture of sand and black steel fibers saturated with saline water. Numerical and experimental study of a passive solar still integrated with an external condenser for natural circulation loop (NCL) for hot and cold weather conditions. Single slope solar still integrated with semitransparent photovoltaic module (c-Si) (top cover), passive condenser and DC fan. Studied the effect of packing factor of different solar cell PV technology.

3

5.1 kg/m2-d productivity; Economical and less complex than the forced circulation mode. (a) First effect-60% (b) Second effect- 22% (c) Third effect- 18% of the total distillate output. 5-8 l/m2-d productivity on using the preheated saline water for domestic purposes. (a) 53.2% enhancement with external condenser (b) 116% with external condenser and using nanofluid (a) 7.9 kg/m2-d productivity for midday solar intensity of 700 W/m2. (b) 5.8 kg/m2-d to 7.7 kg/m2-d enhancement in productivity for the rise in ambient temperature from 10 0C to 30 0C. 43.7% efficiency 7.15 kg/m2 per daily productivity. 39.49% enhancement in productivity as compared to the conventional solar still. Production of potable water around 0.75l/h. It is improved more than 0.95 l/h with use of air flow over the passive condenser. Daily productivity of freshwater around 35% using a glass condenser with black steel fibers inside the water basin. Using the heat sink condenser increases the daily productivity from 31% in the case of using only saline water to 52% in the case of using black steel fibers in the basin. Using an umbrella of 20 cm wide at the top of the aluminum plate condenser decreases the daily productivity by 26%. Maximum daily output is 4.73 kg/m2 and 2.71 kg/m2 for summer and winter conditions respectively. Self-sustained passive system delivers both electrical power and potable water (two-in-one controlled output). Significant enhancement in productivity and overall thermal efficiency at low packing factor as compared to conversional solar still.

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

Fig. 1. a) Schematic view of “purging mode” in single slope solar still integrated with a semitransparent PV module (c-Si) and passive condenser (SSSS-SPV-PC). b) Schematic view of “circulation mode” in single slope solar still integrated with a semitransparent PV module (c-Si) and passive condenser (SSSS-SPV-PC). c) Semitransparent PV module (c-Si) (1.05 m× 0.66 m) having different values of packing factor.

studied for 20 kg basin water mass, under the clear sky day of the month May (2015) of New Delhi, India climatic conditions. The packing density or packing factor of PV affects the output power of the module as well as its operating temperature; and it depends on the shape of the solar cells used. Therefore, the effect of packing factor ( c = 0 , 0.25, 0.45, 0.65 and 0.85) of the solar cell of semitransparent PV module has been investigated. Moreover, other PV technology (c-Si, p-Si, a-Si, CIGS, CdTe etc.) has also been tested to examine the system performance. We studied the heat transfer characteristics; overall thermal and electrical energy; overall energy (thermal and electrical) efficiency; and productivity of the system. Moreover, cost analysis have also been performed to find the cost per liter of potable water produced by the system.

(i) "Diffusion" from high vapour concentration in the still to the lower concentration in the condenser. (ii) "Purging" of water vapour due to the relative pressure difference between still and condenser [Fig. 1 (a)], (iii) "Natural circulation" due to density difference between air inside still and condenser [Fig. 1(b)]. As shown in Fig. 1(a), "Purging" of water vapour from the still to the condenser is due to the relative higher solar still pressure caused by the continuous evaporation and heating. The rate of water vapour purging can be estimated by first calculating the incremental change inside the solar still pressure at any instant of time; and then balancing back the solar still and condenser pressures. The natural circulation mode is basically due to the relative density difference between the solar still and the condenser; if there is a gap at the bottom of the condenser as shown in Fig. 1 (b). In this case, the saturated cold air inside the condenser tends to move downward; whereas the saturated hot air tends to move upward. This rate of air circulation between the solar still and condenser section can be evaluated by equating the "driving" change of pressure generated by the buoyancy force, and the "resisting" pressure drop caused by flow resistance. Moreover, the temperature difference between the condenser and solar still section acts a driving force for the pressure or density difference; and it varies significantly during day hours. Consequently, the circulation of saturated air through the condenser have the tendency to remove the absolute humidity difference between the two temperatures.

