research article design and modelling of water chilling...

Research ArticleDesign and Modelling of Water Chilling Production System bythe Combined Effects of Evaporation and Night Sky Radiation

Ahmed Y Taha Al-Zubaydi and W John Dartnall

School of Electrical Mechanical amp Mechatronic Systems University of Technology Sydney 15 Broadway Ultimo NSW 2007 Australia

Correspondence should be addressed to Ahmed Y Taha Al-Zubaydi ahmedyassintahahotmailcom

Received 24 September 2013 Accepted 2 January 2014 Published 2 March 2014

Academic Editor Czarena Crofcheck

Copyright copy 2014 A Y T Al-Zubaydi and W J Dartnall This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The design and mathematical modelling of thermal radiator panel to be used primarily to measure night sky radiation wet coatedsurface is presented in this paperThe panel consists of an upper dry surface coated aluminium sheet laminated to an ethylene vinylacetate foam backing block as an insulation Water is sprayed onto the surface of the panel so that an evaporative cooling effect isgained in addition to the radiation effect the surface of a panel then is wetted in order to study and measure the night sky radiationfrom the panel wet surface In this case the measuring water is circulated over the upper face of this panel during night time InitialTRNSYS simulations for the performance of the system are presented and it is planned to use the panel as calibrated instrumentsfor discriminating between the cooling effects of night sky radiation and evaporation

1 Introduction

The demand for energy efficient air conditioning systems tominimize the energy consumption worldwide has been animportant issue for researchers since the invention of activeair conditioning system In parallel with the researches con-ducted to create new conventional air conditioning technolo-gies researches to find noncompressor systems took a place

Noncompressor cooling systems have been introducedas low electricity consumption alternatives to mechanicalvapour compression units providing a solution that reducesthe energy consumption and environmental issues in build-ings Absorption and adsorption chillers direct and indirectevaporative air coolers and water passive cooling systemswhich utilize the night sky radiation effect are among therange of noncompressor systems available Radiative coolingis a passive cooling process based on the phenomenon ofheat transfer between earth-based objects and the sky bythe means of long-wave radiation usually when the effectivesky temperature is less than the ground temperature Thetransparency of earthrsquos atmosphere in the infrared range of 8ndash13 120583m (atmospheric window) allows a fraction of the thermalradiation to be absorbed by space especially during the nightand earlymorning where solar short wave radiation is absent

The phenomenon can be applied to cool surfaces andorfluids which in turn can be used in air conditioning appli-cations

Cooling with night sky radiation phenomena could beconsidered as featured technology with capability to be a pas-sive alternative to the conventional air conditioning systemMany researchers have explored the different applications andsystems proposed to cool fluids by means of heat rejection byradiation to the sky Yannas et al [1] presented the worldrsquosbest-known applications of the night sky radiation systemwith mathematical modelling of a roof pond system Spanaki[2] presented a comparison between different roof pondsystems for cooling Tiwari et al [3] presented the analysisof the moving water system in three different cases includingroof pond spray coolinggunny bags and moving water overthe roof

A commercial system known as ldquoWhiteCaprdquo was intro-duced in the United StatesThis system is reported by Bourneand Carew [4 5] TheWhiteCap system employs the coolingof water by night sky radiation convection and evaporationof water in an open water cycle The cold water is storedfor use during the day by direct conduction to the roof(WhiteCap-R) fan coils (WhiteCap-T) or coils entrenched inthe floor slab (WhiteCap-F)TheWhiteCap system enhances

Hindawi Publishing CorporationJournal of Renewable EnergyVolume 2014 Article ID 624502 8 pageshttpdxdoiorg1011552014624502

2 Journal of Renewable Energy

the evaporation heat loss by spraying the water over the roofin the primary stage and the water droplets evaporate asthey travel from the spray outlet to the roof surface Bourneand Carew [4] reported a 47 reduction in annual use ofconventional cooling by using the WhiteCap cooling systemon a 2500-square-meter office building in Los Angeles

The low cooling capacity and the high effectiveness ofambient conditions on the system performance (ie cloudcover and relative humidity) are considered practical lim-itations of the nocturnal cooling by radiation technologyapplications However the system can be applied as a sup-plemental heat sink system with another HVAC system [6]Examples of hybrid systems are presented by Heidarinejadet al [7] and Farmahini Farahani et al [8] Both studiesinvestigated the possible combination of nocturnal radiationcooling systems with conventional systems specifically withan indirect evaporative cooling unit in the first study and adirect evaporative cooling unit in the second

Although the WhiteCap system is available since 1996no theoretical works available present the system mathe-matical modelling In previous work the author presented amathematical modelling of three different systems applyingthe Night sky radiation for water chilling [9] The systemcompared three panels to measure the various effects thefirst panel had a dry radiative surface with an embedded heatexchange water circuit for the purpose of measuring the radi-ant heat The second panel employed a sprayed water flowingover its radiative surface to measure combined effect of (a)heat lost by pre-evaporation during the sprayed water droplettravel through the air (b) evaporation of water flowed overthe radiation surface and (c) radiation from the thin waterlayer surface The third panel is like the second however thewater is running via a gutter at the top so that is flows overthe radiative surface enables the heat loss by radiation andevaporation from a wetted surface The comparison betweenthe three systems shows that the second panel performance isthe best in term of water chilling

