Research Article Modeling Solar Energy Transfer through ...downloads.hindawi.com/archive/2013/480137.pdfISRN Renewable Energy e roof thermal model Solar radiation Sun ( E ) e Conduction

Hindawi Publishing CorporationISRN Renewable EnergyVolume 2013 Article ID 480137 8 pageshttpdxdoiorg1011552013480137

Research ArticleModeling Solar Energy Transfer through Roof Material inAfrica Sub-Saharan Regions

Julien G Adounkpe1 A Emmanuel Lawin2 Cleacutement Ahouannou3

Rufin Offin Lieacute Akiyo4 and Brice A Sinsin1

1 Laboratory of Applied Ecology Faculty of Agronomic Sciences University of Abomey Calavi 03 BP 3908 Cotonou Benin2 Laboratory of Applied Hydrology Faculty of Sciences and Technologies University of Abomey Calavi UAC BP 526 Benin3 Laboratory of Applied Energetic and Mechanics Ecole Polytechnique drsquoAbomey Calavi University of Abomey Calavi03P 1175 Cotonou Benin

4Department of Geography University of Parakou BP 123 Benin

Correspondence should be addressed to Julien G Adounkpe julvictoireyahoocom

Received 29 July 2013 Accepted 28 August 2013

Academic Editors F E Little and M Souliotis

Copyright copy 2013 Julien G Adounkpe et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

As a result of the global warming the atmospheric temperature in sub-Saharan regions of Africa may drastically increase thusworsening the poor living conditions already experienced by people in those regions Roof rsquos thermal insulation capacity mayplay key role in reducing indoor thermal comfort cost In the present study effort is put to model heat transfer through roofsin south Saharan regions Validation of the model was achieved using the slightly sloppy galvanized aluminum-iron sheet roofAtmospheric data were hourly measured during April and June in Ouagadougou Burkina Faso Solar energy values increase from2450 plusmn 050Wm2 in the morning to a maximum of 9001 plusmn 08Wm2 in the early afternoon Ambient temperature follows thesame trend as solar radiation with a maximum at 400plusmn02∘CWind speed varies from 05 to 40plusmn01msThemeasured roof innerwall temperatures agreed excellently with the developed model with a Nash-Sutcliffe Coefficient of Efficiency of 0988 Energy fluxentering the room through the roof varies from 631 plusmn 03Wm2 earlier in the morning to a maximum of 1153 plusmn 05Wm2 in theearlier afternoon These results shall help to better design human habitat under changing climate conditions in the sub-Saharanregions

1 Introduction

Ever since the appearance of human beings on earth besidefood and other basic needs shelters or dwelling places havebeen of major preoccupation Human beings have set uptheir homes utilizing materials from the nature To protectthemselves from rain heat wind cold snows or any sortof enemies human beings have invented at very early ageshabitat which has evolved from the caves natural physicaldwellings to the modern houses known today [1] One of themost important elements of a house is its roof Indeed insub-Saharan countries and most countries on the earth roofmust stand rainy seasons and during periods of elevated heatmust provide certain comfort [2]The effectiveness of the roofin terms of comfort and sustainability requires the thermal

insulation capacity and the mechanical strength of materialsemployed

The shapes of roof are adapted to the type of climateof a given region [3] Over the world there are more than30 types of roof [4] Moreover many factors contribute tothe differences among the types of roof The most importantfactors are the technology the materials the environmentand the mere habit [4] For instance plat roof dominates indry regions while cone shape roof dominates in semi-dryregions such as some parts of Africa Short eaves gable rooftype is widely observed both in Europe and North Americawhile deep eaves are dominant in Masson Asia [4]

Over ages as human shelters roofs have evolved fromwhat was then called traditional roofing to what is knownnowadays to be the modern roofing In most sub-Saharan

2 ISRN Renewable Energy

countries traditional roofing is still at use most importantlyin rural areas

Traditional roofs made of indigenous or local materialssuch as woods for stands or frames and straws (Figure 1)leaves or herbs and so forth for covertures have thermalisolation properties Their main drawback is their relativelyshort life which forces the users to rebuild basically almostafter every rainy season [2]

Modern roofs are made of metal sheets (Figure 2) rein-forced concrete and so forth Iron aluminum and zinc mostoften protected against wear are used as roof coverings andhave mechanical resistances characterized by their relativelylong life Galvanized iron sheet finds use in developing worldbasically where high rainfall is registered annually [5] Themain handicap of the modern roofing is their low isolationcapacity

In the light of climate change and all its adverse effects andgiving the fact that increasing number of houses are adoptingthe modern roofing along with high thermal comfort costcombining traditional roofing and modern roofing at onehand andmodifyingmodern existing roofs on the other handto get indoor comfort at an affordable cost are of interest[6]

Green or vegetative roofs are in use in several Europeanand American countries [7] Several problems notably thethermal isolation leading to the reduced energy consumptionand energy conservation [8] and noise reduction are solvedby green roofing [9] However those benefits linked to greenroofs are more significant for extremely compact tropicalcities with severe shortage of ground-level green spaces andintense Urban Heat Island effects [10 11]

Moreover green roofing is not much in use in southSaharan regions for several reasons First those regions haveno space problem and there are few compact cities wheresuch a technique could be deployed Second the constructionand the maintenance costs of those green roofing are waybeyond what people in those regions could bear

Climate change is a challenging situation to humanhabitat as far as their thermal comfort in houses In adry and hot climate of Mexicali in Mexico a city of sameclimate characteristics as Ougagougou where the presentstudy was conducted a field study was done consisting onthe determination of electrical energy consumption of lowincome dwellers and their perception of thermal comfort inaccordance with the design and the building material [12]

