Solar Thermal SystemsSolar Thermal SystemsCameron JohnstoneCameron Johnstone

Department of Mechanical EngineeringDepartment of Mechanical Engineering

Room M6:12Room M6:12

cameron@esru.strath.ac.uk

Do All Energy Resources Originate Do All Energy Resources Originate from the Sun ?from the Sun ?

30%30%47%47%

23%23%

0.21%0.21%

0.06%0.06%

Hydro Hydro

Wind & Wave Wind & Wave

Bio-fuels Bio-fuels

7x 107x 10-9-9%% 12.7 MW / 12.7 MW / 4kg/s Oil4kg/s Oil

60 million AGR’s60 million AGR’s

Not quiteNot quite

Solar DataSolar Data

Statistics:Statistics:

diameter of Sun 1.39 x 10diameter of Sun 1.39 x 1066 km km

diameter of Earth 12.7 x 10diameter of Earth 12.7 x 1033 km km

distance from Earth 1.5 x 10distance from Earth 1.5 x 1088 km km

transmission time 500s transmission time 500s

Nuclear fusion at SunNuclear fusion at Sun

=>=> Surface Temp. Surface Temp. 5800K 5800K

Core Temp. Core Temp. 8 x 10 8 x 1066 - 40 x 10 - 40 x 106 6 KK

Density = 80 / 100 x waterDensity = 80 / 100 x water

inner core

outer core

convecting zone

photoshpere

reversing layer

chromoshpere

corona

The SunThe Sun

• The ultimate source of energy in the sun is a The ultimate source of energy in the sun is a nuclear nuclear fusionfusion reaction, heating core to about 10 reaction, heating core to about 1077 K K

• Energy from fusion reaction emitted as X-rays, Energy from fusion reaction emitted as X-rays, gamma rays and high-energy particles known as gamma rays and high-energy particles known as neutrinosneutrinos

• Radiation heats passive layers of gas in sun’s outer Radiation heats passive layers of gas in sun’s outer atmosphere to around 5800K. These layers then atmosphere to around 5800K. These layers then radiate energy to the earth.radiate energy to the earth.

Solar DataSolar Data

RotationRotationEarthEarth = 1/ 24 hours = 1/ 24 hoursSunSun = 1/ 4 weeks= 1/ 4 weeks

27 days @ equator27 days @ equator30 days @ polar regions30 days @ polar regions

Radiant Flux Density (RFD)Radiant Flux Density (RFD) (Irradiance or Insolation)(Irradiance or Insolation)

1.35kW/m1.35kW/m22 (outer space) (outer space)1 kW/m1 kW/m22 (sea level) (sea level)

- due to Albedo effect- due to Albedo effect and and absorption in atmosphere absorption in atmosphere

Solar Spectral EmissionSolar Spectral Emission

Wavelength band =>Wavelength band => 0.3 0.3 m - 2.5 m - 2.5 m (shortwave)m (shortwave)Makeup:Makeup: < 0.4 < 0.4m (ultraviolet) 9% of RFDm (ultraviolet) 9% of RFD

0.4 0.4 m < m < < 0.7 < 0.7 m (visible) 45% of RFDm (visible) 45% of RFD > 0.7 > 0.7 m (infrared) 46% of RFDm (infrared) 46% of RFD

Black Body RadiationBlack Body Radiation

• Radiant energy reaching the earth from the sun closely Radiant energy reaching the earth from the sun closely approximates radiation from a black body at a approximates radiation from a black body at a temperature of about 5800 K. temperature of about 5800 K.

• A back body is an object that radiates energy according A back body is an object that radiates energy according to the following equation: (Stefan-Boltzmann constant = to the following equation: (Stefan-Boltzmann constant = 5.67× 105.67× 10–8–8W/mW/m22KK44))

•

• Representing the maximum possible energy emitted by Representing the maximum possible energy emitted by a body at temperature T. a body at temperature T.

• In reality the quantity of energy emitted by all real In reality the quantity of energy emitted by all real bodies will be less than this.bodies will be less than this.

)1(4ATQR )1(4ATQR

• The radiant energy from the sun can be thought of as The radiant energy from the sun can be thought of as discrete “packets” of energy known as a discrete “packets” of energy known as a photonsphotons

• The energy carried by an individual photon (The energy carried by an individual photon (EE) is given as ) is given as the product of its frequency the product of its frequency vv and a quantity known as and a quantity known as Planck’s constant (Planck’s constant (h = h = 6.626 × 106.626 × 10–34–34 Js) Js)

• This equation shows that photons and consequently This equation shows that photons and consequently radiation with a high frequency has the greatest energy. radiation with a high frequency has the greatest energy.