In this work the author presented the second system pre-sented in the previous work [9] with a detailed mathematicalmodelling to enable researchers to use it as a design guidefor future work In order to satisfy the above objective it wasdecided to construct a panel having similar principles of theWhiteCap system By using this panel the separate effects ofevaporative cooling and night sky radiative cooling may bededuced from the recorded data In this work we discussedthe design and mathematical modelling of the system (ieradiator panel with sprayer) The system under investigationis described in Figure 1 The layout of the system (Figure 1)consists of a radiator panel with a well-insulated back sidewhich is used to simulate the principles of the system similarto theWhiteCap systemWater is sprayed onto the panel flowfor a measured distance and then returned to the storagetank and pumped again The contact of the water with theair causes mass loss by the evaporation through the processmake-up water to the tank is a necessity The make-up watertemperature is different from the water temperature in thestorage tank and this is considered in the calculations Thewater temperatures in the tank spray nozzle inlet water pondinlet and water pond outlet are the data collected

Radiator paneland

Circulation pump

Water storage tankMake-up

water

Tr1

Tr2

Td

(Arp hfg Cpw)

Vs Ts

120588w Cpw

Figure 1 Experimental setup for the radiative coolingmeasurementsystems-radiator panel with sprayer

This paper discusses the theoretical work of the project bypresenting mathematical modelling and a performance sim-ulation with the Transient System Simulation Tool (TRNSYS)software package [9 10] The results are analysed to optimizethe design parameters and to analyse the contribution ofthe three heat transfer phenomena that occur in differentapplications of cooling water using the night sky radiationeffect We also study the feasibility of producing chilled waterfor space cooling applications The simulation results will beanalysed and compared with the experimental results in alater stage of the project

2 System Description and Modelling

21 The Effective Sky Temperature The heat exchangebetween the radiator plate and the sky occurs in a wavelengthrange of 8 to 14 120583m or what is known as the atmosphericwindowThe sky is considered to be a black body of equivalenttemperature 119879sky or the effective sky temperature In the liter-ature [11ndash13] many equations have been introduced to calcu-late119879sky as a function of the ambient temperature cloudinessfactor and the emissivity of the clear sky which in turn isa function of ambient temperature relative humidity andatmospheric pressure Berdahl andMartin [11 13] introducedan equation to calculate the clear sky emissivity as follows

120576sky = 0711 + 0005119879dp + 73 times 10minus5

1198792

dp

+ 0013 cos [2120587 time24

] + 12 times 10minus5

(119875atm minus 119875ℎ) (1)

where 119879dp is the dew point temperature (∘C) 119875atm is theatmospheric pressure (atm)119875

ℎ

is the atmospheric pressure atelevation ℎ (m) above sea level and the variable (time) is thehour of the day In the TRNSYS software package the Type 69calculates the effective sky temperature 119879sky (K) using Martinand Berdahlrsquos [13] equation as follows

119879sky = 119879amb(120576sky + 08 (1 minus 120576sky) 119862clo)14

(2)

where 119862clo is the sky cloudiness factor (0-1) supplied byTRNSYS Type 69

Journal of Renewable Energy 3

22 Thermal Panel Description A thermal panel for the pur-pose of cooling water with night sky radiation was designedusing basic materials which cost little and make the laboureasier The assembly consisted of an aluminium plate withdimensions of 3000mm long 2000mm wide and 2mmthick The dimensions were chosen to fit the size of a pieceof EVA foam supplied directly by the manufacturerThe platewas fixed to a 30mmthick EVA foamblock of closed cell foammade from ethylene vinyl acetate and blended copolymers Inthe open cycle water system water is sprayed over the roofsurface and flows onto the low sloped surface for a distanceof 119871 (m) before being collected and returned to the tankThe operation is repeated during the night (Figure 1) Waterexchanges heat with the ambient air by means of evaporationand convection and to the sky by radiation The relativetemperature of the water in the tank will be changed by theend of the operating period In the following the modellingof each process is presented

221WaterDropletModelling In this section the calculationof the sprayer water droplet final temperature and thequantity of evaporativemass will be discussedThemodellingof water droplet energy balance has been presented earlier byAl-Zubaydi et al [9] A numerous number of water dropletsformed by the nozzle will travel through the air to the waterpond on the panel surface performing a heat andmass trans-fer with the surrounding air The process is assumed to be aquasisteady state that varies with the ambient temperature inthe formof Fourier seriesThewater droplet boundary systemenergy balance is presented in Figure 2 [14] The quantity ofheat stored in the droplets over the period of time Δ119905 is

Δ = total (3)

The internal energy of the system is calculated by

Δ = 119898119889

sdot 119862119901119908

sdotΔ119879119889

Δ119905 (4)

where 119898119889

is the mass of the droplet (kg) 119862119901119908

is the specificheat capacity of the water (JkgsdotK) and Δ119879

119889

is the differencebetween the droplet final temperature 119879

1198892

and initial temper-ature 119879

1198891

(K)The heat transfer between the droplets the surroundings

and the ambient air is the sum of all heat transfers by convec-tion radiation evaporation and condensation