Sustainable buildings have been designed by architects forthe improvement of indoor environmental quality basicallyincluding the provision of comfortable temperatures andhumidities The usersrsquo perceptions of thermal comfort hadbeen surveyed in 36 sustainable commercial and institutionalbuildings in 11 countries [13] The focus of those studiesamong others was the overall thermal comfort in buildingsHowever few studies deal with the specific thermal contribu-tion of the roof to the house The possibility of roof light forindoor comfort was explored in order to design an innovativeroofing system for the tropics with plenty of sunshine andhigh humidity [14]

In recent years great interests have been noticed inthe field of solar radiation modeling Models have been

Figure 1 Traditional roofing in South Sahara AfricaThe roof coveris made of straws and needs to be renewed after each rainy season

Figure 2 Typical modern roof type in Sub-Sahara Africa Most ofthe roofs are made of metal sheets basically iron sheet with slightslope and oriented south

developed to evaluate both global and diffuse solar radiationsEmploying a sensor FLA613-GS that gives direct currentproportional to global radiation the global solar radiancewasevaluated [15] In 2011 an estimation of diffuse solar radiationon horizontal plane was performed in three cities of Nigeriain west Africa Correlation between the clearance index andthe diffuse to global solar radiation ratio was employed inthe estimation of the diffuse radiation The model efficiencyis proven worldwide according to the authors [16] Further-more real time monitoring of global solar radiation wasachieved designing a model of TCPIP with an embeddedinternet based data acquisition system [17] Even thoughscientists in the field of solar energy have developed modelsto monitor solar radiation in the literature to the best of ourknowledge it was not possible to see effort related to roofmodeling linked to solar energy in the south Saharan regionof Africa

The present study aims at modeling heat transfer throughroofs in sub-Saharan region in order to predict the roofcontribution to the overall heat of the room and to selectroof materials that lower comfort cost in those regions whereabout 70 of the room overall heat comes from the roof [18]

2 The Roof Thermal Model

As it is known a model is meant to be the simplest way oflooking at a complex phenomenon The conceptualization of

ISRN Renewable Energy 3

The roof thermal model

Solarradiation

Sun (E)

e Conduction

Radiation (Ts)Convection (Ta)

Tpe

Tpi

Tr

Figure 3 Model of heat flux exchanged between the roof and itssurroundings where 119890 = thick of the sheet or roof 119879r = temperatureof the room 119879a = ambient temperature 119879s = temperature of thesky 119879pe = the roof outer wall temperature 119879pi = the roof inner walltemperature and 119864 = solar radiation

the heat flux through the roof of a house can be expressed asfollows (Figure 3)

120593 = incoming flux minus out going flux

120593 =120582

119890(119879pe minus 119879pi)

(1)

where

120593 is the heat flux through the roof

120582 the thermal conductivity of the sheet (roof)

119890 is the thick of the sheet

119879pe and119879pi the external and internal wall temperaturerespectively

In fact 119879pe and 119879pi are obtained through studious math-ematical calculations that require an energy balance to beestablished at the interfaces atmosphere-roof and roof-room

A roof exposed to the solar radiation 119864 is the center ofthree modes of heat transfer conduction convection andradiation

When there is between two bodies a temperature gra-dient heat travels from the hotter to the colder thus thedifference tends to resolve spontaneously Essentially trans-fers between two bodies implement three distinct processessimultaneous or not conduction convection and radiation

21 Conduction Two bodies at different temperaturesbrought into contact exchange heat by conduction where theheat flows from the hottest to the coldest In the case of thepresent study heat flows within the roof body from the outerwall to the inner wall of the roof due to the temperaturegradient between the external and the internal walls of theroof

22 Convection When a body and a fluid (water air etc) atdifferent temperatures are in contact there is heat exchangeby forced convection (when the speed of circulation of thefluid is imposed) or natural (otherwise)

23 Radiation Any living or inanimate object whose temper-ature is above absolute zero (minus27315∘C) emits electromag-netic radiations that carry a certain amount of energy Tworemote objects exchange heat by emission or radiation Thesun is object of such a radiation towards the earth and theother planets

A roof exposed to the solar radiation is the center ofthermal exchanges characterized by the following thermalcoefficients

(i) Coefficient of Thermal Conductivity 120582 It represents theamount of heat which passes through the body per meter in asecond for a temperature difference of 1∘C Its unit isWm∘C

A material will be more heat conductor as its coefficientof thermal conductivity is high

(ii) Absorption Coefficient 120576po It represents the fraction ofsolar radiation absorbed by the roof 120576po is unitless

(iii) Emissivity The roof has the property of emitting partof radiation received towards the sky and towards the roomcharacterized respectively by emissivity coefficients 120576

119890and 120576119894

These coefficients characterize the radiation in the infrared

(iv) Coefficient of Convection h It characterizes the heatexchange and represents the flow per unit area of contactand degree (Wm2∘C) ℎ

119894for internal convection and ℎ

119890for

external convection

24 Adjacent Fluids to the Roof At both sides of the roofthere is heat exchange between the roof and the room air andthe atmospheric air characterized by physical parameters (120582

119890

119862pe 120588119890 120583119890) and a flow velocity

3 Energetic Balance of the Roof

The roof exchanges heat with its surroundings as it receivessolar radiation 119864

(i) At the Roof External Wall Consider

120593abs = 120576119890 sdot 119864

120593lostconv 119890 = ℎ119890 sdot (119879pe minus 119879a)

120593lostrad 119890 = 120590 sdot 120576119890 sdot (1198794

pe minus 1198794

S )

(2)

(ii) Heat Recovered from the Roof (Material) by ConductionConsider

120593cond =120582

119890sdot (119879pe minus 119879pi) (3)