2. System description When a passive condenser is added to the solar still (Fig. 1(a) and Fig. 1(b)), most of the water vapors get transferred to the condenser chamber and condensed there on the rear/side wall of the condenser. As discussed above, this cold condenser which is almost at ambient temperature acts as a heat and mass sink. This suction or extraction of water vapors by the external condenser from the solar still cavity continuously maintains the solar still at low pressure. There are there different modes of vapor transfer in solar still-condenser coupled system viz. (i) diffusion, (ii) purging, and (iii) natural circulation. These are stated as below: 4

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

Body of the solar still is made of glass-fibre-reinforced plastic (GRP) with an area 1.0m × 0.6m . Its inner rectangular surface is painted mat black to absorb the maximum transmitted (via condensing cover) solar radiation. The semitransparent PV module of area 1.05 m× 0.66 m is placed as a top cover with an inclination angle of 30o . A passive condenser (aluminium) of area 1.5 m× 0. 25m has been integrated on the rear side of the solar still. A DC fan (2 V, 1A) of has been connected at the top of the rear wall of the modified solar still as shown in Fig. 1(a). The system faces due south (latitude 28°35′ N, longitude 77°12′ E, altitude 216 m) to receive the maximum solar radiation. Saline water (salinity 10,000 ppm) is poured in the basin through an inlet provided at the rear wall of the solar still. In “semitransparent photovoltaic module” (SPV), transparent glass cover is used on the front side as well as backside. The efficiency of glass to glass (semitransparent) PV module is higher due to direct transmission of incident solar radiation through the non-packing area of the module [36,37]. The “packing factor” of the module is the ratio of total area of solar cells to the area of PV module as explained earlier in previous section. The semitransparent PV module (1.05 m× 0.66 m) having different values of packing factor is shown in Fig. 1(c). Moreover, higher value of packing factor of the PV module; lower ohmic losses between two consecutive solar cells; and lower temperature of the PV module can increase the overall electrical efficiency of the SPV module. The reduction in temperature of the module is possible by withdrawing the thermal energy associated with the PV module. In present system, the generated electrical energy of the SPV module is used to run a DC fan. The net electrical energy can be utilized to fulfill the requirement of daily electricity in rural areas or some other applications. Following Shyam et al. [38], the power of fan used in the proposed system is only 2 W (maximum); whereas, the total electrical output of the semi-transparent photovoltaic module is obtained of the order of kWh. Consequently, the fan power has been ignored in the present study. Apart from the conversion of the solar radiation into electricity by the SPV module, remaining portion of the incident solar radiation has been transmitted through the non-packing area of the SPV module. Fraction of incident solar radiation is reflected to ambient from the front and back transparent glass cover (double reflection) of the SPV module. As the basin water temperature increases through direct absorption of solar radiation and heat transferred by the blackened surface (thermal storage), the evaporation mechanism takes place (via purging mode) in the solar still cavity. The running DC fan enhances the vapor transfer rate from the solar still cavity into the condenser chamber. As explained in previous section, the condenser acts as a heat and mass sink which continuously sucks water vapor from the solar still; and condensation takes place in the condenser chamber. Eventually, the condensed water trickles into the measuring jar placed at the bottom side of the integrated condenser under gravity. The proposed condenser is passive and adds no complexity to the design, operation, and maintenance of the simple basin solar still. Further, the productivity (yield) can be improved by natural circulation (due to density difference between air inside solar still and condenser) of water vapor [1,36].

3.2. Blackened surface

Tw ) Ab + w g2 (1

hbw (Tb

= hbw (Tb

Tw ) Ab + Uba (Tb

c ) I (t ) Am = h1 (Tw

Tm ) Am + (Mw Cw )

+ (UA)SL (Tw

(2)

Ta ) Ab

dTw dt

Ta ) A s + mf cf (Tw

(3)

Tcond)

3.4. (iv) Passive condenser

mf cf (Tw

Tcond ) = Utcond, a (Tcond

(4)

Ta ) Acond + mcond L v

The efficiency of solar cell can be expressed as [32]

=

c

o [1

o (Tc

(5)

To)]

Where, o is the efficiency at standard test condition i.e., at I (t) = 1000 W/m2 and T0 = 250 C and Tc is the average solar cell temperature. Electrical efficiency of PV module can be expressed as m

=

(6)

g c c

From Eq. (1), expression of solar cell temperature (Tc ) can be expressed as c g c I (t ) Am

Tc =

c g cI

(t ) Am + Am (Utc, a Ta + Ubc, w Tw ) (7)

Am (Utc, a + Ubc, w )

From Eq. (2), the basin temperature (Tb) can be expressed as 2 w ) b g (1

(1

Tb =

c ) I (t ) Am

+ hbw Tw Ab + Uba Ta Ab (8)

Ab (hbw + Uba )

On solving Eq. (3) using Eq. (7) and (8), one can get hbw

2 w ) b g (1

(1

c ) I (t ) Am + hbw Tw Ab + Uba Ta Ab

Ab (hbw + Uba )

= h1 Tw

c g c I (t ) Am

+ (UA)SL (Tw

Tw Ab + w g2 (1

c g c I (t ) Am + Am (Utc, a Ta + Ubc, w Tw )

Am (Utc, a + Ubc, w ) Ta ) As + mf c f (Tw

c ) I (t ) Am

Am + (Mw Cw )

dTw dt

(9)