Essentially when evaporation occurs no condensationtakes part in the thermodynamic process and the value ofheat transfer by condensation is reset to zero The total heattransfer from a droplet boundary system is given by

total = conv + rad minus evap (5)

where

conv = ℎconv sdot 119860119889 sdot (119879amb minus 119879119889) (6)

rad = 120576water sdot 119860119889 sdot 120590 sdot (1198794

sky minus 1198794

119889

) (7)

evap = evap sdot ℎ119891119892 (8)

Qcon

Qrad

Qevap

Qcond

ΔU

Figure 2 Water droplet energy balance

where ℎconv is the coefficient of thermal convection (wm2sdotK)and ℎ119891119892

is the evaporation enthalpy of water vapor (Jkg)119860119889

is the surface area of the droplet (m2)119898119889

is the single dropletmass (kg) 120590 is the Stefan-Boltzmann constant (567 times 10minus8wm2 sdotK4) and 120576water is the water surface emissivity (value setto 1) By substituting (9)ndash(13) in (8) and rearranging we get

1198791198892

= 1198791198891

+Δ119905

119898119889

sdot 119862119901119908

times [ℎ119888

sdot 119860119889

sdot (119879119886

minus 119879119889

)

+ 120576water sdot 119860119889 sdot 120590 sdot (1198794

sky minus 1198794

119889

) minus evap sdot ℎ119891119892]

(9)

where 1198791198892

is the water drop final temperature (K) and 1198791198891

is the water droplet initial temperature (K) ℎ119888

and evapvalues can be calculated with the following equations themass evaporation rate evap (kgs)

evap = ℎ119898 sdot 119860119889 sdot [120588drop minus 120601120588atm] (10)

where ℎ119898

is the mass transfer convection coefficient (ms) 120588119889

is the specific humidity of saturated air evaluated at the waterdroplet temperature (kgm3) 120588amb is the specific humidity ofsaturated air evaluated at the ambient temperature (kgm3)and 120593 is the relative humidity of the ambient air ()

ℎ119898

is derived from the Sherwood number [14]

Sh1015840119863

= 2 + 06Sc13Re12 (11)

where Re is the Reynolds number of the droplet and is givenby

Re =119863119889

119904119889

Vair (12)

where119863119889

is the droplet diameter (m) 119904119889

is the droplet velocity(ms) and Vair is the kinematic viscosity for air (m2s) Thevariable Sc is the Schmidt number and is given by

Sc =Vair119863vap

(13)

where 119863vap is the water vapour diffusivity in air (m2s)[026119864minus4m2s] [15] After calculating the Sherwood numberthe value of ℎ

119898

is given by

ℎ119898

=Sh1015840119863

sdot 119863vap

119863 (14)


Qevap Qsolar Qcond Qconv Qrad

Qback

ΔUmwohfo mwihfi

Figure 3 Water pond energy balance

The coefficient of thermal convection ℎ119888

can be derivedfrom the Nusselt number equation

Nu =ℎconv119863119889119896air

(15)

where 119896air is the air thermal conductivity (Wmsdotk) In forcedconvection between the droplet and the wind the Nusseltnumber can be calculated by the Ranz and Marshal [15]equation

Nu = 2 + 06Pr13Re12 (16)

ThePrandtl number Pr can be found in the air propertiestable or calculated as a function of air dynamic viscosity V

119886

specific heat of the air 119862

119901119886

and air thermal conductivity 119896airwith formula [16]

Pr =119862119901119886

V119886

119896air (17)

By substituting the outputs of (11) and (16) in (15) thesubstitute equation (15) output in (14) the value of ℎconv willbe

ℎconv =119896air [2 + 06Pr

13Re12]119863119889

(18)

With the values of ℎ119888

and evap calculated from (16) to(24) the new temperature of the droplet119879

1198892

can be estimatedthis temperature will be the initial temperature of the secondpart of the water cooling system the panel pondThe amountof water entering the water pond boundary system is theinitial mass flow rate of the sprayer minus the evaporatedlosses

1198982119904

= 1198981119904

minus (119889

sdot Δ119905 sdot1198981119904

119898119889

) (19)

222 Radiative Panel Mathematical Modelling Similar tothe water droplet the panel pond control volume can berepresented as a typical thermodynamic control volume(Figure 3) As can be seen the heat transfer to and from thesystem boundary is in the form of evaporation conduction

convection solar and radiation in addition to heat transferdue to water entering and leaving the system

Similar to the water droplet energy equation the waterpond energy equation is

119898119908 rp sdot 119862119901119908 sdot

119879rp2 minus 119879rp1

Δ119905= cond + solar minus conv minus rad sky

minus evap minus back + wi minus wo

(20)

where 119898119908 rp is the mass of the water in the water pond (kg)

cond is the heat added by condensedwater (kJs) Solar is theheat absorbed by the panel water pond due to solar radiation(kJs) conv is the heat convection between the water pondand ambient air (kJs) rad sky is the heat exchange betweenthe water in the roof pond and the sky by radiation (kJs)evap is the evaporation heat exchange between water and theambient air (kJs) back is the heat transfer between the waterand the ambient air through the panel layers (kJs) and wiand wo are the energy rates added to the panel pond waterby the water added and water leaving the system boundary(kJs)

As in (3) for the water droplet the energy equation canbe rewritten to calculate the temperature of the water leavingthe panel pond

