Solar Thermal Energy Lecture 1

7/30/2019 Solar Thermal Energy Lecture 1

1/26

97Copyright Gang Chen,

or 2.997 Direct Solar/Thermalto

Electrical Energy Conversion

Importance of Heat

2.9

MIT

F

Courtesy of Lawrence Livermore National Laboratory. Used with permission.


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yrightGa

Direct Solar/Ther

ergy ConversionGasoline100 kJ

10kJ 30kJ 35kJ

Parasiticheat losses Coolant Exhaust

9kJ10kJ6kJ

Exhaust

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or2.

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27

Cop

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F997

malt

Elec

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Vehicle Systems

In US, transportation uses ~26% of total energy.

Coolant

Gasoline100kJ

10kJ

30kJ35kJ

9kJ

10kJ

6kJ Auxiliary

Driving

Mechanical losses

Parasiticheat losses Exhaust

Photo from Wikimedia Commons,http://commons.wikimedia.org
http://commons.wikimedia.org/http://commons.wikimedia.org/http://commons.wikimedia.org/http://commons.wikimedia.org/


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onve

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Heating

TE Recovery

PVElectricity

Oil or

Natl Gas

Entropy

Thermal Power

Electrical Power

Heating

TE Recovery

PVElectricity

Oil or

Natl Gas

Oil or

Natl Gas

Entropy

Thermal Power

Electrical Power

Co-Generation in Residential Buildings

In US, residential and

commercial buildings

consume ~35% energysupply

Photo by bunchofpants on Flickr.

Image removed due to copyright restrictions.Please see any photo of the Honda freewattMicro-CHP system, such as http://www.hondanews.

com/thumbnails/2007/4/3/13644_preview.jpg

Refrigeration &Refrigeration &AppliancesAppliances
http://www.flickr.com/photos/bunchofpants/244046303/http://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpghttp://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpghttp://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpghttp://www.flickr.com/photos/bunchofpants/244046303/http://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpghttp://www.hondanews.com/thumbnails/2007/4/3/13644_preview.jpg


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olar/Therm

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Conversion

Industrial Waste Heat

Fig. ES.1 in Hemrick, James G., et al. "Refractories for Industrial Processing:Opportunities for Improved Energy Efficiency." DOE-EERE Industrial TechnologiesProgram, January 2005.

Photos byarbyreed and toennesen on Flickr.
http://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www.flickr.com/photos/19779889@N00/3771842427/http://www.flickr.com/photos/19779889@N00/3771842427/http://www.flickr.com/photos/toennesen/1191861308/http://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdfhttp://www.flickr.com/photos/19779889@N00/3771842427/http://www.flickr.com/photos/toennesen/1191861308/http://www1.eere.energy.gov/industry/imf/pdfs/refractoriesreportfinal.pdf


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Renewable Heat Sources

Photos by Jon Sullivan at http://pdphoto.org/ and NASA.
http://pdphoto.org/http://pdphoto.org/


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Solar Thermal

http://www.treehugger.com/Solar-Thermal-Plant-photo.jpg

http://media.photobucket.com/

Images by Sandia National Laboratories and NREL.

Photos of solar hot water tubes removed due to

copyright restrictions. Please see, for example,

http://image.made-in-china.com/2f0j00KeoavBGJycbN/

rpyiUnpressurized-Solar-Water-Heater-VERIOUS-.jpg

Co irect

http://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpg
http://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpghttp://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpghttp://www.treehugger.com/Solar-Thermal-Plant-photo.jpghttp://www.treehugger.com/Solar-Thermal-Plant-photo.jpghttp://media.photobucket.com/http://image.made-in-china.com/2f0j00KeoavBGJycbN/Unpressurized-Solar-Water-Heater-VERIOUS-.jpghttp://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpghttp://image.made-in-china.com/2f0j00KeoavBGJycbN/Unpressurized-Solar-Water-Heater-VERIOUS-.jpghttp://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpghttp://image.made-in-china.com/2f0j00KeoavBGJycbN/Unpressurized-Solar-Water-Heater-VERIOUS-.jpghttp://image.made-in-china.com/2f0j00KeoavBGJycbN/Unpressurized-Solar-Water-Heater-VERIOUS-.jpghttp://ns2.ugurpc.com/productsimages/solarevacuatedtube_202160.jpghttp://media.photobucket.com/http://www.treehugger.com/Solar-Thermal-Plant-photo.jpg