(iii) At the Roof Internal Wall Consider

120593lostconv 119894 = ℎ119894 sdot (119879pi minus 119879room)

120593lostrad 119894 = 120590 sdot 120576119894sdot 119878 sdot (119879

4

pi minus 1198794

room) (4)


(iv) Heat Balance on the Roof One has

120593119890= 120593abs = 120593lostconv 119890 + 120593lostrad 119890 + 120593cond (5)

120576119890sdot 119864 = [ℎ

119890sdot (119879pe minus 119879a) + 120590 sdot 120576119890 sdot (119879

4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

(6)

120593119904= 120593recover room = 120593

119892+ (120593lostconv 119894 + 120593lostrad 119894) (7)

Knowing that 120593119892= 119874

120593recover room = 120593cond = 120593lostconv 119894 + 120593lostrad 119894 (8)

120582

119890sdot (119879pe minus 119879pi) = [ℎ119894 sdot (119879pi minus 119879room) + 120590 sdot 120576119894 sdot (119879

4

pi minus 1198794

room)]

(9)

Combining (6) and (9) leads to the system of twoequations where the unknowns are 119879pe and 119879pi both areraised to power 1 and 4

120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

120582

119890sdot (119879pe minus 119879pi) = [ℎ119894 sdot (119879pi minus 119879room)

+120590 sdot 120576119894sdot (1198794

pe minus 1198794

room)]

(10)

31 Modeling ℎ119890 ℎ119890is the external convection coefficient

between the outside ambient air and the roof We madethe assumption that this exchange is governed by forcedconvection because for simplicity the external wind speedis maintained constant for a defined time slot Thus thefollowing formulas were used to evaluate

ℎ119890= 57 + 38119881 for 119881 le 4ms

ℎ119890= 75119881

08 for 119881 gt 4ms(11)

where 119881 is the velocity of the wind

32 Modeling ℎ119894 The roof internal side exchanges heat with

the room by natural convection with air inside the roomwithhi which is the convection coefficient given by

ℎ119894=(Nu sdot 120582

119890)

119871 (12)

where Nu is Nusselt number 119871 is length of the roof and 120582119890is

thermal conductivity of the air Out of these three parametersonly119871 can be easily knownTheNusselt number value is givenby the correlation

Nu = (Gr sdot Pr)119898 (13)

where Gr is Grashof number Pr is Prandtl number and 119860and119898 are constants Pr and Gr given for air are respectivelyPr asymp 07 and Grashof number can be calculed by

Gr =120573119892Δ120579120588

2

1198901198713

1205832

119890

(14)

where 120573 is the inverse of the average temperature of the airfilm Δ120579 is temperature difference between the air film andthe roof internal wall 120582

119890is thermal conductivity of the air 120588

119890

is density of air film (Kgsdotmminus3) 120583119890is dynamic viscosity of the

air (Nsdotmminus2sdotSminus1) and 119892 = 981ms2 is gravity intensity120582119890 120588119890 and 120583

119890are tabulated values of the air for a

given air temperature film work For the convenience of thenumerization the air characteristics were linearized and therelationships found are directly used in the program

33 Modeling 120582119890 120588119890 and 120583

119890 Here we give the linear relation-

ships obtained after linear regression in regression domainsquite correct (119903 rarr 1 minus1 minus099 099) (in Kgm3)

120582119890

=

1825 times 10minus4+ 815 times 10

minus6119879 for 200 le 119879 lt 300


minus6119879 for 300 le 119879 lt 350


minus6119879 for 350 le 119879 le 400

120588119890

=

2 9300 minus 59 10 times 10minus4119879 for 200 le 119879 lt 300


1 8058 minus 23 08 times 10minus4119879 for 350 le 119879 le 400

120583119890

=


minus9119879 for 200 le 119879 lt 300


minus9119879 for 300 le 119879 lt 350


minus9119879 for 350 le 119879 le 400

(15)

where 119879 (in K) is the temperature of the air film estimated at119879 = 119879r + 10 during day time and 119879 = 119879r minus 5 at night

34 Modeling 119879s the Temperature of the Sky Estimation ofthe temperature of the sky can be achieved through threedifferent formulae depending on the atmospheric conditions

119879s = 119879a minus 12 or 119879s = 120576119879a14 (16)

120576 is emissivity of the sky which can take two forms

120576 = 1 minus 0161 sdot exp [minus000077 (119879a minus 273)]2

or 120576 = 0787 minus 0764 ln(119879v273

)

(17)

where 119879v is the vapor temperatureOf those three formulas the second one was found to fit

the best the overall model taking into account the level of


error acceptability Hence to evaluate the temperature of thesky the present model uses the following 119879s equation

119879s = [1 minus 0161 sdot exp [minus000077 (119879a minus 273)]2

] 119879a14 (18)

4 Method and Material

41 Study Area

411 Climate The study was conducted near the Universityof Ougadougou Ouagadougou Burkina Faso a city knownto be located in the Soudano-Sahelian zone The climate ischaracterized by a unimodal precipitation regime with arainfall of about 600mm per year Rainfall events are mainlygenerated by the dynamic of the West African Monsoon(WAM) The rainy season stretches from mid-May to mid-October with an average temperature of 30∘C But the keyperiod is known to be June-July-August-September (JJAS)which totalized more than 80 of the seasonal rainfall Thecold season runs fromDecember to January with aminimumtemperature of 19∘C The maximum temperature during thehot season which runs from March to May can reach 45∘CThe harmattan a dry and cold wind from late Novemberto mid-February blows north-east with a high temperaturegradient between daytime and night that can reach Relativeair humidity varies from 20 in March during dry season to80 in August during rainy season with a mean of 49 [19]This provides thermal comfort even with high temperatures

