11/1/2012

1

Solar Energy Basics Lecture 3 Thermal Systems

Sergio CaparedaBAEN, TAMU

Available Solar Radiation

• Solar or short wave radiation – 0.3 – 3μm range• Long wave radiation – radiation originating from

sources at temperatures near ordinary ambient temperatures (wavelengths > 3 um).

• Instruments to measure solar radiation– Pyrheliometer – measured direct solar radiation– Pyranometer – measures global (direct + diffuse)

radiation– Pyranometer with shaded ring – measures diffuse

solar radiation

Designing Flat Plate Collectors• Basic equation

• whereQu = useful energy (MJ) also qu=Qu/Ac

Ac = collector area (m2)S = incident solar radiation (MJ/m2h)UL= overall heat loss coefficient (W/m2C)Tpm = mean plate temperature (oC)Ta = ambient temperature (oC)

)]([ apmLcu TTUSAQ

Equation Development• An alternate equation is given by

• where, Tf = mean fluid temperature, andF’ = is the collector efficiency factor (It is difficult to measure Tpm)

• Another simplified equation

whereTin = inlet water temperatureF”= collector flow factorFR = F’F’’ = collector heat removal factor

)]([' afLcu TTUSFAQ

)](['''aiLcu TTUSFFAQ

)]([ aiLRcu TTUSFAQ

p

Lc

Lc

pR Cm

FUAUACm

F

'

exp1

p

Lc

Lc

pR

CmFUA

FUACm

FFF

'

'''' exp1

11/1/2012

2

• Example. Calculate the daily useful gain and efficiency of an array of 10 solar collector modules installed in Boulder, CO. Other data: Ti = 40C; m = 0.03 kg/s; Cp = 4,190J/kgC; UL = 8 W/m2-h; F’ = 0.841

Time Ta (oC) IT(MJ/m2h)

S (MJ/m2h)

UL(Ti-Ta) qu(MJ/m2h)

Efficiencyη

7-8 -11 0.02 0.01 1.46 0.00 0.008-9 -8 0.43 0.35 1.38 0.00 0.00

9-10 -2 0.99 0.82 1.21 0.00 0.0010-11 2 3.92 3.29 1.09 1.76 0.4511-12 3 3.36 2.84 1.07 1.42 0.4212-1 6 4.01 3.39 0.98 1.93 0.481-2 7 3.84 3.21 0.95 1.81 0.472-3 8 1.96 1.63 0.92 0.57 0.293-4 9 1.21 0.99 0.89 0.08 0.074-5 7 0.05 0.04 0.95 0.00 0.00

Sum 19.79 7.57

• Solution1. Dimensionless collector mass flow rate is

2. Flow factor

3. Heat removal factor

4. Average loss rate from 10-11 am

5. Useful energy gain per unit collector area

6. Collector efficiency for this hour and daylong efficiency

7. Daily useful gain for all collectors

35.9841.01

82190,4

sec03.0

2

2

'

xJWsx

WxmCmx

kgCJxkg

FUACm

Lc

p

948.035.91exp135.9exp1

'

''''

p

Lc

Lc

pR

CmFUA

FUACm

FFF

797.0948.0*841.0exp1'

p

Lc

Lc

pR Cm

FUAUACm

F

hmMJTTU aiL2/09.13600*)240(*8)(

hmMJxAQq

c

uu

26 /76.110)09.129.3(797.0

%)45(45.092.376.1 or

Iq

AIQ

T

u

cT

u %)38(38.079.1757.7 or

Iq

T

uday

MJxQu 1501057.7*2*10 6

Solar Dryer with Rockbed Heat Storage

Concentrating Collectors• Concentrating collectors – deliver energy at

temperatures higher than those possible with flat plate collectors

• Collector configurations

11/1/2012

3

Area Concentration Ratio (ACR)• ACR – the ratio of the area of aperture to

the area of receiver.

• Equation for parabolic dish

• The collector flow factor is

• Calculations similar to flat plate collectors with more solar radiation absorbed.

areareceiverareaaperture

AAACR

r

a

)( aiL

a

rRau TTU

AASFAQ

p

Lr

Lr

pR

CmFUA

FUACm

FFF

'

'''' exp1

Solar Distillation SystemsProcesses1. Evaporation, e2. Condensation, c3. Radiation, r4. Convection, c,5. Conduction, k

Governing equation:

b = basin, g = glass cover, and transmittance of cover

dt

dTmCqqqqG bbpkgbcgbrec ,,

c

TAMU Solar Still Designs

2.9L/m2/day2.2L/m2/day

1.2 L/m2/day

2.2L/m2/day

Electricity Generation Costs for Renewables

Electricity Generation Cost (2008) Cents/kWh

Combined cycle gas turbine 3-5

Wind 4-7

Biomass gasification 7-9

Remote diesel generation 20-40

Solar PV central station 20-30

Solar PV distributed 20-50

Solar Thermal 15-20

Source: Solar Buzz, 2008 at http://www.solarbuzz.com