PhotonsPhotons

)2(hvE )2(hvE

• Wavelength and frequency are related by the Wavelength and frequency are related by the equation: equation:

• Substituting for for frequency:Substituting for for frequency:

• The shorter the wavelength (higher frequency) the The shorter the wavelength (higher frequency) the greater the energy of the radiation/photon.greater the energy of the radiation/photon.

PhotonsPhotons

)3(v

c )3(

v

c

)4(hc

E )4(hc

E

Planck’s LawPlanck’s Law

• Wavelength or frequency of emitted radiation is Wavelength or frequency of emitted radiation is related to the temperature of the emitting body by related to the temperature of the emitting body by Planck’s law, this gives the rate of energy (Planck’s law, this gives the rate of energy (QQ) ) radiated at any wavelength, λ(μm), by a black body radiated at any wavelength, λ(μm), by a black body of temperature T (K). of temperature T (K).

• The quantity QThe quantity Qλλ is known as the emissive power of is known as the emissive power of

the black body.the black body.

)5()1( /

1

2 Tce

CQ )5(

)1( /1

2 Tce

CQ

CC11- 3.742 x 10- 3.742 x 108 8 W W mm44/m/m22

CC22- 1.44 x 10- 1.44 x 104 4 KK

Spectral distribution T=5800K

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

0.1 1 10 100

Wavelength (micro m)

Em

issi

ve p

ow

er (

W/m

^2-m

icro

m)

Spectral distribution T=5800K

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

0.1 1 10 100

Wavelength (micro m)

Em

issi

ve p

ow

er (

W/m

^2-m

icro

m)

Planck’s LawPlanck’s Law

Establishing the Sun’s equivalent Establishing the Sun’s equivalent ‘Black Body’ Temperature‘Black Body’ Temperature

Wien’s Displacement LawWien’s Displacement Law

mm = = C Cww

T Tabsabs

where: where: mm = Wavelength of max. energy ( = Wavelength of max. energy (m)m)

CCww = Wien’s constant 2820 ( = Wien’s constant 2820 (m K)m K)

T = Absolute temp. (K)T = Absolute temp. (K)

  

For global irradiance For global irradiance mm ≈ 0.5 ≈ 0.5 m m

Solar energy: Air massSolar energy: Air mass

Air mass (AM) = Air mass (AM) = 1/ Cos 1/ Cos Air mass 1Air mass 1 at Equatorat EquatorAir mass 1.5 at latitudes 48.5Air mass 1.5 at latitudes 48.5Air mass 2Air mass 2 at latitudes 60at latitudes 60

EarthEarth

AtmosphereAtmosphere

XX11

XX22

xx22 > x > x11

Components of IrradianceComponents of Irradiance

For perpendicular surfacesFor perpendicular surfaces

Beam (GBeam (Gbb)) =>=> 0% - 90%0% - 90%

Diffuse (GDiffuse (Gdd)) =>=> 10% - 100%10% - 100%

  

Total irradianceTotal irradiance G = GG = Gbb + G + G

dd

  For inclined surfaceFor inclined surface

GGbb = G = Gbb x Cos x Cos

Total irradianceTotal irradiance G = GG = Gbb + G + G

dd

Angles associated with the Angles associated with the Solar PlaneSolar Plane

ZenithZenith angleangle = = angle of decline from the angle of decline from the overhead position.overhead position.

Azimuth angleAzimuth angle = = angle of difference from solar angle of difference from solar noon.noon.