119879rp2 = 119879rp1 +Δ119905

119898119908 rp sdot 119862119901119908

sdot [Qcond + solar minus conv minus rad sky

minusevap minus back + wi minus wo]

(21)

Calculations of heat and energy transfers between the sys-tem and the boundary can be derivatives using the basic heattransfer equation many works presenting the mathematicalmodelling of the panel pond system can also be referenced[17ndash22]The amount of heat dissipated to the sky by radiationis a function of the pond emissivity the sky temperature andthe pondwater temperature other factors having an effect arethe humidity ratio clouds and radiation wavelength whichhave a direct effect on changes to the emissivity and skytemperature values The rad sky is given by

rad sky = ℎrad sky sdot 119860 rp sdot (119879119908 rp minus 119879sky) (22)

where ℎrad sky is the sky radiation heat transfer coefficient(Wm2sdotk) 119860 rp is the panel surface area (m2) 119879

119908 rp is thetemperature of the water in the pond (K) and 119879sky is theeffective sky temperature (K)

During the day solar heat is added to water in the pondarea the amount of heat added depends on the amountof solar irradiation flux (119868solar) and the panel pondrsquos solarabsorptivity (120572solar) The heat absorbed by water from solarirradiation is given by

solar = 120572solar119860 rp119868solar (23)


Consider that conv is the heat transfer from water to theambient by convection this heat can be calculated by

conv = ℎrp conv119860 rp (119879rp minus 119879amb) (24)

The convection heat transfer coefficient (ℎrp conv) is afunction of the type of flow rate laminar flow or turbulentflow and the (ℎrp conv) general equation is

ℎrp conv = Nu119871

sdot119870amb119883rp

(25)

where 119870amb and 119883rp are the thermal conductivity of theambient air and the distance water flows over the panelwhile Nu

119871

is the Nusselt number which is dissimilar to thewater droplet (10) in the case of panel pond flow its valuedepends on the nature of convection (forced or natural) [16]The water mass evaporation rate from panel pond rp evapneeds to estimate the value of heat dissipated from water byevaporation By recalling (4) and replacing the droplet surfacearea by the panel surface area we get

rp evap = ℎ119898 rp sdot 119860 rp sdot [120588119908 rp minus 120588atm] (26)

where 120588119908 rp and 120588atm are the water density at saturation

temperature pressure and atmospheric pressure respectively(kgm3) ℎ

119898 rp (ms) the mass transfer coefficient is calcu-lated from the Sherwood number (Sh1015840

119883

) and the binary massdiffusion coefficient (119863vap) is calculated as

ℎ119898 rp =

Sh1015840119883

119863vap

119883rp (27)

Under forced convection conditions the Sherwood num-ber is

Sh1015840119883

= 0644Re12119883

Sc13 (28)

and the Nusselt number is

Nu119883

= 0644Re12119883

Pr13 (29)

When the value of rp evap is calculated with (27) valueabove zero indicates that evaporation has taken place andthe heat transferred by evaporation from the water to theatmosphere is

evap = ℎ119892 sdot rp evap (30)

The energy of water entering and exiting from the systemboundary (Δ119864

119908

) is

Δ119864119908

= ℎ119891wiwi minus ℎ119891wowo (31)

The ℎ119891wi and ℎ119891wo are the enthalpies ofwater entering and

exiting the pond and wi wo are themass flow rate of waterentering pond The wo is estimated to be the entering watermass flow rate after subtracting the evaporating mass rate

The heat transfer through the back of the panel (back) isa function of the back material thermal conductivity and isgiven by

back = ℎ119887rp119860 rp (119879w rp minus 119879119887) (32)

where 119879119887

is the back layer temperature The ℎ119887 rp is the heat

transfer coefficient between the back layer and the pondwater

ℎ119887 rp =

119870plate

119889119909plate+119870foam119889119909foam

(33)

Two identical panels with the dimensions of 2400mmlong and 900mm wide were constructed from aluminumsheets insulated from the bottom to eliminate the heattransfer from the back side The criteria that determined thepanel size included the aim to make a portable prototype andto minimize the labor As planned the water will flow overthe inclined panels during the night and will be presprayedin one case to evaluate the contribution of water spray overthe panel

3 Results and Discussion

Results presented in the following section are based onthe simulation performance of the described system withTRNSYS software package the standard weather data fileTMY2 based on Australian weather data in summer (2829January) and on the following input data for the systems

(i) total panel area for wet surface Aws = 600m2 WaterTank Volume VT = 250 L

In the simulation the panel is treated as a roof sloped by30∘ facing south The simulation performed in two differentlocations in Australia that is Sydney (humid weather) andAlice Spring (hot and dry area)

The system cold water temperature variation during theassigned simulation period from 2100 hours to 600 hours inthe followingmorning is plotted in Figure 4The pumpwaterflow rate varied in several simulation runs to optimize thesystem performance the results show that the temperature inthe tank dropped to 118∘Cby the end of the period in the clearnight arid conditions of Alice Springs using the open cyclesystem with sprayer However the high relative humidityrates in Sydney compared to Alice Springs (Figure 6)resulted in a less cooling rate in the water as shown inFigure 5 That is mainly related to the reduction of the heattransfer by evaporation (Q evap) from both drop and waterlayer