412 Study Sites The study was undertaken at a site locatedinside the campus of the University of Ouagadougou wherethe study materials were installed The geographic character-istics of the site are as follows 12∘221015840461910158401015840N 1∘291015840587710158401015840Oand elevation 295m

42 Material The experimental boxes are made of wood ontop of which galvanized iron sheets cover is placed to serveas the roof The boxes were put at a height of 1m above theground at points where no influence from building shadetrees or other can affect the measurements

43 Solar Radiation Measurement For the solar radiationmeasurement several equipments are available depending onthe type of solar radiation of interest either global diffuseor direct Global solar radiation is the sum of the direct andthe diffuse The versatile CM-11 pyranometer was used tomeasure the global radiation in Finland Estonia Poland andSweden the pyranometer PP-1 for the diffuse one and theactinometer AT-50 for the direct solar radiation in Latviaand Lithuania [20] Those are very high technology thatwas not available to us at the moment of the experimenta-tion However we used a CMP-pyranometer that fulfils therequirements of IEC 61215 and IEC 60904-X for the accuratemeasurement of irradiance for photovoltaic and thermal solardevicesThat pyranometer was used as reference instrumentsto test and certify PV cells for power plant projects It wasproven very accurately and efficient That instrument wasplaced close to the box at the same height from the ground

Table 1 Solar radiation SR (Wm2) wind speed V (ms) andambient temperature are recorded on an hourly basis

Time Solarradiation (E)

Wind speed(V ms)

Ambienttemperature(119879a∘C)

700 1300 10 275800 3542 20 317900 6307 30 3391000 7759 30 3571100 8533 30 3741200 9001 30 3841300 8481 20 3971400 7519 20 4001500 5722 20 4051600 3393 20 3991700 1062 20 3921800 175 20 370

44 Temperature Gauges Temperature gauges were posi-tioned everywhere needed the ambient temperature theroom temperature the external and internal roof wall tem-peratures and so forthThe ambient temperature ismeasuredat a height of 5m above the ground The gauges wereelectrically connected to the temperature sensor that givesa simultaneous read-out of all temperatures with decimalabsolute error

45 Wind Speed Measurement Two main types of instru-ments that measure wind speed are the rotating cupanemometer and the propeller anemometer Both types ofanemometers consist of two subassemblies the sensor andthe transducer The sensor is the device that rotates by theforce of the wind The transducer is the device that generatesthe signal suitable for recording Most of the time the signalneeds to be conditioned by signal conditioner and displayedby loggers and recorder In the present study the rotating cupanemometer was employed

5 Results and Discussion

The atmospheric parameters recorded were solar irradiationwind speed and ambient temperature Those parameterswere recorded hourly during April and June on clear skydays A typical set of measurements is reported in Table 1

It is very important to understand that the measurementswere done on a regular basis of one hour interval for 24 hoursa day The data shown in Table 1 and the following are just anextraction of the one for which solar energy was not null andthat the solar influence can be observed on the temperaturesIn fact from 7 pm to 6 am solar radiation was zero

The bands between 15∘ and 35∘ north and south aroundthe earth receive the greatest amount of solar energy [21]but the equatorial belt between 15∘N and 15∘S latitude is themost irradiated Burkina Faso Mali Niger and the northernpart of Benin Togo and Nigeria inWest Africa are located in


Table 2 Ambient temperature (119879a) solar irradiance (SR) windspeed (V) and the galvanized ion sheet roof room temperature (119879r)the roof inner wall temperature measured (119879pim) and simulated(119879pis) and energy flux entering the room were reported

Time(H)

119879a(∘C)

SR(Wm2)

V(ms)

Al-Fe119879r 119879pim 119879pis Flux

830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)

Solar direct radiation and ambient temperature versus time

Solar radiationAmbient temperature

Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)

Figure 4 Solar direct radiation (Wm2) and ambient temperature(∘C) recorded at a typical clear sky day of April

these regions [22] Consequently those countries are subjectto important solar irradiance and thus have high solar energypotentials

The solar radiation variation observed and registered inthe present study is in accordance with the one observedin various cities of Nigeria [16] and elsewhere [23ndash25] eventhough solar irradiance is latitude dependent At higherlatitudes gt than 25∘ high radiations can be observed as proofof high potential solar energy availability for various solarenergy applications For example a 5-year cumulative annualglobal solar radiation was found to be 1693Kwhm2dayin Spain (latitude 42∘N 49∘W) and 1841 Kwhm2day inMalta (latitude 36∘N 145∘E) where June and July are themonths that receive the greater sunshine [26] giving theproof that solar radiation decreases with the latitude and

determines the regional houses architecture [14] Radiationdata recorded at 12 sites around the central part of theBaltic Sea (latitude varies from 54∘N 15∘E to 61∘N 24∘E)from 1996 to 2000 showed June to be the month of highestsolar radiation in most part of the region with an averagedaily total of 209MJm2 at Visby (5769∘N 1835∘E) [20]However hourlymeasurements literature data are the ones tocompare those of the present study with Hourly monitoringof ambient temperature solar global or direct radiation isan important mean for engineers and building designers toselect construction materials that correspond to the specificclimate Such reports are rather scarce while yearly monthlyand daily mean values are the most reported in the literature[14 21 26] In a study conducted in Ajaccio France ambienttemperature solar irradiance wind speed and direction andso forth were recorded every minute A perfect relationshipbetween the instantaneous increases of ambient temperatureand solar irradiance is observed (Table 2) Both curvesambient temperature and solar irradiance well shaped ina Gaussian like form present their respective maximum atabout 1pm [25] unlike their counterparts of the presentstudy where there is a gap of about 2 hours between themaximum of the solar irradiance (1pm) and the ambienttemperature (3pm) This can be explained by the presenceof dust (fine particles) in the air hindering the ambientair to cool down as the sun is setting causing a delay ofapproximately 2 hours between the solar irradiance and theambient temperature