Characteristics of Solar MaterialsCharacteristics of Solar MaterialsAll materials have the following characteristicsAll materials have the following characteristics

TransmissionTransmission (())AbsorptanceAbsorptance (())ReflectanceReflectance (())

  For any material:For any material: + + + + = 1 = 1

Solar collector componentsSolar collector components

Protective cover (c) -Protective cover (c) - high high value valueAbsorber/collector plate (p)-Absorber/collector plate (p)- high high value valueShading device (optional) -Shading device (optional) - high high value value

Solar power absorbed into collector

1

Power loss from collector

2

Useful power from collector

3

Solar CollectorSolar Collector

Absorbed power in a solar collectorAbsorbed power in a solar collector

Given by (1):Given by (1):

QQPP = G A = G A ccpp

  

where:where: QQPP = absorbed power (W) = absorbed power (W)

G = total irradiance (W/mG = total irradiance (W/m22))

A = area of solar collector (mA = area of solar collector (m22))

cc = transmission factor of cover = transmission factor of cover

pp = absorptance factor of collector plate = absorptance factor of collector plate

Power loss in a solar collectorPower loss in a solar collector

Given by (2):Given by (2):

QQLL = U A (T = U A (Tcc - T - Taa))  

where:where: QQLL = power lost (W) = power lost (W)

U = collector U value (W/mU = collector U value (W/m22K)K)

TTcc = temperature of collector plate (K) = temperature of collector plate (K)

TTaa = temperature of ambient (K) = temperature of ambient (K)

Power supplied by a solar collectorPower supplied by a solar collector

Derived from Derived from Hottel - WhillierHottel - Whillier equation (3): equation (3):

  = (1) – (2)= (1) – (2)

QQSS = GA = GA ccpp - [UA (T - [UA (Tcc - T - Taa)])]

Solar power absorbed into collector

Power loss from collector

Useful power from collector

1

2

3

Solar CollectorSolar Collector

Solar collector performance Solar collector performance characterisationcharacterisation

The stagnation temperature method The stagnation temperature method

QQsupsup = 0 = 0loss from collector is equal to the power absorbed at the loss from collector is equal to the power absorbed at the collector plate: collector plate: 

QQabs abs = Q= Qlossloss

For a conventional flat plate collector, the collector For a conventional flat plate collector, the collector temperature (Ttemperature (Tcc) at stagnation:) at stagnation:

GA GA ccpp = = UA (TUA (Tcc -- T Taa))

TTcc = = GA GA ccpp ++ T Taa

UAUA

Solar concentratorsSolar concentrators

Focusing beam irradiance (GFocusing beam irradiance (Gbb) incidental on ) incidental on

a large surface area onto a smaller absorbing a large surface area onto a smaller absorbing area.area.

  

Effective operation requires:Effective operation requires:

-- complex tracking and control systemscomplex tracking and control systems  

Concentrator Gb

Collector

Concentration ratio of concentratorConcentration ratio of concentrator

• Concentration RatioConcentration Ratio (X) (X)  

X =X = AAaa

AAcc  

• Where:Where: AAaa - projected area of concentrator- projected area of concentrator

(2 dimensional image)(2 dimensional image)

AAcc - collector area- collector area

Power supplied to an evacuated collector (1)

Power Absorbed (Qabs)

 Qabs = Gb Aa a g c

 Where: Gb - beam irradiance (W/m2)

a - reflectivity of parabolic surface

g - transmissivity of glazed cover

c - absorbtivity of collector

GbConcentrator

Collector

Power loss from an evacuated Power loss from an evacuated collector (2)collector (2)

Qloss = Ac [ Tc4 - Tg

4 ] 

Where: - emissivity of collector surface - Boltzman’s constant (5.669 x 10-8 W/m2K4)Tc - collector surface temperature (K)

Tg - glazing temperature (K)

Solar power absorbed into collector

Power loss from collector

Useful power from collector

1

2

3

Solar CollectorSolar Collector

Power supplied by the evacuated Power supplied by the evacuated collector (1) – (2)collector (1) – (2)

Power supplied (Power supplied (QQsupsup):):

= Q= Qabsabs – Q – Qlossloss

= = ( ( GGb b AAaa aa gg cc ) – ( ) – ( A Acc [ T [ Tcc44 - T - T

gg44 ] ) ] )

Performance appraisal/ comparison under stagnated conditions:Performance appraisal/ comparison under stagnated conditions:

QQsupsup = 0 = 0 Q Qabs abs = Q= Qlossloss

  

GGb b AAaa aa gg cc = = A Acc [ T [ Tcc44 - T - T

gg44 ] ]  

Stagnation temperature is:Stagnation temperature is:  

TTcc44 = = GGb b AAaa aa gg cc + T+ T

gg44

AAcc

Collector efficiencyCollector efficiencyDefined as power delivered (useful power) divided by GDefined as power delivered (useful power) divided by G tottot

Eff

icie

ncy

Eff

icie

ncy

(%)

(%

)

Temperature rise Temperature rise T T ( (°C°C))

Unglazed collectorUnglazed collector

Single glazed collectorSingle glazed collector

Double glazed collectorDouble glazed collector

Evacuated concentrator collectorEvacuated concentrator collector

Analysis is an iterative process because so many variables Analysis is an iterative process because so many variables including:including:

- solar radiation intensity,solar radiation intensity,- temperature of the solar collector, temperature of the solar collector, - effectiveness and efficiency of the heat exchange effectiveness and efficiency of the heat exchange processesprocesses- temperature of the hot water in the tank. temperature of the hot water in the tank.