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Direct Energy Conversion

COLD SIDE

HOT SIDE

Thermoelectrics

Thermophotovoltaicshttps://reader009.{domain}/reader009/html5/0423/5add4

Photovoltaicshttp://www.solareis.anl.gov/images/photos/Nrel_flatPV15539.jpg

Image removed due to copyright restrictions.

Please see http://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpg

Image by Nadine Y. Barclay, USAF. Courtesy of John Kassakian. Used with permission.
http://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpghttp://web.archive.org/web/20071011185223/www.eneco.com/images/science-new.jpg


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Solar Spectrum

0 0.50

200

400

600

1800

TerrestrialSolar

Spectrum(W/m2

m)

AM1.5 Solar Spectrum

Energy Usable for Silicon PV Cells

Bandgap of Silicon(1.1 m)

1600

1400

1200

1000

800

1 1.5 2 2.5 3Wavelength (m)


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a

h

h

0

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v0 2 4 6 8 10 12

Irradiance

From Emitter

0 2 4 6 8 10 120

00

0.5

1.0

1.5

SelectiveAbsorber

Emitter

TPV Cell

Thermal Management

0 0.5 1.0 1.5 2.0 2.5 3.00

Optical Concentrator

EmissivityA

bsorptance

Wavelength (m)Wavelength (m)

Pow

er(W/m2m

)

Power(W/m2m

)

(d)

(b)

Solar Thermophotovoltaics

Theoretical maximum efficiency: 85.4%; comparable to that of inf inite

number of multi-junction cells, but with only a single junction PV cell.

Key Challenges: Selective surfaces absorbing solar radiation but re-

emitting only in a narrow spectrum near the bandgap of photovoltaic

cells, working at high temperatures.

1500 SolarInsolation

1000

500

Wavelength (m)(a)

1.5E4 Absorber

1.0E4

5 10 151.5

0.5E4 (c) Selective Emitter1.0

0.5


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Solar Thermoelectrics

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.5 1.0 1.5 2.0 2.5

EF

FICIENCY(%

)

AVERAGE FIGURE OF MERIT ZT

700 C

400 C

150 C200 C

Tcold

=30 C

600 C500 C

250 C

Thot

-Tcold

(b)

Low materials cost and low capital cost, potentially high efficiency. Key Challenges: Develop materials with high thermoelectric figure of

merit; and selective surfaces that absorb solar radiation but do not

re-radiative heat.


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1st Law of Thermodynamics

SystemQ W

Environment

Boundary

WQdtdE

WQdEWQEE

&&==

= 121212

StateProperties:

Process

Independent

Process

Dependent

Quantities

...Energy)(Internal +++= UPEKEE]m-J/Korkg,-[J/KHeatSpecific 3

dTdu

C=

Closed System

Open System

Closed:


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2nd Law of Thermodynamics

)0(Sgen12 += genboundary

ST

QSS

=0dS

cc

hh

TQ

TQ

=0

Entropy

ChangeState

Properties

EntropyTransfer

EntropyGeneration

Heat Reservoir Th

Heat Reservoir Tc

W

Qh

Qc

During a cycle:

No entropy generation

Maximum Efficiency

(Carnot Efficiency)hc

hch

h T

TQQQ

QW

=== 1Th=223

oC, Tc=23oC, =40%

Th=5800 K, Tc=300 K, =95%Thermal power plant ~40%, IC engines ~25%


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Microscopic Picture of Entropy

= lnBkS=1

P

For Isolated Systems Microstate: a quantummechanically allowed state

A total ofmicrostate Principle of equal probability:

each microstate is equallypossible to be observed

kB=1.38x10-23 J/K ---Boltzmann constant

Boltzmann Principle

Constant Temperature

and Closed Systems)/()( TkE BAeEP =

Constant Temperature

But Open Systems

()(

EAeEP =

--- chemical potential (driving force for mass diffusion);average energy needed to move a particle in/out off a system