Tcond )

From Eq. (4), the condenser temperature (Tcond ) can be expressed as

Tcond =

(mf cf ) T w

(mcond ) L v + Acond (Utcond, a ) Ta (10)

(A cond Utcond, a + mf cf )

On substituting Eq. (10) in Eq. (9), one can get (Appendix B),

dTw + aTw = f (t ) dt

(11)

Expressions of “a” and "f (t )" are given in appendix B. The solution of first order differential Eq. (11) can be written as

Tw =

f (t ) [1 a

e

a t]

+ Tbw 0 e

a t

(12)

Tbw0 is the basin water temperature at t = 0. Using the thermo physical properties of water (Table A1) and vapor (Table A2), the basin temperature can be obtained from Eq. (12). The hourly productivity (yield) obtained from the system is estimated from Eq. (13) as given below

Following basic assumptions given by Sahota and Tiwari [39] the energy balances of different components of the proposed system are given below:

Mw =

he ( Tw

Tcond) + mf cf (Tw

Tcond) Lv

Utcond, a (Tcond

Ta ) Acond

× 3600

(13)

3.1. PV module

(t ) Am = Utc, a (Tc

c ) I (t ) Am

3.3. Basin water

3. Thermal modeling

c g cI

2 w ) b g (1

(1

Ta ) Am + Ubc, w (Tc

Tw ) Am +

Where, L v is the latent heat of vaporization [33]. Unknown terms in above equations are given in appendix B. Relation of natural convective heat transfer coefficient (HTC) can be expressed as

c g c I (t ) Am

(1) 5

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

(Nu) w =

hbw X = C (GrPr )n K

(14)

where, C = 0.54 and n= ¼ horizontal plate facing upward [33], Prandlt

(Gr ) w =

number,

2 L3

g

(Pr ) w =

( ); µCp K

Grashof

w

number,

T

µ2

w

Internal evaporative, convective and radiative HTCs can be obtained as Pw Tw

Evaporative HTC; he = (0.016273) hc

Pcond Tcond

(15)

Convective HTC: hc = (0.844)( (16) hr = eff [(Tw + 273) 2 + (Tcond + 273)2] Radiative HTC; [Tw + Tcond + 546] Total internal HTC can be expressed as

T )1/3

(17)

h1 = he + hr + hc where;

(

Px = exp 25.317

(Pw Pcond )(Tw + 273) 2.689 × 105 Pw

5144 Tx + 273

)

;

T = (Tw

Tcond ) + Fig. 2. Hourly variation of solar intensity and ambient temperature for a clear sky day of the month May (2015) of New Delhi climate.

;

Effective emissivity (

eff )

is given as

1 eff

=

1 w

+

1 cond

1.

Electrical energy of the proposed system can be obtained as

E=

m Am I

Net present value (NPV ) = P + R1 × (CRF )n (18)

(t )

+ [Rn1× (SFF )n1 + Rn2 × (SFF )n2 + …Rnk × (SFF )nk ]

Net electrical gain can be expressed as

Enet = E

(19)

Pfan

Cost per liter (Cl ) =

Thermal gain of the system can be expressed as

Qth = mf cf (Tw

Overall thermal energy gain can be expressed as

Qovr = Qth + as th

E 0.38

(21)

mf cf (Tw

The analysis has been carried out for the climatic conditions of New Delhi, India (northern hemisphere) and the climatic data (solar radiation and ambient temperature, Fig. 2) of a clear sky day of the month May (2015) has been obtained from the India Meteorological Department (IMD), Pune, India. The hourly solar intensity at 300 inclination of the PV module (facing due south) has been evaluated using Liu and Jordan formulae. Numerical constants and specification of different components of the proposed systems are given in Table 2. Following equations obtained in previous section, the methodology has been executed in MATLAB 2016a in order to study the daily performance of passive single slope solar still integrated with semitransparent PV module and passive condenser for different packing factors of the solar cell of different PV technologies (c-Si, p-Si, a-Si, CIGS, CdTe etc.): (a)Different heat transfer coefficients (HTCs) of the system have been calculated using design parameters using thermo-physical properties of water (Table A1) and vapor (Table A2). (b)From the estimated HTCs, hourly temperature of solar cell (Eq. (7)), blackened surface (Eq. (8)), passive condenser (Eq. (10)), and basin water (Eq. (12)); and solar cell efficiency (Eq. (5)) and module efficiency (Eq. (6)) of the system has been obtained. (c)Hourly productivity (yield) the proposed system has been calculated from of Eq. (13). (d)Electrical energy (Eq. (18)), net electrical gain (Eq. (19)), thermal gain (Eq. (20)), overall thermal energy gain (Eq. (21)); thermal energy efficiency (Eq. (22)) and overall thermal energy efficiency (Eq. (23)) of the system has been evaluated. (e)Cost analysis of the system have been executed to get the per liter cost of potable water (Eq. (24)-Eq. (28)). For better understanding, the flow chart of the methodology of the proposed system is given below:

Tcond ) (22)

Am I (t )

Overall thermal energy efficiency of the system can be obtained as ovr

=

th

+

c

(23)

0.38

where, 0.38 is known as conversion factor in power plant i.e. conversion efficiency of thermal energy (low grade energy) to electrical energy (high grade energy) in thermal power plant [40]. 3.4.1. Cost analysis formulation Cost analysis of the system provide option for the designers to find an alternative techniques for the improvement of the system performance. In the present cost analysis, the replacement period of copper condenser, and semitransparent PV module has been chosen as 10 and 25 years respectively. Following Tiwari and Sahota [1], the cost and salvage value of different components of proposed systems are given in Table 6. Mathematical expressions of unit cost per liter (Cl ) , uniform annual cost (UAC), net present value (NPV), shrinking fund factor (SFF), and capital recovery factor (CRF) is expressed as follows:

Uniform annual cost (UAC ) = (NPV × CRF ) + (MS × CRF )

S × SFF (24)

Capital recovery factor (CRF ) = Shrinking fund factor(SFF ) =

1)n

i (i + (i + 1)n

i (i + 1)n

1 1

(28)

4. Methodology

Thermal energy efficiency of the proposed system can be obtained

=

(27)

The estimated values of these expressions are presented in Table 7. The cash flow diagram of the system is shown below: where, P -present cost, S - salvage value, MS - maintenance cost, n life span of the system, and Rnk - replacement factor.

(20)

Tcond )

UAC Y

S × (SFF )n

(25) (26) 6

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Table 2 Numerical constants used in computation. Dimensions of passive DSSS

Constants

Numerical value

Ab

1.0 m× 0.6 m

Lg

0.003 m

Am A cond

1.05 m× 0.66 m 1.5 m× 0. 25m

Lcond

0.05 m

n

36 1100rpm 6.31A 21.40V 100Wp 12W

Cw

N Isc Voc Pmax Pfan Kg Kb K cond Lb

300 0.780 (W/m )

0.035(W/m ) 210 (W/m ) 0.0045 m

w

5.67×10-8 (W/m2K4) 4188 (J/Kg ) 0.9 0.05 0.8 0.6

0

0.15

c g

b

0 g

Mw mv

0.045/ 0.95

20kg 0.001kg /s

5. Results and discussion

Fig. 3. Hourly variation of solar cell temperature and solar cell efficiency of the SPV module for different packing factors of solar cell (c-Si).

Present study involves the daily performance of modified single slope solar still integrated with semitransparent photovoltaic module (top cover), passive condenser, and DC fan (Fig. 1 (a)) in purging mode. Analysis has been carried out for a typical clear sky day (hot weather conditions) of the month May of New Delhi climatic condition (Fig. 2). Hourly variation of solar cell temperature and solar cell efficiency of semitransparent PV module for different packing factors of solar cell ( c = 0.25, 0.45, 0.65, and 0.85) is presented in Fig. 3. It is clear that the solar cell efficiency decreases as the temperature of solar cell increases as expected. Moreover, the solar cell efficiency decreases with increase in packing factor of the solar cell which is credited to the fact that higher packing factor of the solar cell allows minimum transmission of

incident solar radiation through the non-packing area of the semitransparent PV module ; hence, raises the solar cell temperature and lowers the solar cell efficiency. The analysis of the proposed system for c = 0 is also carried out which is corresponds to the conventional singe slope solar still integrated with passive condenser and double glazed top glass cover. The proposed passive system has also been tested for other types of PV technologies i.e. p-Si, CIGS, CdTe, and a-Si etc. Therefore, hourly variation of solar cell temperature and solar cell efficiency of for these different PV technologies has been presented in Fig. 4 for βc = 0.25 (lower value) and 0.85 (higher value). 7

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Fig. 4. Hourly variation of solar cell temperature and solar cell efficiency of the SPV module for different packing factors of solar cell of different PV technologies for packing factor (a) 0.25 and (b) 0.85.

Fig. 5. Hourly variation of basin water temperature for different packing factors of solar cell (c-Si) of the SPV module.

Fig. 6. Hourly variation of passive condenser temperature for different packing factors of solar cell of the SPV module (c-Si).

Table 3 Specifications of the different PV modules [36].