The convective heat transfer coefficient value from (6) and(24) is proportional to the wind velocity Analysis of windvelocity data (Figure 7) against the storage tank water tem-perature in Figures 4 and 5 indicates that the convection effectadded heat to the water thus minimizing the cooling processby radiation The cloudiness factor (119862clo) for the selected daydid not exceed 019 on average in Sydney and 002 in AliceSprings thus the negative effect of clouds was eliminatedThe analysis of the simulation results built on a simulation


1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank

Figure 4 Water cooling with nocturnal cooling effect in AliceSprings using the system described in this work

10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank

Figure 5 Water cooling with nocturnal cooling effect in Sydneyusing the system described in this work

0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity

Figure 6 Relative humidity rate in the two locations

0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs

Figure 7 Wind velocity in the four locations

571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)

Figure 8 Net sky radiation in two different geographical locations

time step of 10 seconds indicates that the system recordedhigher net sky radiation value in Sydney than that in AliceSpring (Figure 8)This is strongly related to the absence of thehigh evaporation rate of water where the water temperaturehas dropped to a lower value and reduced the temperaturedifference between the water and the sky temperature (usedin (7) and (22))

The net long wave radiations from the radiator panel inthe 2 selected locations are 592Wm2 in Sydney and around47Wm2 in Alice Springs (Figure 8) calculated from (7) and(23) Although the relative humidity in Alice Springs is lowerthan in Sydney the effect of the higher ambient temperaturein Alice Springs reduced the rate of the net sky radiation rate

The storage tank water temperature in both cases was setto a start temperature of 25∘C Lower start-up temperatureresulted in lower storage tank final temperature For examplein Alice Spring weather a start temperature of 22∘C resultedin final temperatures that were 25∘C lower than this for astart temperature of 25∘C But the results show that evenunder unfavourable conditions the systems have the capacityto cover a fraction of the cooling demand Generally the sim-ulations indicate that sufficient radiative cooling is obtainedin periods with modest or above air humidity and ambientnight temperatures cooling below 20∘C in most cases


4 Conclusion

In this research a brief literature review of several researchescovering the phenomenon of long wave radiation to the skywas presented The thermal behaviour of a system utilizingthis technology was described by a detailed mathematicalmodelling These models simulated different climatic condi-tions The simulation results specify that the net long waveradiation to a clear sky on an Australian summer night issufficient to cool the water in a storage tank with a totalvolume of 260 litres to low temperature (as low as to 13degrees lower than the starting temperature of 25∘C) Themathematical modelling and simulation results will be usedin future research to set up experimental prototype systemsto validate the simulation results

Nomenclature

119860119889

Water droplet surface area (m2)119860 rp Panel surface area (m2)119862clo Sky cloudiness factor (mdash)119862119901119908

Specific heat capacity of the water (Jkg K)119862119901119908

Fluid specific heat capacity (Jkgsdot∘C)119863 Droplet diameter (m)119863vap Binary mass diffusion coefficient (m2s)wi Energy added to pond system boundary (kJs)wo Energy leaving pond system boundary (kJs)ℎconv Convective heat transfer coefficient (Wm2 sdot ∘C)ℎ119898 rp The mass transfer coefficient (kgs)ℎ119891119892

Evaporation enthalpy of water vapor (Jkg)ℎrad sky Sky radiation heat transfer coefficient (Wm2sdotk)ℎrp conv Convection heat transfer coefficient (Wm2sdotK)ℎrad Radiative heat transfer coefficient (Wm2 sdot ∘C)119868solar Solar irradiation flux (Wm2)119870amb Ambient air thermal conductivity (WmsdotK)119870 Thermal conductivity of material (Wm2sdotK)119898119889

Mass of the water droplet (kg)evap Water droplet mass evaporation rate (kgs)119898119908 rp Mass of the water in the roof pond (kg)

rp evap Mass evaporation rate (roof pond) (kgs)Nu119871

Nusselt number (mdash)119899 Number of parallel channels in radiator (mdash)119875atm Atmospheric pressure (atm)119875ℎ

Atmospheric pressure at elevation ℎ (atm)119876119888

Convection specific heat transfer (Wm2)cond The heat added by condensed waterSolar Heat due to solar radiation (kJs)conv Convection heat transfer (kJs)rad sky Radiation heat transfer (kJs) (kJs)evap Evaporation heat transfer (kJs)back Heat transfer rate from radiator back (kJs)119876rad Radiative heat exchange (W)Re119883

Reynolds number (mdash)Sh1015840119883

Sherwood number (mdash)119879amb Ambient temperature (∘C)119879dp Dew point temperature (∘C)1198791198891

Droplet initial temperature (K)

1198791198892

Droplet final temperature (K)119879sky Effective sky temperature (K)119879119908 rp Temperature of the water in the pond (K)119880119887

Heat loss coefficients of the panel back (Wm2 sdot∘C)119880119901

Heat loss coefficients of the panel front (Wm2 sdot∘C)119880119903

Radiator overall heat loss coefficient (Wm2 sdot ∘C)119881119908

Wind velocity (ms)119883rp Distance of water flow over the roof pond (m)120576rad The emissivity of radiator plate (mdash)998779119879119889

