Solar EnergyPart 3: Thermo-solar

San Jose State UniversityFX Rongère

February 2008

Thermo-solar

Absorption of the solar radiation Heating of a fluid to transfer energy

to a process Differences come from the type of

solar collectors and from the type of working fluid

Thermodynamics The state of a system of pure material at the

equilibrium is determined by two variables: Energy: E, e (lower case per unit of mass)

Entropy: S, s

Energy balance: conservation – Closed system

Entropy balance: no conservation – Closed system

AA

AA

Closed

WQdt

dE

A A

A

Closed T

Q

dt

dS

First law

Second law

0

Definition of the Entropy

Ludwig Boltzmann’s grave in Vienna

Thermodynamics “Thermodynamics is a funny subject. The first time you

go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, it doesn't bother you any more.”

“The second law of thermodynamics holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations - then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

Thermodynamics (2)

Open system (mass transfer) Energy balance

Entropy balance

).( AAAA

AA

AA

AOpen

khmWQdt

dE

AA

AA A

A

Open

smT

Q

dt

dS.

Thermodynamics (3)

Material characteristics provide relations with Pressure and Temperature

Ideal gas:

),(

),(

).(.

TPss

TPuu

kuMeME

P

dPR

T

dTCpds

dTCpdh

dTRCpdTCvdu

..

.

).(.

T

dTCds

dPvdTCdh

dTCdu

.

..

.

Incompressible fluid:

KmolJR ..314.8 1

Heat exchange

Energy balance:

2

'

2,

244

2,

2,

..

).(

..

.

.

.

dTgradk

dTTh

dTT

da

da

hm

cond

ambconv

sky

diffussol

directsol

es

Efficiency

oC

0 38 76 114 152 190 228 266 304oF

Eff

icie

ncy

(%

)

A

hmEfficiency

diffusSoldirectSol

es

.

.

,,

Absorber

Up to 30oC (80oF) – Swimming pools

Flat-plate Collector

Up to 80oC (150oF) – Home heating, Water heating

Sometimes vacuum is made in the collector to prevent convection

Glass decreases radiation and convection Insulation is usually of polyurethane foam or mineral wool, sometimes mineral fiber insulating materials like glass wool, rock wool, glass fiber or fiberglass are used.

All technologies use selective surface coating to: Maximize solar radiation

absorption Minimize collector emission

Selective surface coating

Black chrome, black nickel, and aluminum oxide with nickel (galvanization) Titanium-nitride-oxide layer, (steam in vacuum process)

0

0.5

1

1 2 3

Wave length λ, μm

Em

issi

vity

, Ab

sorp

tivi

ty, ε

λ, a

λ

Evacuated Tube Collectors

Over 80oC (150oF) up to 160oC (300oF) – Industrial porcess

How a heat pipe works?

Evaporation process capture more energy by mass unit than one-phase flow. Example, water and steam:

Lv=2,260 kJ/kg, Cp=4.18 kJ/kg/K required flow is about 50 times lower than for

water heating

Size is smaller, loss are reduced The flow is maintained in natural

convection if the collector is angled over the horizontal

Pool heating

Sizing the collector and the pump

ASHRAE ch. 4ASHRAE ch. 48

Step1: Heat transfer

CIRCULATION

CIRCULATIONADDITION

Step2: Heat transfer modeling

Radiation heat transfer

244

2,

2,

..

.

.

dTT

da

daQ

sky

diffussol

directsolA

rad

Radiation absorbed by water

0%

20%

40%

60%

80%

100%

0 0 1 10 100 1,000

Depth (cm)

Abso

rbed s

ola

r ra

dia

tion (%)

aΣ = .8 to .9εΣ = .8 to .9

Source: R Siegel, J R. Howel Thermal Radiation Heat Transfer Hemisphere Publishing 1981

Step2: Heat transfer modeling

Convective heat transfer

airwLairte TTAL

kC

..Pr.Re.. 3

18.0

2, ).( dTThQ ambconv

Aconv

airL

LV

.

Re

Parameter Signification SI American

Cte Empirical constant 0.037 0.037

kair Air conductivity 0.026 [W/ m/ K] 0.015[Btu.ft/ (h.ft2.oF)]

L Length of the swimming pool in wind direction

[m] [ft]

V Wind speed [m/ s] [ft/ h]

νair Air viscosity 14.3 10-6 [m2/ s] 0.554 [ft2/ h]

A Swimming pool area [m2] [ft2]

T Temperature [K] [oF]

Φconv Convective transfer [W] [Btu/ h]

Source: ASHRAE Application Handbook p 49-2

Step2: Heat transfer modeling

Convective Heat Transfer

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0 2 4 6 8 10

Wind speed (m/s)

Con

vect

ion

coeff

ecie

nt

W/m

2/K

Step2: Heat transfer modeling

Evaporation

FaVCCppLv

Am

dLvmQ

awA

evap

evapA

evap

)..).(.(

..