From the analysis, it has been found that the basin water temperature decreases with increase in packing factor and found to be higher during noon hours (Fig. 5). As discussed above, lower packing factor allows the transmission of more solar radiation through the nonpacking area; consequently, it is directly absorbed by the basin water in addition to the stored thermal energy transferred by the basin liner; hence, raises its temperature. The maximum value of basin water temperature is found to be around 75.8 for c = 0 during noon hours (Table 4) as expected because transmission of solar radiation is through double glazed cover only. Basin water temperature decreases with increase in packing factor/ area of the module. It has been found that basin water temperature is higher for c-Si SPV module among all other types of PV technologies (lower for a-Si SPV module). It is due to different temperature coefficient, thickness, absorptivity of solar cell; and module efficiency (Table 3). Hourly variation of condenser temperature for different packing factors of solar cell is shown in Fig. 6. Same variation of condenser temperature has been observed as found for the basin water temperature for all proposed PV technologies. The condenser temperature is found to be significantly lower than the basin water temperature. It is due to the location of the passive condenser on the rear side of the solar still such that it is not directly exposed to the sunlight; hence its temperature is maintained lower. Moreover, the condenser temperature is found to be higher for lower value of the packing factor of the solar cell for all PV technologies. It is due to the

PV Technology

Module efficiency,

0

Temperature coefficient, ref

c-Si p-Si a-Si CdTe CIGS

16 14 6 8 10

(

1)

0.0040 0.0040 0.0026 0.0020 0.0045

Packing factor,

Absorbtivity,

0.89 0.89 1 1 1

0.9 0.9 0.85 0.8 0.8

Table 4 Maximum value of basin water temperature and condenser temperature with cSi SPV module. Packing factor ( c )

Basin fluid temperature ( )

Condenser temperature ( )

0 0.25 0.45 0.65 0.85

75.86 66.53 57.64 47.68 41.64

52.45 48.05 41.42 34.43 29.54

8

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earlier. The evaporative HTC is higher during noon hours due to more availability of solar radiation in this period. It decreases gradually for higher values of the packing factor of all SPV modules. The condenser acts as a heat and mass sink which continuously sucks evaporated water vapor from the solar still cavity. The condensation takes place at the rear wall of the condenser as shown in Fig. 1(a). The variation of thermal energy, electrical energy, and overall thermal energy of the system has been estimated for different packing factors of SPV module as shown in Fig. 9. The packing factor c = 0 , delivers only thermal energy corresponds to the doubled glazed top cover. On increasing the packing factor, thermal energy gain decreases and electrical energy gain increases as predicted. The maximum value of thermal and electrical energy gain is found to be 3.98 kW h and 0.38 kW h ( c = 0.85) respectively for c-Si based SPV module as compared to other SPV module technology. The electrical energy produced by the system is utilized to run a DC fan. Apart from it, the remaining or extra electrical energy can be used to fulfill the electricity requirement especially in rural areas. It clearly implies that this modified passive distillation system is self-sustained system; and its two-in-one controllable output (electrical power generation and potable water production) option is very significant which full-fills our both demands. The electrical, thermal and overall energy efficiency of the system can be controlled or limited by changing the packing factors of the SPV module according to our requirement. On analyzing other SPV modules with different solar cell technology; the estimated values of thermal energy, electrical energy, and overall thermal energy have been found to be higher for c-Si (Eth = 3.66 kW h; Eel = 0.121 kW h; Eovr = 3.978 kW h) and lower for a-Si (Eth = 2.51 kW h; Eel = 0.0721 kW h; Eovr =2.699 kW h) solar cell based SPV modules for both c = 0.25; these estimated values found to be higher for c = 0.85 (Fig. 10). The electrical, thermal and overall energy efficiency of the system for different packing factors of the SPV module of different technologies is presented in Fig. 11 (c-Si) and Fig. 12 (other SPV technologies). The electrical energy efficiency increases with increase in packing factor and found to be higher around 11.6% for c-Si based SPV module and lower for a-Si type for c = 0.85. On the other hand, thermal energy efficiency of the system is found to be higher around 44.2% for c-Si (only) for c = 0.25 (lower packing factor). From Fig. 11 and Fig. 12, one can observe that the overall thermal energy efficiency increases gradually with increase in packing factor and found to be higher, 57.5% (c-Si only) for c = 0.85. As predicted, the thermal energy efficiency decreases and electrical energy efficiency increases with increase in packing factor of the SPV module for all different SPV technologies.

Fig. 7. Hourly variation of natural convective heat transfer coefficient (basin liner to water) for different packing factors of solar cell of the SPV module (cSi).