Probability

) /(kBT)


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Maxwell distribution

A box of gas

molecules

( )22y2x vvv2

1zmE ++=( )

++

= Tkm

APB

zx 2

vvv

exp)v,v,v(

22

y

2

x

zy

All Probability must normalize to one

( )

++

=

Tkm

AB

z2

vvvexpdvdvdv1

22

y

2

x

zyx2

=A

(

)

++

= Tkm

TkmP B zBx 2 vvvexp2)v,v,v(22

y

2

x

2/3

zyMaxwellDistribution

3/ 2mkBT


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One molecule

=E

( ) ( )

++++=

Tkm

AmEB

zz

2

vvvexpvvv

2

1dvdvdv

22

y

2

x22

y

2

xzyx

TkE B2

3=Equipartition Principle: every quardratic term in microscopic

energy contributes kBT/2.

meV26/106.1

105.14

5.14300KJ/K1038.1

19

21-

23

=

===

eVJJ

TkB

Oxygen Atom at 300 K

How much

Is kBT at room

temperature

1067.116

300/1038.133kv

27

23

B

==

KJmT

-2110 J

K=220 m/s

kg


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Fermi-Dirac Distribution

From quantum mechanics Energy levels are quantized Each quantum state can have

maximum one electron

Planck-Einstein Relation Planck constant h=6.6x10-34 Js,

kh/p:Momentum

:Energy

h

====

hE

)2/( h=h Consider one quantum state with an energy E at constant

temperature T. The state can have zero electron (n=0) or oneelectron (n=1). What is the average number of electrons if

one does many observations?

+

==

= TkE

TkAAe BBTkE

nB

exp1exp1

)/()(

1,0

Average number of electrons in the state

h


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ersion

Fermi-Dirac Distribution

1exp

1)/()(

1,0 +

== =

TkE

AenfB

TkEn

B

Average number of electrons in the state

Fermi-Dirac

Distribution

0

0.2

0.4

0.6

0.8

1

-0.1 -0.05 0 0.05 0.1

FERMI-D

IRACDISTRIBUTION

E- (eV)

1000 K

300 K100 K

At T=0K, is calledFermi level, Ef

F=1 for E


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)

Natural Frequency

1 =2

Energy of Mode E=n+1h n = 2Basic vibrational energy quanta his called a phonon

Photons and Phonons

From quantum mechanics

EM waves are quantized, basicenergy quanta is called a photon

Photon has momentum

Planck-Einstein Relation Each quantum state of photon (an

EM wave mode) can have only

integral number of photons

h/p:Momentum

:Energy h==

=hE

2/(Js;106.6 34 hh == h

One Photon

Energy of a quantum state:

2n

1=

+= hnE

Zero point energyClassical Oscillator

M

Spring

MK

=hk

0,1,2...

0,1,2...


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Bose-Einstein Distribution

0

1

2

3

4

5

0 0.1 0.2 0.3 0.4 0.5

BOSE-EINSTEINDISTRIBUTIO

N

FREQUENCY (X1014 Hz)

5000 K

1000 K

300 K

100 K

Consider one quantum statein thermal equilibrium

)/()(

)(TkE

n BnAeEP =

1exp

1

=

TkEf

B

Average number of

photons/phonons in one

mode (quantum state)