= (1198791198892

minus 1198791198891

) (K)120576water Water surface emissivity (mdash)120572solar Roof pond solar absorbing (mdash)120590 Stefan-Boltzmann constant (Wm2 sdot K4)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] S Yannas E Erell and J L Molina Roof Cooling Techniques ADesign Handbook Earthscan London UK 2006

[2] A Spanaki ldquoComparative studies on different type of roofponds for cooling purposes literature reviewrdquo in Proceedingsof the 2nd PALENC Conference and 28th AIVC Conference onBuilding Low Energy Cooling and Advanced Ventilation Tech-nologies in the 21st Century Crete Greece September 2007

[3] G N Tiwari A Kumar andM S Sodha ldquoA reviewmdashcooling bywater evaporation over roofrdquo Energy Conversion and Manage-ment vol 22 no 2 pp 143ndash153 1982

[4] R C Bourne and C Carew ldquoDesign and implementation of anight roof-spray storage cooling systemrdquo in Proceedings of theACEEE Summer Study on Energy Efficiency in Buildings Wash-ington DC USA 1996

[5] DOE Technical Installation Review December 1997WhiteCapRoof Spray Cooling System US Department of Energy 1997

[6] Y Man H Yang J D Spitler and Z Fang ldquoFeasibility study onnovel hybrid ground coupled heat pump system with nocturnalcooling radiator for cooling load dominated buildingsrdquo AppliedEnergy vol 88 no 11 pp 4160ndash4171 2011

[7] GHeidarinejadM Farmahini Farahani and S Delfani ldquoInves-tigation of a hybrid system of nocturnal radiative cooling anddirect evaporative coolingrdquo Building and Environment vol 45no 6 pp 1521ndash1528 2010

[8] M Farmahini FarahaniGHeidarinejad and SDelfani ldquoA two-stage system of nocturnal radiative and indirect evaporativecooling for conditions in Tehranrdquo Energy and Buildings vol 42no 11 pp 2131ndash2138 2010

[9] A Y T Al-Zubaydi J Dartnall and A Dowd ldquoDesign con-struction and calibration of an instrument for measuring theproduction of chilled water by the combined effects of evapora-tion and night sky radiationrdquo in Proceedings of the InternationalMechanical Engineering Conference and Exposition (IMECE rsquo12)Houston Tex USA 2012

[10] S AKleinWA Beckman JWMitchell and J ADuffieTRN-SYS 16mdashA Transient System Simulation Program User ManualSolar Energy Laboratory University of Wisconsin MadisonWis USA 2004


[11] P Berdahl and M Martin ldquoEmissivity of clear skiesrdquo SolarEnergy vol 32 no 5 pp 663ndash664 1984

[12] R W Bliss Jr ldquoAtmospheric radiation near the surface of theground a summary for engineersrdquo Solar Energy vol 5 no 3pp 103ndash120 1961

[13] M Martin and P Berdahl ldquoCharacteristics of infrared skyradiation in the United Statesrdquo Solar Energy vol 33 no 3-4 pp321ndash336 1984

[14] D K Kondepudi Introduction to Modern ThermodynamicsJohn Wiley amp Sons New York NY USA 1st edition 2008

[15] W E Ranz and W R Marshal ldquoEvaporation from dropsmdashpartIIrdquo Chemical Engineering Program vol 48 pp 173ndash180 1952

[16] D K Kondepudi Introduction to Modern ThermodynamicsJohn Wiley amp Sons New York NY USA 2008

[17] P F Incropera and PDDeWitt Fundamentals of Heat andMassTransfer John Wiley amp Sons Hoboken NJ USA 5th edition2002

[18] A M Al-Turki and G M Zaki ldquoEnergy saving through inter-mittent evaporative roof coolingrdquo Energy and Buildings vol 17no 1 pp 35ndash42 1991

[19] S S Kachhwaha P L Dhar and S R Kale ldquoExperimental stud-ies and numerical simulation of evaporative cooling of air witha water spraymdashI Horizontal parallel flowrdquo International Journalof Heat and Mass Transfer vol 41 no 2 pp 447ndash464 1998

[20] P Gandhidasan ldquoSimplified model for the behaviour of a roof-spray cooling systemrdquo Applied Energy vol 34 no 1 pp 69ndash771989

[21] S N Kondepudi ldquoA simplified analytical method to evaluatethe effects of roof spray evaporative coolingrdquo Energy Conversionand Management vol 34 no 1 pp 7ndash16 1993

[22] M S Sodha U Singh A Srivastava and G N Tiwari ldquoExperi-mental validation of thermalmodel of open roof pondrdquoBuildingand Environment vol 16 no 2 pp 93ndash98 1981

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Submit your manuscripts athttpwwwhindawicom


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EnergyJournal of


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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


the evaporation heat loss by spraying the water over the roofin the primary stage and the water droplets evaporate asthey travel from the spray outlet to the roof surface Bourneand Carew [4] reported a 47 reduction in annual use ofconventional cooling by using the WhiteCap cooling systemon a 2500-square-meter office building in Los Angeles