Fig. 8. Hourly variation of evaporative heat transfer coefficient for different packing factors of solar cell of the SPV module (c-Si).

fact that convective heat from the bottom or back side of the SPV module in solar still cavity is continuously transferred by the built-in DC fan into the condenser chamber; hence raises the condenser chamber. This convective heat transfer rate is higher for the higher value of packing factor of the solar cell (higher solar cell temperature). Again it is found to be higher for c-Si solar cell based SPV module and lower for a-Si based SPV module for fix value of the packing factor. The maximum value of the condenser temperature obtained during noon hours is given in (Table 4). Fig. 7 depicts the hourly variation of natural convective heat transfer coefficient for different values of packing factor of the solar cell. The natural convective HTC is found to be higher for lower value of the packing factor. It happens because for lower packing factor higher transmission of solar radiation takes place through the non-packing area of the SPV module; and gets absorbed by the basin liner which ultimately raises its temperature. Therefore, basin liner transfers higher amount of stored thermal energy to the basin water via mode of natural convection and it is higher for c = 0 (doubled glazed transparent cover). It is found to be higher for c-Si SPV module and follows the enhancement order as c-Si > p-type > CIGS > CdTe > a-Si. Another thermo-physical characteristic of the system evaporative HTC (hourly variation) is presented in Fig. 8; and the same trend has been observed for all PV solar cells as found for convective HTCs. It is found to be higher (for c-Si) for lower value of the packing factor as explained

Fig. 9. Variation of electrical, thermal, and overall thermal energy gain with different packing factors of solar cell (c-Si). 9

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Fig. 10. Variation of electrical, thermal, and overall thermal energy gain with different types of technologies for packing factor (a) 0.25 and (b) 0.85.

places (zero non-packing area); hence the system will provide minimum distilled output. The efficiency of proposed system can be further improved by developing transparent solar cells in PV module technology (specifically c-Si). Fig. 13 depicts the variation of solar cell efficiency with packing factor of the SPV module for different solar cell technologies. It has been observed that solar cell efficiency decreases with increase in packing factor of the SPV module. The solar cell efficiency is found to be higher for c-Si and follows the enhancement order as c-Si > ptype > CIGS > CdTe > a-Si. This higher efficiency at lower packing factor is due to the fact that solar cell temperature increases on increasing the packing area or packing factor; and hence, efficiency decreases as shown in Fig. 3. Correlations ( c = a 2 + b + c with R2 value) have been developed between solar cell efficiency and packing factor by fitting second order polynomial for all different technologies as shown in above Fig. 13. Fig. 14 shows the variation of productivity of the system with packing factor of the SPV module. It has been observed that productivity decreases with increase in packing factor which happens due to less transparent area (for higher packing factor) of the top cover (SPV module) exposed to the incident solar radiation. Therefore, less solar radiation is transmitted in the solar still cavity through the non-packing area; and eventually reduces the evaporation rate; hence productivity. The maximum productivity of the system is found to be 4.92 kg/m2 for 2 c = 0 ; whereas, it is found to be 4.12 kg/m for c-Si SPV module for = 0.25 . It further decreases on increasing the packing factor of the c SPV module. Apart from c-Si; it has been observed that other types of

Fig. 11. Variation of electrical, thermal, and overall thermal energy efficiency with different packing factors of solar cell (c-Si).

Ideal value of the packing factor is unity butit is fit not for our proposed system-as it will give only electrical output (minimal distilled output). It is due to the fact that the whole surface which is exposed to the solar radiation has been cover with solar cells and maximum portion of it will be converted to the electrical part. Very minimum transmission takes

Fig. 12. Variation of electrical, thermal, and overall thermal energy efficiency with different types of technologies for packing factor (a) 0.25 and (b) 0.85. 10

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Fig. 13. Variation of solar cell efficiency with packing factor of the SPV module for different technologies. Table 6 Cost and salvage value of different components of the system. Parameters

FRP body @ 340/ kg Iron stand Inlet/Outlet nozzle Iron clamp Gaskets Silicon gel Semitransparent PV module ( = 0.9) DC Fan Copper condenser @ 441/kg Fabrication cost and other changes Net Cost of the system Average salvage value of the system after 30 years, if inflation remains @ 4%. Average salvage value of the system after 50 years, if inflation remains @ 4%.

Fig. 14. Variation of productivity (yield) of the solar still obtained at different packing factors of solar cell (c-Si).

c-Si p-Si CIGS CdTe a-Si

c

= 0. 25

4.12 (kg) 4.01 3.86 3.67 3.53

c

= 0. 85

1.78 1.61 1.53 1.44 1.31

(Rs . )

($)

4,500 8,00 200 200 200 200 6,000 4,00 1,000 3,000 16,500 5,351

64.72 11.50 2.87 2.87 2.87 2.87 86.31 5.75 14.38 43.15 237.34 76.97

11,726

168.67

*1 US $ = 69.52 Rs. on 20 May 2019.