Usually =0

Bose-Einstein Distribution


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Heat Transfer Modes

Heat Conduction

Thot Tcold

Fourier Law

L

[W]dxdTkAQ =&

[ ]2W/mT)-k( == dxdT

kq& Heat Flux

Thermal

Conductivity

[W/m-K]Materials Property

y

x

yy

ux

uy

Ta

uuu

FluidFluidFluid

TwT

xx

uy

xx

uyx

uy

TaTa

w

Convection

Newtons law of cooling

( )aw TThAQ =&Convective Heat

Transfer Coefficient

[W/m2K]Flow dependent

Natural Convection

Forced Convection

Thermal Radiation

Thot Tcold

Stefan-BoltzmannLaw for Blackbody

4TAQ =&

Stefan-Boltzmann Constant

=5.67x10-8 W/m2K4 Heat transfer

44

coldhot TTAFQ = &Emissivity of

two surfaces

View factor

F=1 for twoparallel plates

Cross-

Sectional

Area


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Heat Conduction

Heat Conduction

Thot

Tcold

L

thcoldhotcoldhot

RTTLTTkAQ ==&1D, no heat generation

Thermal ResistancekAL

Rth =

10-2

10-1

100

101

102

103

104

105

101

102

103

Thermalco

nductivity(W/mK)

Temperature (K)

Quartz single

crystal (// to c-axis)

Water

(saturated)

Fused quartz

Ice

Steam

(saturated)

Stainless steel

(type 304)

Copper

Silicon

Diamond

Air

(1 atm)

Helium

(1 atm)

Thot TcoldRth

Convection hARth1

=

Q

&

CurrentHeat


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ersion

Heat Conduction: Kinetic Picture

qx

x

Hot Cold

xvx

qx

x

Hot Cold

xvx

( ) ( )vxxvxxx xx

nEv2

1nEv

2

1+ =

dxdT

k===

)=

dx

dTC

3

vdx

dT

dT

dU

3

v

dx

d(Env-vq

2

2

xxx

= v31

CkThermal Conductivity

Energy per particle: E [J] Number of particles per

unit volume: n [1/m3]

Average randomvelocity of particles v

Average time betweencollision of two particles

---relaxation timeAverage distance

travelled betweencollision =v---Meanfree path

Volumetric specific heat

[ ]KdTdUC 3mJ=cC =

Density

q

Specific heat per unit mass


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Thermal Radiaton: Plancks Law

Inside the Cavity

EM Wave InEquilibrium at

Temperature T

Perfectly

Reflecting Wall

at TFrequency Angular Frequency =2Wavelength

Wavevector magnitude k=2/

=cWavevectork=(kx,ky,kz)

222

zyx kkkcck ++==(k): Dispersion relation (linear)

k

xxx

xx

xxx

Lnk

nL2

2

,...2,...,22,2

==

Basic Relations

How much energy in the cavity?

( )( )

( )TfL

dk

L

dkL

dk

TfL

dkL

dkL

dkTfU

zz

y

yx

xz

zy

yx

xn n nx y z

,

)/2()/2()/2(

2

,)2/2()2/2()2/2(

2

,2

000

1 1 1

hh

h

=

=

=

=

==

Two polarization


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( )( )( )

( )( ) ( )

( )

dudDTf

dcTf

V

UcdcTf

VdkkTf

VdkdkdkTf

VU zyx

==

=

=

==

0

0

32

2

0

2

0

3

2

0

3

3

,

,

4,8

2

4,8

2

,8

2

hhhh

h

D()-density of states perunit volume per unit

angular frequency interval

Energy density per interval( ) ( ) ( )

1exp

1

,

32

3

=

=

Tkc

DTfu

B

hh

hPlancks law

Solid Angle

dAp

2R

dAd p=whole space

4

Intensity: energy flux per unitsolid angle

( ) ( )44 23

3

==c

cuI

h

Per unit wavelength interval

( ) ( ) 45

==

cddI

I h

Plancks law

1h

exp 1kBT

1exp

2hc

1kBT


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( ) ( ) 1exp

1

4 22

3

=

=

TkcAIAQ

B

hh

&

Q&

Total

( ) 40

TAdQQ == &&10

-1

100

101

102

103

10

0 2 4 6 8 10

EMIS

SIVEPOWER(W

/cm

2m

)

WAVELENGTH (m)

5600 K

2800 K

1500 K

800 K

Emissive Power

Wiens displacement law

mK2898max =T


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http://ocw.mit.edu

2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies

Fall 2009

For information about citing these materials or our Terms of Use, visit:http://ocw.mit.edu/terms.
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Solar Thermal Energy Lecture 1

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