Hourly mean temperatures of modern roofs are reported[14] However the solar irradiance on which depends thetemperature behavior was not reported Interesting enoughthe Gaussian shape was observed and the maximum indoortemperatures for various roofs were reached by 2 pm bysome roofs and 4 pm by othersThese results are in line withwhat we obtained for the validation of the model employingthe galvanized iron sheet (Figure 4) The room temperatureincreases from 375∘C at 830 am to reach a maximumvalue of 401∘C by 300 pm and decreases to 380∘C by600 pm having the same trend as the solar irradiance whichincreases from426Wm2 by 830 am to reach amaximumof8538Wm2 by noon and decreases to 30Wm2 The 2-hoursgap between the maximums of the ambient temperature andthe solar irradiance was observed However this gap was notobserved between the room temperature the roof inner walltemperature and the solar irradiance A temperature gradientof about 20∘C was observed between the room temperatureand the roof inner wall temperature giving the proof thata substantial gradient of temperature can be achieved ifsubsequent ceiling was made in buildings

A similar study conducted [24] shows similar relation-ships between solar irradiance and ambient temperaturewhere the maximal solar irradiance of 430 Wm2 attainedat 100 pm shift with the ambient temperature maximumof 466∘C observed at 200 pm In contrary while the roomtemperature in the present study is quite different from theambient temperature the one from [24] observed was similarto the ambient temperature The difference comes from theventilation of the room while in the present no ventilation


Simulated temperatures versus measured temperature

30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)

Temperature of the roomMeasured roof inner wall temperatureSimulated roof inner wall temperature

Tem

pera

ture

s (∘C)

Figure 5 This graph shows a perfect agreement between simulatedroof inner wall temperatures in green (119879pis) andmeasured roof innerwall temperatures in red (119879pim) the temperature of the room is inblue

is done As it is known ventilation reduces temperatureThisexplains the observed phenomenon

More importantly the measured and simulated tem-peratures of the roof inner temperature were comparedFigure 5 not only shows a gap of 20∘Cmaximum between theroof temperature and the room temperature but also moreimportantly the similarity between simulated and measuredroof inner wall temperatures

51 Model Calibration and Verification for Validation Amodel is always a simplification of the complex reality ofnatural phenomenaThis simplification has the merit of bothrepresenting the reality in all its extent and keeping acces-sibility and understandings to those not very well acknowl-edgeable of the given field However the constructed modelmay not be capable of producing a response that is entirelyin line with the behavior of the observed phenomenon [27]Therefore a model after being elaborated needs to be testedwith the whole set of data that are available is in short themodel needs to be calibrated The calibration of a modelrequires that the overall complexity of the mechanism underinvestigation to be taken into account [28]

For the calibration of the present model a suitable rangeof error acceptability has been adopted after several trialsThe linearization of the tabulated temperatures to fill in thesoftware made for the model the temperature of the airfilm the sky temperature and other parameters in a repeatediterative process were achieved Even the parameters assumedto be invariant were changed to see how well the modeladjusts to them [28]

The verification procedure tests the entire reality of thephenomenon The final step is the validation which entails abroader set of data and possibly allows comparisonwith othermodels dealing with the same observationsModel validationis related to the process of decision making Thus the currentmodel has been validated and can serve as a successful toolin the hands of experienced acknowledgeable persons in thefield

The qualitative model performance assessment isachieved employing some statistical criteria to compare thedata from the measurements and the one produced by themodel These statistical criteria are considered objective andprovide unbiased indicators of the model performance [28]The lower the Mean Absolute Error or the Bias Percentagevalue the better the performance of the model Howeverthe Root Mean Square Error (RMSE) which measures thescatter of the residuals or the Relative Root Mean SquareError which is the normalized RMSE is more expressive thanthe two others In our study the RMSE is calculated usingthe following formula

RMSE = [

[

sum119873

119894=1(119876

mod119894

minus 119876meas119894

)2

119873

]

]

12

(19)

The RMSE value computed shows the closeness of the modelto experimental data

Furthermore the Nash-Sutcliffe Coefficient of Efficiency(NSE) defined as follows

119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)

where 119883obs is observed values and 119883model is modeled valuesat time 119868 is generally used to quantitatively describe theaccuracy of model outputs The closer the model efficiencyis to 1 the more accurate the model is The computed NSEvalue for the present model efficiency (0988) confirms thatthe theoretical formulation proposed here for the roof innertemperature is realistic

6 Conclusion

The present study has the merit of establishing for thefirst time in West Africa relationships between direct solarradiation at ground level and atmospheric temperature andbetween atmospheric temperature and indoor temperatureThe model that is developed will be of great interest totropical buildings designers climate engineers and anyoneinterested in indoor comfort cost-benefit analysis in theline of global warming Further studies are underway to testvarious materials used as roof covers in sub-Saharan regionof Africa

Acknowledgments

The authors are thankful to la Cooperation Francaise forthe partial support to this study and the former Ecole Inter


Etats des Ingenieurs de lrsquoEquipement Rural for providing thecomfortable working environment

References

[1] J M Jahi K Aiyub K Arifin and A Awang ldquoHuman habitatand environmental change from cave dwellings to megacitiesrdquoEuropean Journal of Scientific Research vol 32 no 3 pp 381ndash390 2009

[2] GRET Toitures en Zones Tropicales Arides vol 1 SOFIAC ParisFrance 1984

[3] GRET Bioclimatisme en Zone Tropicale Construire avec leClimat SOFIAC Paris France 1986