decreases with increase in life span of the system at fixed interest rate but increases with increase in interest rate at fixed life span of the system. The cost per liter (Cl ) obtained from the proposed systems has been evaluated for 30 year and 50 year life span of the system and different interest rates. We would like to clarify that the value of Cl have been estimated by considering the semitransparent PV module (c-Si) with packing factor of 0.85. In general, this suggest that for lower value of the packing factor, price of the module will be lower (due to less number of solar cells); and it will give enhanced annual productivity but at the cost of lower electrical energy. Consequently, the value of UAC will be dropped; and final value of Cl decreases (0. 0431 $ / l for = 0.65, i = 4%, n = 30). It has been observed that Cl decreases with increase in interest rate for given life span of the system; and it also decreases with increase in life span of the system. It happens due to higher value of UAC with increase in in interest rate and life span of the system. The value of Cl is found to be 0.0466 ($ / l), 0.0673 $ /l , 0.0792 $ /l at i = 4%, 8%, and 10% interest rate respectively for 30 years life span Cl of the system. Whereas, is found to be 0.0385 ($ / l), 0.0618 $ /l , 0.0753 $ /l at i = 4%, 8%, and 10% interest rate respectively for 50 years life span of the system. The value of Cl ($ / l) will vary on considering different technologies (c-Si, p-Si, CIGS, CdTe, and a-Si) of semitransparent module (each have different price) depending on price of the module.

Table 5 Productivity (distilled output in kg/m2) of the systems for different types of PV technology. Type of PV technology (Solar cell)

Cost

c = 0 (double glazing)

4.92 4.78 4.58 4.39 4.21

SPV technology provides lower value of distilled output for fix value of the packing factor; it follows the enhancement order (productivity) as cSi > p-Si > CIGS > CdTe > a-Si (Table 5). As discussed above, potable production efficiency of the system can further be improved by replacing the solar cells with transparent solar cells of SPV module (particularly c-Si); and we can also extend our limit of packing factor up to unity. In the cost, the net present value (NPV), uniform annual cost (UAC), shrinking fund factor (SFF), capital recovery factor (CRF), and cost per liter of potable water (Cl ) has been evaluated at different interest rates (4%, 8%, and 10%) for the 30 year and 50 year life span of the proposed systems (Table 7). It has been observed that NPV increases with increase in interest rate for fixed life span of the system. On the other hand, NPV increases with increase in life span of the system at any fixed interest rate. The UAC shows opposite variation to NPV such that it 11

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Table 7 Net present value, capital recovery factor, shrinking fund factor, uniform annual cost, and cost/liter obtained from the system. Years (n )

Interest rate, i (%)

NPV (Rs . )

CRF

SFF

UnaCost (Rs . )

Cost per liter (Rs. /l )

Cost per liter (USD ($)/l )

30

4 8 10 4 8 10

18,377 17,285 17,048 18,377 17,286 17,048

0.0578 0.088 0.1061 0.0466 0.0817 0.1009

0.0178 0.0088 0.0061 0.0066 0.0017 0.00086

1,062.7 1,535.4 1,808.4 855.47 1,413 1,719.5

3.24 4.68 5.51 2.68 4.30 5.24

0.0466 0.0673 0.0792 0.0385 0.0618 0.0753

50

6. Conclusions

well as potable water production) option is very significant which fullfills our both demands. The electrical, thermal and overall energy efficiency of the system can be controlled by changing the packing factors of the SPV module according to our requirement. The efficiency of proposed system can be further improved by developing the transparent solar cells in PV module technology (specifically c-Si-based on results). The value of Cl is found to be 0.0466 ($ / l), 0.0673 $ /l , 0.0792 $ /l at i = 4%, 8%, and 10% interest rate respectively for 30 years life span of the system; and it decreases on increasing the life span of the system (n = 50). The value of Cl ($ / l) vary on considering different technologies (c-Si, p-Si, CIGS, CdTe, and a-Si) of semitransparent module depending on price of the module.

Worldwide, in the developing nations, it is difficult to meet the electricity requirement in rural areas. Conventional solar distillation system is popular in rural areas. The built-in-condenser and PV integrated (top cover) solar distillation system not only fulfill the electricity requirement but also enhance the system productivity as compared to the conventional solar distillation systems. Numerical analysis shows that overall thermal efficiency of the proposed system is higher (ƞ = 57.5%) for higher value of the packing factor c = 0.85; and lower for c = 0 (double glazing case- ƞ = 41.1%) and c = 0.25 (ƞ = 53.1%) of c-Si SPV module among other SPV technologies. All the outputs (electrical, thermal, overall thermal energy/efficiency; and potable water production) follows the enhancement order of SPV technology as c-Si (max) > p-Si > CIGS > CdTe > a-Si (min.). It can be concluded that higher packing factor of SPV module can be suggested to fulfill both the electricity requirement as well as production of potable water. Otherwise, the SPV module with low packing factor can be considered if electricity production is not a prime concern (minimum to run a DC fan). This modified passive distillation system is self-sustained system; and its two-in-one controllable output (electrical power generation as

7. Recommendation The effect of different solar cell technologies viz. c-Si, p-Si, a-Si, CIGS, CdTe and HIT etc. can be analyzed by incorporating different nanofluids in the proposed system. Also, cost analysis can be performed to check the economic viability of the system.