The low cooling capacity and the high effectiveness ofambient conditions on the system performance (ie cloudcover and relative humidity) are considered practical lim-itations of the nocturnal cooling by radiation technologyapplications However the system can be applied as a sup-plemental heat sink system with another HVAC system [6]Examples of hybrid systems are presented by Heidarinejadet al [7] and Farmahini Farahani et al [8] Both studiesinvestigated the possible combination of nocturnal radiationcooling systems with conventional systems specifically withan indirect evaporative cooling unit in the first study and adirect evaporative cooling unit in the second

Although the WhiteCap system is available since 1996no theoretical works available present the system mathe-matical modelling In previous work the author presented amathematical modelling of three different systems applyingthe Night sky radiation for water chilling [9] The systemcompared three panels to measure the various effects thefirst panel had a dry radiative surface with an embedded heatexchange water circuit for the purpose of measuring the radi-ant heat The second panel employed a sprayed water flowingover its radiative surface to measure combined effect of (a)heat lost by pre-evaporation during the sprayed water droplettravel through the air (b) evaporation of water flowed overthe radiation surface and (c) radiation from the thin waterlayer surface The third panel is like the second however thewater is running via a gutter at the top so that is flows overthe radiative surface enables the heat loss by radiation andevaporation from a wetted surface The comparison betweenthe three systems shows that the second panel performance isthe best in term of water chilling

In this work the author presented the second system pre-sented in the previous work [9] with a detailed mathematicalmodelling to enable researchers to use it as a design guidefor future work In order to satisfy the above objective it wasdecided to construct a panel having similar principles of theWhiteCap system By using this panel the separate effects ofevaporative cooling and night sky radiative cooling may bededuced from the recorded data In this work we discussedthe design and mathematical modelling of the system (ieradiator panel with sprayer) The system under investigationis described in Figure 1 The layout of the system (Figure 1)consists of a radiator panel with a well-insulated back sidewhich is used to simulate the principles of the system similarto theWhiteCap systemWater is sprayed onto the panel flowfor a measured distance and then returned to the storagetank and pumped again The contact of the water with theair causes mass loss by the evaporation through the processmake-up water to the tank is a necessity The make-up watertemperature is different from the water temperature in thestorage tank and this is considered in the calculations Thewater temperatures in the tank spray nozzle inlet water pondinlet and water pond outlet are the data collected

Radiator paneland

Circulation pump

Water storage tankMake-up

water

Tr1

Tr2

Td

(Arp hfg Cpw)

Vs Ts

120588w Cpw

Figure 1 Experimental setup for the radiative coolingmeasurementsystems-radiator panel with sprayer

This paper discusses the theoretical work of the project bypresenting mathematical modelling and a performance sim-ulation with the Transient System Simulation Tool (TRNSYS)software package [9 10] The results are analysed to optimizethe design parameters and to analyse the contribution ofthe three heat transfer phenomena that occur in differentapplications of cooling water using the night sky radiationeffect We also study the feasibility of producing chilled waterfor space cooling applications The simulation results will beanalysed and compared with the experimental results in alater stage of the project

2 System Description and Modelling

21 The Effective Sky Temperature The heat exchangebetween the radiator plate and the sky occurs in a wavelengthrange of 8 to 14 120583m or what is known as the atmosphericwindowThe sky is considered to be a black body of equivalenttemperature 119879sky or the effective sky temperature In the liter-ature [11ndash13] many equations have been introduced to calcu-late119879sky as a function of the ambient temperature cloudinessfactor and the emissivity of the clear sky which in turn isa function of ambient temperature relative humidity andatmospheric pressure Berdahl andMartin [11 13] introducedan equation to calculate the clear sky emissivity as follows

120576sky = 0711 + 0005119879dp + 73 times 10minus5

1198792

dp

+ 0013 cos [2120587 time24

] + 12 times 10minus5

(119875atm minus 119875ℎ) (1)

where 119879dp is the dew point temperature (∘C) 119875atm is theatmospheric pressure (atm)119875

ℎ

is the atmospheric pressure atelevation ℎ (m) above sea level and the variable (time) is thehour of the day In the TRNSYS software package the Type 69calculates the effective sky temperature 119879sky (K) using Martinand Berdahlrsquos [13] equation as follows

119879sky = 119879amb(120576sky + 08 (1 minus 120576sky) 119862clo)14

(2)

where 119862clo is the sky cloudiness factor (0-1) supplied byTRNSYS Type 69




Δ = total (3)


Δ = 119898119889

sdot 119862119901119908

sdotΔ119879119889

Δ119905 (4)

where 119898119889



119889


1198892


1198891





where



sky minus 1198794

119889

) (7)

evap = evap sdot ℎ119891119892 (8)

Qcon

Qrad

Qevap

Qcond

ΔU






1198791198892

= 1198791198891

+Δ119905

119898119889

sdot 119862119901119908

times [ℎ119888

sdot 119860119889

sdot (119879119886

minus 119879119889

)


sky minus 1198794

119889


(9)

where 1198791198892





where ℎ119898



ℎ119898


Sh1015840119863

= 2 + 06Sc13Re12 (11)


Re =119863119889

119904119889

Vair (12)

where119863119889



Sc =Vair119863vap

(13)


119898

is given by

ℎ119898

=Sh1015840119863

sdot 119863vap

119863 (14)



Qback

ΔUmwohfo mwihfi




Nu =ℎconv119863119889119896air

(15)