[4] M Ueda ldquoRoof types visualisation for human habitats indi-catorrdquo Department of Computor Software University of Aizu(unpublished)

[5] A E Obia H E Okon S A Ekum E E Eyo-Ita and EA Ekpeni ldquoThe influence of gas flare particulates and rainfallon the corrosion of galvanized steel roofs in the Niger DeltaNigeriardquo Journal of Environmental Protection vol 2 pp 1341ndash1346 2011

[6] X Bai ldquoIntegrating global environmental concerns into urbanmanagement the scale and readiness argumentsrdquo Journal ofIndustrial Ecology vol 11 no 2 pp 15ndash29 2007

[7] K Veisten Y Smyrnova R Klaeligboe M Hornikx M Mosslemiand J Kang ldquoValuation of green walls and green roofs assoundscape measures including monetised amenity valuestogether with noise-attenuation values in a cost-benefit analysisof a green wall affecting courtyardsrdquo International Journal ofEnvironmental Research and Public Health vol 9 no 11 pp3770ndash3788 2012

[8] K S Liu S L Hsueh W C Wu and Y L Chen ldquoA DFuzzy-DAHP decision-making model for evaluating energy-savingdesign strategies for residential buildingsrdquo Energies vol 5 no11 pp 4462ndash4480 2012

[9] T Takakura S Kitade and E Goto ldquoCooling effect of greenerycover over a buildingrdquo Energy and Buildings vol 31 no 1 pp1ndash6 2000

[10] C Y Jim ldquoGreen-space preservation and allocation for sustain-able greening of compact citiesrdquoCities vol 21 no 4 pp 311ndash3202004

[11] C Y Jim ldquoEcological design of sky woodland in compact urbanHong Kongrdquo inGreening Rooftops for Sustainable Communitiespp 1ndash15 Green Roofs for Healthy Cities Baltimore Md USA2008

[12] R A Romero G Bojorquez M Corral and R GallegosldquoEnergy and the occupantrsquos thermal perception of low-incomedwellings in hot-dry climate Mexicali Mexicordquo RenewableEnergy vol 49 pp 267ndash270 2013

[13] G Baird and C Field ldquoThermal comfort conditions in sus-tainable buildingsmdashresults of a worldwide survey of usersrsquoperceptionsrdquo Renewable Energy vol 49 pp 44ndash47 2013

[14] K M Al-Obaidi M Ismail and A M Abdul Rahman ldquoAninnovative roofing system for tropical building interiors sep-arating heat from useful visible lightrdquo International Journal ofEnergy and Environment vol 4 no 1 pp 103ndash116 2013

[15] ZDostalM Bobek and J Zupa ldquoThemeasuring of global solarradiancerdquo Acta Montanistica Slovaca vol 13 no 3 p 357 2008

[16] M S Okundamiya and A N Nzeako ldquoEstimation of diffusesolar radiation for selected cities in Nigeriardquo IRSN RenewableEnergy vol 2011 Article ID 439410 6 pages 2011

[17] S Awasthi and P Mor ldquoWeb based measurement system forsolar radiationrdquo International Journal of Advanced ComputerResearch vol 2 no 4 pp 2277ndash7970 2012

[18] K C K Vijaykumar P S S Srinivasan and S Dhandapani ldquoAperformance of hollow clay tile (HCT) laid reinforced cementconcrete (RCC) roof for tropical summer climatesrdquo Energy andBuildings vol 39 no 8 pp 886ndash892 2007

[19] L L BayalaMonographie de la Ville de Ouagadougou Ministerede lrsquoEconomie 2009

[20] S Keevallik andK Loitjarv ldquoSolar radiation at the surface in theBaltic Properrdquo Oceanologia vol 52 no 4 pp 583ndash597 2010

[21] J A Duffie Solar Engineering of Thermal Processes JohnWilleyamp Sons New York NY USA 1980

[22] F Kreith and J F Kreider Principles of Solar EngineeringHemisphere Publishing New York NY USA 1978

[23] S I Khan and A Islam ldquoPerformance analysis of solar waterheaterrdquo Smart Grid and Renewable Energy vol 2 pp 396ndash3982011

[24] V H Hernandez-Gomez J J Contreras Espinosa D Morillon-Galvez J L Fernandez-Zayas and G Gonzalez-Ortiz ldquoAnalyt-ical model to describe the thermal behavior of a heat dischargesystem in roofsrdquo Ingeniera Investigacion y Tecnologia vol 3 no1 pp 33ndash42 2012

[25] F Motte G Notton C Cristofari and J-L Canaletti ldquoA build-ing integrated solar collector performances characterizationand first stage of numerical calculationrdquo Renewable Energy vol49 pp 1ndash5 2013

[26] C Yousif G O Quecedo and J B Santos ldquoComparison ofsolar radiation in Marsaxlokk Malta and Valladolid SpainrdquoRenewable Energy vol 49 pp 203ndash206 2013

[27] R LDoneker T Sanders A Ramachandran KThompson andF Opila ldquoIntegrated modeling and remote sensing systems formixing zone water quality managementrdquo in Proceedings of the33rd IAHR Congress Vancouver Canada 2009

[28] M Benedini andG TsakirisModel Calibration andVerificationPrintforce Alphen aan den Rijn The Netherlands 2013

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


countries traditional roofing is still at use most importantlyin rural areas

Traditional roofs made of indigenous or local materialssuch as woods for stands or frames and straws (Figure 1)leaves or herbs and so forth for covertures have thermalisolation properties Their main drawback is their relativelyshort life which forces the users to rebuild basically almostafter every rainy season [2]