21

2

Source:ASHRAE Application Handbook p 4-6

Type of swimming pools Factor of activity (Fa)

Residential swimming pools 0.5

Condominium 0.65

Thermal baths 0.65

Hotel 0.8

Public swimming pools or Schools 1

Whirlpools, spas 1.5

Wave pools, water slides 1.5 (minimum)

Parameter Signification SI American

C1 Empirical constant 0.088 [W/ m2/ Pa] 95 [Btu/ (h.ft2.inHg)]

C2 Empirical constant 0.779 [J / m3/ Pa] 0.425 [Btu.min/ (h.ft3.inHg)]

Lv Latent heat for water vaporization

2,260,000 [J / kg] 972 [Btu/ lb]

V Wind speed [m/ s] [ft/ h]

pw Saturation pressure at outside air dew point

[Pa] [inHg]

A Swimming pool area [m2] [ft2]

pa Saturation pressure at water temperature

[Pa] [inHg]

mevap Evaporation rate [kg/ s] [lb/ h]

Dry and Moist Air

0 20 40 60 80 1000.000

0.010

0.020

0.030

0.040

0.050

T [F]

Hu

mid

ity

Ra

tio

Pressure = 1.0 [atm]

0.2

0.4

0.6

0.8

30 F 45 F

60 F

75 F

AirH2O

Dew Point

Kg water/kg air

Saturation pressure of air:Pa=Humidity Ratio*Atm Pressure

Step2: Heat transfer modeling

Conduction in the ground

2

'

. .. dTgradkQ condA

Cond

kcond: Conductivity of the soil (1 to 3 W/m/K – 0.6 to 1.8 Btu/hr/ft/oF)

Step3: Balance Equation

WheatercircWCityA

evap

Acond

Aevap

Aconv

Arad

AAAA

AA

AA

AOpen

TTCmTTCm

QQQQ

khmWQdt

dTCM

dt

dE

....

).(..

.

mcirc= Masse of water divided by 8 hours

C= Thermal capacity of the water (4,180 J/kg/K, 1 Btu/lb/oF)

Step4: Sizing the collector

Max Temperature elevation: 8oF Solar radiation:

Ex: facing south with 30o of tiltTotal Solar Radiation on a panel (Tilt 30)

San J ose J une 21, 2007

0

100

200

300

400

500

600

700

800

900

1000

0:00 6:00 12:00 18:00 0:00

Time

Rad

iation

(W

/m2)

Direct Tilt 30

Diffuse

Total

Step4: Sizing the collector

Efficiency: .8 Flow rate:

Required energy:

Required area:

8.28600,3.8

.

600,3.8

VVMmcirc

Resource: http://www.flasolar.com/php/pool_panels_entry.php

0 38 76 114 152 190 228 266 304

VV

TCmcirc .6454.4.180,4.8.28

..

VVV

AreaPanelsol

.9.0900.8.0

.645

.8.0

.645_

Units: SI

Step 5: Simulation

Heat Transfer Modes - Without Solar Heating

24oC

-200

0

200

400

600

800

5 10 15 20

Time

Heat

Tra

nsf

er

(W/m

2)

Convection

Water addition

Evaporation

Solar Radiation

If no shade and good wall insulation, solar radiation absorbed by the pool easily compensates the heat loss by evaporation and convection:

Absorbed solar radiation: 280 kWh/day

Without Solar Collector

Temperature gain in a day is about 4.5oC for 13oC, 3oC for 18oC and 2oC for 24oC.

Temperature gain during the day

without Solar heating

-2

-1

0

1

2

3

4

5

6

0 4 8 12 16 20 24

Time

Tem

pera

ture

gai

n (

oC)

13

18

24

With Solar Collector

Temperature gain in a day is about 10oC for 13oC, 8.5oC for 18oC and 7oC for 24oC. Temperature gain during the day

Solar heating (South)

-4

-2

0

2

4

6

8

10

12

0 4 8 12 16 20 24

Time

Tem

pera

ture

gai

n (oC

)

13

18

24

Addition: 300 kWh/day

Savings compared to gas heater:

10 Therm/day$ 12/day

Cost:$ 100/m2

$ 4,500Use: 60 days/yearPay back: 6 years

With Solar Collector

South-East orientation provides faster heating in the morning but less overall energy.

Addition: 290 kWh/day

Temperature gain during the day

Comparison at 24oC

-2

0

2

4

6

8

10

0 4 8 12 16 20 24

Time

Tem

pera

ture

gai

n (

oC)

Collector FacingSouth

Collector FacingSouth-East

Without SolarCollector

Step 6: Installation

Typical installation of a solar collector for pool heating:

Step 7: Sizing the pump and pipes

Some orders of magnitude

hp