Calculate the resulting heat transfer rate and energy Calculate the resulting heat transfer rate and energy balance at each time stepbalance at each time stepHottel-Whillier and Bliss equation has (F) componentHottel-Whillier and Bliss equation has (F) component

Solar water heating exampleSolar water heating example

)]([ apccr TTUAGAFQ

A 3mA 3m22 flat plate solar collector with the following characteristics is flat plate solar collector with the following characteristics is used to heat a 72 litre hot water tank. If there is no draw off of used to heat a 72 litre hot water tank. If there is no draw off of water calculate:water calculate:

i)i) the maximum stagnation temperature reached, the maximum stagnation temperature reached, ii)ii) the maximum water temperature within the storage tank, andthe maximum water temperature within the storage tank, andiii)iii) the mean hourly collector efficiency the mean hourly collector efficiency

collector “U” value (W/mcollector “U” value (W/m2 2 K)K) 3.53.5

collector absorptance (collector absorptance ()) 0.90.9

transmissivity of cover (transmissivity of cover ()) 0.740.74

effectiveness of collector plate (F)effectiveness of collector plate (F) 0.90.9

initial water temperature (initial water temperature (C)C) 1010density of water (kg/mdensity of water (kg/m33)) 10001000specific heat capacity of water (J/kg specific heat capacity of water (J/kg K)K) 42004200

water flow rate (l/s)water flow rate (l/s) 0.020.02

A 3m2 flat plate solar collector with the following characteristics is used to heat a 72 litre hot water tank. If there is no draw off of water calculate:i) the maximum stagnation temperature reached, ii) the maximum water temperature within the storage tank, andiii) the mean hourly collector efficiency

collector “U” value (W/m2 °K) 3.5collector absorptance (a) 0.9transmissivity of cover (t) 0.74effectiveness of collector plate (F) 0.9initial water temperature (°C) 10density of water (kg/m3) 1000specific heat capaity of water (J/kg °K) 4200water flow rate (l/s) 0.02 Time Mean hourly irradianceAir temperature Double Glazed Collector

Gb (W/m2) Gd (W/m2)(W/m2) (°C) Qin Qloss Qsup dT T water Tc stag Efficiency 9:00 - 10:00 50 180 230 8 459.54 21 394.686 4.698643 14.69864 51.76571 0.57200910:00 - 11:00 300 150 450 11 899.1 38.83575 774.2378 9.217117 23.91576 96.62857 0.5735111:00 - 12:00 710 130 840 14 1678.32 104.1155 1416.784 16.86648 40.78224 173.84 0.56221612:00 - 13:00 880 110 990 16 1978.02 260.2135 1546.026 18.40507 59.18731 204.3829 0.52054713:00 - 14:00 720 130 850 18 1698.3 432.4667 1139.25 13.5625 72.74981 179.7429 0.44676514:00 - 15:00 410 150 560 18 1118.88 574.873 489.6063 5.828647 78.57845 124.56 0.29143215:00 - 16:00 250 170 420 17 839.16 646.5738 173.3276 2.063424 80.64188 96.92 0.13756216:00 - 17:00 30 190 220 15 439.56 689.2397 -224.7117 -2.67514 77.96674 56.86286 -0.340472