Nu = 2 + 06Pr13Re12 (16)


119886


119901119886


Pr =119862119901119886

V119886

119896air (17)


ℎconv =119896air [2 + 06Pr

13Re12]119863119889

(18)



1198892


1198982119904

= 1198981119904

minus (119889

sdot Δ119905 sdot1198981119904

119898119889

) (19)




119898119908 rp sdot 119862119901119908 sdot

119879rp2 minus 119879rp1



(20)




119879rp2 = 119879rp1 +Δ119905

119898119908 rp sdot 119862119901119908



(21)













(25)


119871






119883


ℎ119898 rp =

Sh1015840119883

119863vap

119883rp (27)


Sh1015840119883

= 0644Re12119883

Sc13 (28)


Nu119883

= 0644Re12119883

Pr13 (29)




119908

) is

Δ119864119908






where 119879119887



ℎ119887 rp =

119870plate

119889119909plate+119870foam119889119909foam

(33)









1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity


0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs


571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)






4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















Δ = total (3)


Δ = 119898119889

sdot 119862119901119908

sdotΔ119879119889

Δ119905 (4)

where 119898119889



119889


1198892


1198891





where



sky minus 1198794

119889

) (7)

evap = evap sdot ℎ119891119892 (8)

Qcon

Qrad

Qevap

Qcond

ΔU






1198791198892

= 1198791198891

+Δ119905

119898119889

sdot 119862119901119908

times [ℎ119888

sdot 119860119889

sdot (119879119886

minus 119879119889

)


sky minus 1198794

119889


(9)

where 1198791198892





where ℎ119898



ℎ119898


Sh1015840119863

= 2 + 06Sc13Re12 (11)


Re =119863119889

119904119889

Vair (12)

where119863119889



Sc =Vair119863vap

(13)


119898

is given by

ℎ119898

=Sh1015840119863

sdot 119863vap

119863 (14)



Qback

ΔUmwohfo mwihfi




Nu =ℎconv119863119889119896air

(15)


Nu = 2 + 06Pr13Re12 (16)


119886


119901119886


Pr =119862119901119886

V119886

119896air (17)


ℎconv =119896air [2 + 06Pr

13Re12]119863119889

(18)



1198892


1198982119904

= 1198981119904

minus (119889

sdot Δ119905 sdot1198981119904

119898119889

) (19)




119898119908 rp sdot 119862119901119908 sdot

119879rp2 minus 119879rp1



(20)




119879rp2 = 119879rp1 +Δ119905

119898119908 rp sdot 119862119901119908



(21)













(25)


119871






119883


ℎ119898 rp =

Sh1015840119883

119863vap

119883rp (27)


Sh1015840119883

= 0644Re12119883

Sc13 (28)


Nu119883

= 0644Re12119883

Pr13 (29)




119908

) is

Δ119864119908






where 119879119887



ℎ119887 rp =

119870plate

119889119909plate+119870foam119889119909foam

(33)









1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity


0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs


571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)






4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Qback

ΔUmwohfo mwihfi




Nu =ℎconv119863119889119896air

(15)


Nu = 2 + 06Pr13Re12 (16)


119886


119901119886


Pr =119862119901119886

V119886

119896air (17)


ℎconv =119896air [2 + 06Pr

13Re12]119863119889

(18)



1198892


1198982119904

= 1198981119904

minus (119889

sdot Δ119905 sdot1198981119904

119898119889

) (19)




119898119908 rp sdot 119862119901119908 sdot

119879rp2 minus 119879rp1



(20)




119879rp2 = 119879rp1 +Δ119905

119898119908 rp sdot 119862119901119908



(21)













(25)


119871






119883


ℎ119898 rp =

Sh1015840119883

119863vap

119883rp (27)


Sh1015840119883

= 0644Re12119883

Sc13 (28)


Nu119883

= 0644Re12119883

Pr13 (29)




119908

) is

Δ119864119908






where 119879119887



ℎ119887 rp =

119870plate

119889119909plate+119870foam119889119909foam

(33)









1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity


0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs


571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)






4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of























(25)


119871






119883


ℎ119898 rp =

Sh1015840119883

119863vap

119883rp (27)


Sh1015840119883

= 0644Re12119883

Sc13 (28)


Nu119883

= 0644Re12119883

Pr13 (29)




119908

) is

Δ119864119908






where 119879119887



ℎ119887 rp =

119870plate

119889119909plate+119870foam119889119909foam

(33)









1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity


0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs


571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)






4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















1012141618202224262830

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


10

12

14

16

18

20

22

24

26

21 22 23 24 1 2 3 4 5 6Time t (hr)

Tem

pera

ture

T (C

)

T ambT tank


0

20

40

60

80

100

21 22 23 24 1 2 3 4 5 6

RH (

)

SydneyAlice Springs

Time t (hr)

Relative humidity


0

2

4

6

8

10

21 22 23 24 1 2 3 4 5 6

Win

d (m

s)

Time t (hr)

SydneyAlice Springs


571

446

0

10

20

30

40

50

60

SydneyAlice Springs

(Wm

2)






4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















4 Conclusion


Nomenclature

119860119889













1198791198892






= (1198791198892

minus 1198791198891




References




























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















research article design and modelling of water chilling...

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