Appendix A

Table A1 Thermo physical properties of vapor [36,41]. Quantity

Symbol

Expression

Specific heat

Cv

Density Thermal conductivity Viscosity Latent heat of vaporization of fluid

kv µv L

999.2 + 0.1434 × (Tv ) + 1.101 × (Tv2) (6.7581E 8) × (Tv3) 353.44/(Tv + 273.15) 0.0244 + (0.7673 E 4) × (Tv ) (1.718 E 5) + (4.620E 8) × (Tv ) (3.1625 E+ 6) + [1 (7.616E 4) × (Tv ))]; for Tv > 70

v

(2.4935E + 6)[1 × Partial vapor pressure Thermal expansion coefficient

P (x )

(Tv3))];

exp 25.317

(9.4779E

4) × (Tv ) + (1.3132E

7) × (Tv2)

(4.7974 E

3)

for Tv < 70

(

5144 T (x ) + 273

)

1/(Tv + 273.15)

v

Table A2 hermo physical properties of water [42]. Quantity Density

Symbol

Expression

Cw

Viscosity

µw

Thermal conductivity

kw

0.0107 × Tw2 + 0.00082 × Tw2.5

999.79 + 0.0683 × Tw

w

Specific heat

4.217

0.00561 × Tw + 0.00129 × Tw1.5

(2.303E

0.000115 × Tw2 + (4.149E

5) × Tw3

6) × Tw2.5

1 (557.82

2 19.408 × Tw + 0.136 × Tw

0.565 + 0.00263 × Tw

12

(3.116E

3) 4) × Tw

0.000125 × Tw1.5

(1.515E

6) × Tw2

0.000941 × Tw0.5

Journal of Energy Storage 24 (2019) 100809

V. Saini, et al.

Appendix B

a=

f (t ) =

(mf cf )2

2 hbw Ab2 + hbw Ab + h1 Am + (UA)SL + mf cf (AH )1

1 Mw Cw 1 Mw Cw

hbw (mcond ) L v (J1 + J2) + + Ta (AH )1 (AH )3

h1 Ubc, w Am (AH ) 2

(AH )3

Uba Ubw Ab (AH )1

+ (UA)SL

h1 (AH )2

Acond Utcond, a + (Am Utc , a )

(AH )1 = Ab (hbw + Uba ); (AH ) 2 = Am (Utc, a + Ubc, w ); (AH )3 = (Acond Utcond, a + mf cf ) 2 w ) b g (1

J1 = (1

Utc, a =

hbw

Kg Lg

+

1 h0

c ) I (t ) Am ; J2

1

; Ub, a =

2 w ) b g (1

(1

2 w g (1

=

1

1 Kb + Lb hi

c ) I (t ) Am

; Ubc , w =

c )I

(t ) Am ; J3 =

Kg Lg

+

1 hi

+ hbw Tw Ab + Uba Ta Ab

c g c I (t ) Am

c g c I (t ) Am

1

+ Am (Utc, a Ta + Ubc, w Tw )

Am (Utc, a + Ubc , w )

+ mf cf Tw

(mf cf ) T w

c g cI

(t ) Am 1

K cond 1 + Lcond h0

; Utcond, a =

Tw Ab +

Ab (hbw + Uba )

= h1 Tw

c g c I (t ) Am

2 w g (1

c )I

Am + (Mw Cw )

; ho = 5.7 + 3.8v ; hi = 2.8 + 3v

(t ) Am

dTw + (UA)SL (Tw dt

Ta ) As

(mcond ) L v + Acond (Utcond, a ) Ta (A cond Utcond, a + mf cf )

Or

hbw [J1 + hbw (Tw ) Ab + Uba Ta Ab (AH )1

(Tw )(AH )1 ] Ab + J2 =

h1 [(Tw )(AH ) 2 (AH )2

+ (UA)SL (Tw

J3

Ta ) As +

Am (Utc, a Ta + Ubc, w Tw )] Am + (Mw Cw ) m f cf

(AH )3

((Tw )(AH )3

dTw dt

(mf cf ) T w + (mcond ) L v

A cond Utcond, a Ta)

Or

(Mw Cw )

dTw = Tw dt +

2 hbw Ab2 (AH )1

hbw Ab

h1 Am

(UA)SL

hbw (mcond ) L v (J1 + J2 ) + + Ta (AH )1 (AH )3

m f cf +

Uba Ubw Ab (AH )1

(m f c f ) 2 (AH )3

+

+ (UA)SL

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