Single Glazed CollectorQin Qloss Qsup dT T water Tc stag Efficiency

Time G Ta 558.9 33 473.31 5.634643 15.63464 41.87273 0.685957 9:00 - 10:00 230 8 1093.5 76.47161 915.3256 10.89673 26.53138 77.27273 0.67801910:00 - 11:00 450 11 2041.2 163.61 1689.831 20.11704 46.64841 137.7091 0.67056811:00 - 12:00 840 14 2405.7 408.9069 1797.114 21.39421 68.04262 161.8 0.60508912:00 - 13:00 990 16 2065.5 679.5906 1247.318 14.84903 82.89165 143.1818 0.48914513:00 - 14:00 850 18 1360.8 903.3718 411.6854 4.901016 87.79267 100.4727 0.24505114:00 - 15:00 560 18 1020.6 1016.044 4.099975 0.048809 87.84148 78.85455 0.00325415:00 - 16:00 420 17 534.6 1083.091 -493.6419 -5.876689 81.96479 47.4 -0.747942

Solar water heating exampleSolar water heating example

GAGA

UAUATT TTwaterwater

Eff. Eff.

mCmCppTT

Solar Skins/ WallsSolar Skins/ WallsSolar skins/ walls should be a net contributor of energy Solar skins/ walls should be a net contributor of energy

to a building.to a building.Can be of two types:Can be of two types:Thermal Mass or Phase Change storageThermal Mass or Phase Change storage Thermal mass storage:Thermal mass storage:Sensible heating, therefore for Sensible heating, therefore for solar energy input – solar energy input –

collector temperature increase results in system collector temperature increase results in system losses increasinglosses increasing..

Materials:Materials: Rock/ concrete 1 < Cp < 1.4 kJ/ kgKRock/ concrete 1 < Cp < 1.4 kJ/ kgKWater Cp = 4.2 kJ/kgKWater Cp = 4.2 kJ/kgK

Solar Skins/ WallsSolar Skins/ WallsPhase Change Storage:Phase Change Storage:Sensible and Latent heating Sensible and Latent heating - At PC temperature: At PC temperature: While energy input is While energy input is

maintained - Temperature remains constant - Losses maintained - Temperature remains constant - Losses remain constant, improving system efficiencyremain constant, improving system efficiency..

Materials:Materials: CaClCaCl22 saturated solution changes phase saturated solution changes phase (solid to liquid) at 28(solid to liquid) at 28C C Latent heat 198 MJ/ mLatent heat 198 MJ/ m33

Durability: Durability: Proven to over 6000 complete PC cycles ?Proven to over 6000 complete PC cycles ?

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisal

Since heating demand Since heating demand does not occur at time does not occur at time of solar availability, of solar availability, time lags are time lags are introduced by using introduced by using thermal capacity.thermal capacity.

Solar Skins/ Walls: Time lagSolar Skins/ Walls: Time lag

Associated time lags as demonstrated on Strathclyde’s Associated time lags as demonstrated on Strathclyde’s Solar ResidencesSolar Residences

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance AppraisalAppraisal

Temperature swing is cyclic between a maximum (solar Temperature swing is cyclic between a maximum (solar noon) and minimum (early morning) every 24 hour noon) and minimum (early morning) every 24 hour period. period.

For solar applications the frequency of temperature For solar applications the frequency of temperature swing (swing (nn) is a 24 hour period, and determined as ) is a 24 hour period, and determined as

follows:follows:

nn = 1/ time = 1/ time (sec)(sec)

For solar wall applications For solar wall applications nn = 1.157 x 10 = 1.157 x 10-5-5

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance AppraisalAppraisal

Flux absorbed at surface penetrates into the wall Flux absorbed at surface penetrates into the wall and gets diffused. and gets diffused. Diffusion rate of is referred to as the Diffusion rate of is referred to as the Thermal Thermal DiffusivityDiffusivity ( () and calculated as follows:) and calculated as follows:

= k /= k /CpCpwhere:where:

= Thermal diffusivity (m= Thermal diffusivity (m22/s)/s)kk = Thermal conductivity of wall (W/mK) = Thermal conductivity of wall (W/mK) = Density of wall material (kg/m3)= Density of wall material (kg/m3)CpCp = Specific heat capacity of wall (J/kg K) = Specific heat capacity of wall (J/kg K)

Solar Skins/ Walls Performance Solar Skins/ Walls Performance AppraisalAppraisal

The velocity at which energy will travel through the The velocity at which energy will travel through the wall is determined by the thermo-physical properties of wall is determined by the thermo-physical properties of its construction. its construction.

Important when designing the thickness of the wall so Important when designing the thickness of the wall so peak thermal flux occurs at the time of peak heating peak thermal flux occurs at the time of peak heating demand. demand.