Modern roofs are made of metal sheets (Figure 2) rein-forced concrete and so forth Iron aluminum and zinc mostoften protected against wear are used as roof coverings andhave mechanical resistances characterized by their relativelylong life Galvanized iron sheet finds use in developing worldbasically where high rainfall is registered annually [5] Themain handicap of the modern roofing is their low isolationcapacity

In the light of climate change and all its adverse effects andgiving the fact that increasing number of houses are adoptingthe modern roofing along with high thermal comfort costcombining traditional roofing and modern roofing at onehand andmodifyingmodern existing roofs on the other handto get indoor comfort at an affordable cost are of interest[6]

Green or vegetative roofs are in use in several Europeanand American countries [7] Several problems notably thethermal isolation leading to the reduced energy consumptionand energy conservation [8] and noise reduction are solvedby green roofing [9] However those benefits linked to greenroofs are more significant for extremely compact tropicalcities with severe shortage of ground-level green spaces andintense Urban Heat Island effects [10 11]

Moreover green roofing is not much in use in southSaharan regions for several reasons First those regions haveno space problem and there are few compact cities wheresuch a technique could be deployed Second the constructionand the maintenance costs of those green roofing are waybeyond what people in those regions could bear

Climate change is a challenging situation to humanhabitat as far as their thermal comfort in houses In adry and hot climate of Mexicali in Mexico a city of sameclimate characteristics as Ougagougou where the presentstudy was conducted a field study was done consisting onthe determination of electrical energy consumption of lowincome dwellers and their perception of thermal comfort inaccordance with the design and the building material [12]

Sustainable buildings have been designed by architects forthe improvement of indoor environmental quality basicallyincluding the provision of comfortable temperatures andhumidities The usersrsquo perceptions of thermal comfort hadbeen surveyed in 36 sustainable commercial and institutionalbuildings in 11 countries [13] The focus of those studiesamong others was the overall thermal comfort in buildingsHowever few studies deal with the specific thermal contribu-tion of the roof to the house The possibility of roof light forindoor comfort was explored in order to design an innovativeroofing system for the tropics with plenty of sunshine andhigh humidity [14]

In recent years great interests have been noticed inthe field of solar radiation modeling Models have been

Figure 1 Traditional roofing in South Sahara AfricaThe roof coveris made of straws and needs to be renewed after each rainy season

Figure 2 Typical modern roof type in Sub-Sahara Africa Most ofthe roofs are made of metal sheets basically iron sheet with slightslope and oriented south

developed to evaluate both global and diffuse solar radiationsEmploying a sensor FLA613-GS that gives direct currentproportional to global radiation the global solar radiancewasevaluated [15] In 2011 an estimation of diffuse solar radiationon horizontal plane was performed in three cities of Nigeriain west Africa Correlation between the clearance index andthe diffuse to global solar radiation ratio was employed inthe estimation of the diffuse radiation The model efficiencyis proven worldwide according to the authors [16] Further-more real time monitoring of global solar radiation wasachieved designing a model of TCPIP with an embeddedinternet based data acquisition system [17] Even thoughscientists in the field of solar energy have developed modelsto monitor solar radiation in the literature to the best of ourknowledge it was not possible to see effort related to roofmodeling linked to solar energy in the south Saharan regionof Africa

The present study aims at modeling heat transfer throughroofs in sub-Saharan region in order to predict the roofcontribution to the overall heat of the room and to selectroof materials that lower comfort cost in those regions whereabout 70 of the room overall heat comes from the roof [18]

2 The Roof Thermal Model

As it is known a model is meant to be the simplest way oflooking at a complex phenomenon The conceptualization of



Solarradiation

Sun (E)

e Conduction


Tpe

Tpi

Tr




120593 =120582

119890(119879pe minus 119879pi)

(1)

where
















119890and 120576119894




119890for

external convection


119890





120593abs = 120576119890 sdot 119864



pe minus 1198794

S )

(2)


120593cond =120582

119890sdot (119879pe minus 119879pi) (3)




4

pi minus 1198794

room) (4)




120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

(6)

120593119904= 120593recover room = 120593


Knowing that 120593119892= 119874


120582


4

pi minus 1198794

room)]

(9)


120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

120582


+120590 sdot 120576119894sdot (1198794

pe minus 1198794

room)]

(10)



ℎ119890= 57 + 38119881 for 119881 le 4ms

ℎ119890= 75119881

08 for 119881 gt 4ms(11)




ℎ119894=(Nu sdot 120582

119890)

119871 (12)



Nu = (Gr sdot Pr)119898 (13)


Gr =120573119892Δ120579120588

2

1198901198713

1205832

119890

(14)



119890





33 Modeling 120582119890 120588119890 and 120583



120582119890

=


minus6119879 for 200 le 119879 lt 300


minus6119879 for 300 le 119879 lt 350


minus6119879 for 350 le 119879 le 400

120588119890

=




120583119890

=


minus9119879 for 200 le 119879 lt 300


minus9119879 for 300 le 119879 lt 350


minus9119879 for 350 le 119879 le 400

(15)



119879s = 119879a minus 12 or 119879s = 120576119879a14 (16)



or 120576 = 0787 minus 0764 ln(119879v273

)

(17)






] 119879a14 (18)


41 Study Area







Wind speed(V ms)


700 1300 10 275800 3542 20 317900 6307 30 3391000 7759 30 3571100 8533 30 3741200 9001 30 3841300 8481 20 3971400 7519 20 4001500 5722 20 4051600 3393 20 3991700 1062 20 3921800 175 20 370









Time(H)

119879a(∘C)

SR(Wm2)

V(ms)


830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)



Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)