The velocity (The velocity (vv) of the thermal wave is given by:) of the thermal wave is given by:

v = 2 (v = 2 (nn))1/21/2

Solar Skins/ Walls Performance Solar Skins/ Walls Performance AppraisalAppraisalThe temperature at a point through the wall fluctuates around the The temperature at a point through the wall fluctuates around the mean external wall surface temperature experienced over the 24 mean external wall surface temperature experienced over the 24 hour period, Thour period, Tmeanmean at the external surface is: at the external surface is:

TTmeanmean = = 11//22 (T (Tmax max + T+ Tminmin))

The specific temperature fluctuation (The specific temperature fluctuation (T) above or below TT) above or below Tmeanmean at a at a distance (x) metres into the wall is:distance (x) metres into the wall is:

T = TT = T e [ -x ( e [ -x (nn / / ))1/21/2 ] ]where:where:

TT - amplitude of the wall surface temperature from T - amplitude of the wall surface temperature from Tmeanmean over the 24 hour over the 24 hour period i.e. T period i.e. Tmaxmax - T - Tmeanmean((C)C)

x - distance from external surface of wall (m)x - distance from external surface of wall (m)

nn - frequency of temperature swing - frequency of temperature swing

- thermal diffusivity (m- thermal diffusivity (m22/s)/s)

Solar Skins/ Walls Performance Solar Skins/ Walls Performance AppraisalAppraisalMaximum and minimum temperatures at a specific point Maximum and minimum temperatures at a specific point within the wall (Twithin the wall (Txx) is calculated by adding or subtracting ) is calculated by adding or subtracting the temperature swing to/from the mean surface the temperature swing to/from the mean surface temperature :temperature :

TTxx = T = Tmeanmean TT

The Energy (E) stored within the wall is:The Energy (E) stored within the wall is:

E = m CE = m Cpp (T (Tmeanmean – T – Tambamb))Where:Where:

E = energy (j)E = energy (j)m = mass of wall (kg) m = mass of wall (kg) [volume x density][volume x density]

CCpp = Specific heat capacity of wall material (j/kg = Specific heat capacity of wall material (j/kg C)C)

TTamb amb = average outside air temperature over the day= average outside air temperature over the day

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisal

Solar walls assessed via net energy contributions: Solar walls assessed via net energy contributions: Heat flux transferred relative to solar flux available.Heat flux transferred relative to solar flux available.

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisal

Flux capture derived via the Hottel-Whillier Eqn. to give negative values in sufficient irradiance (energy contribution) and positive values in no or low irradiance (energy loss).

Qres = Uc (Tabs - Ta)- Gvwhere:

Qres = Resultant power flux (W/m2)Gv = Incidental irradiance (W/m2)Uc = Collector “U” value (W/m2K)Tabs = Collector absorber temperatureTa = Outside air temperature

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisalThis can be rewritten as:

Qres / (Tabs-Ta) = Uc - ( Gv / (Tabs - Ta))

Since Uc and remain constant, plotting Qres / (Tabs-Ta) against Gv / (Tabs - Ta)

over an extended period of time and under a variance of irradiance conditions gives:

Y = mX + C Analysis of this distribution can determine the following characteristics:

m = collector efficiency ()C = ‘Udark’ value (‘U’ value in no irradiance)

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisal

‘‘U’ valuesU’ values‘‘UUdarkdark’ Wall performance without solar exposure.’ Wall performance without solar exposure.‘‘UUeffectiveeffective’ Wall performance when exposed to the sun ’ Wall performance when exposed to the sun

‘‘UUdarkdark’’

‘‘UUeffectiveeffective’’

m = eff.m = eff.

Solar Skins/ Walls: Performance Solar Skins/ Walls: Performance appraisalappraisal

The summation of all the plotted QThe summation of all the plotted Qresres / (T / (Tabsabs-T-Taa) divided by ) divided by

the number of values plotted (n) gives an average U value the number of values plotted (n) gives an average U value (U(Ueffeff) for the wall examined under a variety of conditions. ) for the wall examined under a variety of conditions.

UUeffeff is defined as follows: is defined as follows:

UUeffeff = = Q Qresres / (T / (Tabsabs-T-Taa))

nn

““Good”, solar walls have negative ‘UGood”, solar walls have negative ‘Ueffeff’ values indicating ’ values indicating

they contribute more power than is lost from them over they contribute more power than is lost from them over

the evaluation period.the evaluation period.