30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Solarradiation

Sun (E)

e Conduction


Tpe

Tpi

Tr




120593 =120582

119890(119879pe minus 119879pi)

(1)

where
















119890and 120576119894




119890for

external convection


119890





120593abs = 120576119890 sdot 119864



pe minus 1198794

S )

(2)


120593cond =120582

119890sdot (119879pe minus 119879pi) (3)




4

pi minus 1198794

room) (4)




120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

(6)

120593119904= 120593recover room = 120593


Knowing that 120593119892= 119874


120582


4

pi minus 1198794

room)]

(9)


120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

120582


+120590 sdot 120576119894sdot (1198794

pe minus 1198794

room)]

(10)



ℎ119890= 57 + 38119881 for 119881 le 4ms

ℎ119890= 75119881

08 for 119881 gt 4ms(11)




ℎ119894=(Nu sdot 120582

119890)

119871 (12)



Nu = (Gr sdot Pr)119898 (13)


Gr =120573119892Δ120579120588

2

1198901198713

1205832

119890

(14)



119890





33 Modeling 120582119890 120588119890 and 120583



120582119890

=


minus6119879 for 200 le 119879 lt 300


minus6119879 for 300 le 119879 lt 350


minus6119879 for 350 le 119879 le 400

120588119890

=




120583119890

=


minus9119879 for 200 le 119879 lt 300


minus9119879 for 300 le 119879 lt 350


minus9119879 for 350 le 119879 le 400

(15)



119879s = 119879a minus 12 or 119879s = 120576119879a14 (16)



or 120576 = 0787 minus 0764 ln(119879v273

)

(17)






] 119879a14 (18)


41 Study Area







Wind speed(V ms)


700 1300 10 275800 3542 20 317900 6307 30 3391000 7759 30 3571100 8533 30 3741200 9001 30 3841300 8481 20 3971400 7519 20 4001500 5722 20 4051600 3393 20 3991700 1062 20 3921800 175 20 370









Time(H)

119879a(∘C)

SR(Wm2)

V(ms)


830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)



Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)









30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

(6)

120593119904= 120593recover room = 120593


Knowing that 120593119892= 119874


120582


4

pi minus 1198794

room)]

(9)


120576119890sdot 119864 = [ℎ


4

pe minus 1198794

S )

+120582

119890sdot (119879pe minus 119879pi)]

120582


+120590 sdot 120576119894sdot (1198794

pe minus 1198794

room)]

(10)



ℎ119890= 57 + 38119881 for 119881 le 4ms

ℎ119890= 75119881

08 for 119881 gt 4ms(11)




ℎ119894=(Nu sdot 120582

119890)

119871 (12)



Nu = (Gr sdot Pr)119898 (13)


Gr =120573119892Δ120579120588

2

1198901198713

1205832

119890

(14)



119890





33 Modeling 120582119890 120588119890 and 120583



120582119890

=


minus6119879 for 200 le 119879 lt 300


minus6119879 for 300 le 119879 lt 350


minus6119879 for 350 le 119879 le 400

120588119890

=




120583119890

=


minus9119879 for 200 le 119879 lt 300


minus9119879 for 300 le 119879 lt 350


minus9119879 for 350 le 119879 le 400

(15)



119879s = 119879a minus 12 or 119879s = 120576119879a14 (16)



or 120576 = 0787 minus 0764 ln(119879v273

)

(17)






] 119879a14 (18)


41 Study Area







Wind speed(V ms)


700 1300 10 275800 3542 20 317900 6307 30 3391000 7759 30 3571100 8533 30 3741200 9001 30 3841300 8481 20 3971400 7519 20 4001500 5722 20 4051600 3393 20 3991700 1062 20 3921800 175 20 370









Time(H)

119879a(∘C)

SR(Wm2)

V(ms)


830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)



Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)









30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















] 119879a14 (18)


41 Study Area







Wind speed(V ms)


700 1300 10 275800 3542 20 317900 6307 30 3391000 7759 30 3571100 8533 30 3741200 9001 30 3841300 8481 20 3971400 7519 20 4001500 5722 20 4051600 3393 20 3991700 1062 20 3921800 175 20 370









Time(H)

119879a(∘C)

SR(Wm2)

V(ms)


830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)



Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)









30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Time(H)

119879a(∘C)

SR(Wm2)

V(ms)


830 330 4260 20 374 522 498 631930 339 5980 16 413 599 600 9611100 355 8400 20 461 640 654 10161200 368 8538 20 503 692 717 11531300 380 8430 20 516 730 727 11531400 384 7154 25 512 654 658 7691500 401 5630 25 501 612 616 6001600 396 1300 05 447 473 475 1301700 385 1140 20 416 427 429 821800 380 300 25 386 375 385 00

20

25

30

35

40

45

0

100

200

300

400

500

600

700

800

900

1000

Time (hour)



Am

bien

t tem

pera

ture

(∘C)

070

0

080

0

090

0

100

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0

Sola

r dire

ct ra

diat

ion

(Wm

2)









30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















30

35

40

45

50

55

60

65

70

75

8008

30

093

0

110

0

120

0

130

0

140

0

150

0

160

0

170

0

180

0Time (hour)


Tem

pera

ture

s (∘C)








RMSE = [

[

sum119873

119894=1(119876

mod119894


)2

119873

]

]

12

(19)



119864 = 1 minussum119899

119894=1(119883obs119894 minus 119883model)

2

sum119899

119894=1(119883obs119894 minus 119883obs)

2 (20)


6 Conclusion


Acknowledgments




References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















References

































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Documents

Research Article Modeling Solar Energy Transfer through ...downloads.hindawi.com/archive/2013/480137.pdfISRN Renewable Energy e roof thermal model Solar radiation Sun ( E ) e Conduction