FlatPlate With Evacuated Tubes(1)

MENG413_Flat-plate solar-heaters

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FLAT PLATE SOLAR HEATING

INTRODUCTION

a) Open trough; loss by evap+ convection+ground conduction+long wave(infrared) radiation

b) Open trough off ground; loses heat by evaporation + convection + long-wave radiation

c) Black closed tank; heat loss by convection to wind + ground conduction+ L.W. radiation

d) Black tank insulated underneath; heat losses by upper convection + radiation

e) Sheltered Black tank, better than before but materials degradable.

f) Metal tube and plate collector (commercial std) &flooded plate(more efficient)

g) Double glazed flat plate; better insulation than (f)

h) Selective surface αshort >> εlong ; radiative losses reduced

i) Evacuated collector; no convection or conduction losses to cover.


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Refinements increase Solar radiation absorbed by heater, or decrease heat loss.

Main part of a solar heating system is the collector, where solar radiation is

absorbed and energy transferred to fluid

Non-concentrating collectors, subject of this chapter, absorb both beam and

diffuse radiation, and are cheaper than concentrators

They are generally preferred for heating fluids up to 80oC.

Water may be heated indirectly, using a heat exchanger. Heating fluid may then

be oil or antifreeze solution; reducing corrosion, eliminating freezing/boiling.

1. Uncovered Enclosed Black Container, Fig5.1d


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Ex1. Heat balance of an unsheltered black bag: A rectangular black rubber bag

1m×1m×0.1m with walls 5 m.m. thick is filled with 100 litres of water, supported

on a thin, non-conductive, horizontal grid well above ground, and exposed to a

solar irradiance G= 750 W/m2, Fig 5.3. Ta=20

oC, Wind speed 5 m/s, αp=0.9 .

Calculate resistance to heat loss from bag; hence estimate maximum water-

temperature and time taken to reach max temperature.

Assuming:(mc)skin<<Cf= (mc)water, Tf is uniform(lumped capacity analysis),Tf=Tp :

L

aff

R

TTAG

dt

dTmc

)()(

(1)

Resistance to convective heat loss: Rv,pa ≡ 1/(hv AL)

Convective heat transfer coefficient , hv depends on wind speed (Re) , air properties

(Pr,k) and Lplate (MENG466). HT eqns give hv= 24.7 W/m2 K; AL≈2 m

2.

Radiative heat flow to sky:

Pr,ps = εpσAL(Tp4 – Ts

4), where Ts=Ta- 6 K

Pr,ps=hr,paAL(Tp-Ta), where ap

spspp

par

par TT

TTTTh

AR

))((12222

,

,

RL = 1 / (1/Rv,pa + 1/Rr,pa)

Assuming Tp=40oC, hr,pa=7.2 W/m

2K yields : RL= 0.015 K/W.

Maximum temperature when dTf/dt= 0, hence from eqn(1):

(Tf - Ta) / RL =α.Ap.G, Ap= 1m2.

yielding Tf,max = 31oC.

To get rough estimate of time, Δt, taken to reach Tf,max, employ eqn(1) at mid-

temperature 25oC to yield: (dTf/dt)25 = 8.1×10

-4 K/s. Hence :

Δt =ΔT/(dTf/dt) = 1.3×104 s = 3.7 h.

Much more accurate predictions may be made by:

System is fixed mass, unsteady, no flow.


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Using Heisler charts(MENG466); or better still solving numerically the

partial differential equations presented in MENG466 for non-uniform Tf .

Taking variation of G with time of day into account, according to previous

chapter.

2. Sheltered Black Container, Fig5.1e

Ex2. The container of Ex1is placed inside a box with a glass lid 3 cm above it 10

cm insulation below. For same external conditions, calculate : RL, Tf,max and Δt to

reach it.


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Conduction loss at base, Pb = (Tp- Tb)/Rb ≈ (Tp – Ta)/Rb ≈ (Tp –Ta)kA/x (2)

For Tp=70oC, eqn(2) yields Pb ~ 15 W which is negligible. Hence heat balance for

water yields (unsteady, fixed mass system):

pa

aff

R

TTAG

dt

dTmc

(3)

Outward heat transfer occurs in 3 stages,Fig5.4b:

i. Heat transfer from plate to glass by free convection of air in gap + long-wave

radiation(~10μm):

to start analysis, assuming Tp = 70oC, Tg=0.5*(Tp+Ta)=45

oC.

for Natural convection between parallel horiz. plates a distance Y apart:

Nu ≡ h .Y/k = 0.062 Ra0.33

; hence Nu= 2.06 and Rv,pg=Y / (k.Nu) =0.52 kW/m2

for 2 infinite parallel plates:

))()(()(

111

)(2121

2

2

2

1

2121

214

2

4

1

2121

21

21

4

2

4

1 TTTTTTTTTT

A

qr

≈ ,2

),(4 21

21

3

2121

21 TTTwithTTT

when (T1-T2)/T1<<T1

hence R = (T1-T2)/q ≈ 3

21

2121

4 T

taking εp= εg = 0.9 for long-wave radiation, eqn(4) yields Rr,pg= 0.16 K/W

ii. Conduction across glass layer:

kglass≈ 1 W/m.K, Δx~ .005m.; hence Rg = Δx /kA is negligibly small; ΔT~0.

iii. Heat transfer from Glass to surroundings by free/forced convection + long-

wave radiation:

Rga =

1

,,

11

gargav RR= 0.031 K/W, same as for previous example.

Neglecting Ta-Ts, overall resistance between plate-top and surroundings:


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WKRR

RRR

Rgargav

g

pgrpgv

pa /15.01111

1

,,

1

,,

To get Tf,max, substitute in (3) for DTf/dt=0, τ = α =0.9, Rpa = 0.15 and G= 750, to

get Tf,max = 95oC.(which is unrealistically high due to assumptions, particularly G

uniform with t)

To get Δt to Tf,max , estimate (dTf/dt)60 as previous example to give Δt=31 hrs.

Better solution accuracy can be obtained by re-iteration but result will still suffer

from assumptions. Still, comparison of results of Ex1,2 shows that the presence of

a glass cover approx quadruples Rpa; yielding water temperatures > 50oC.

3. Plate and Tube Collectors (Commercial application)

Water is confined in parallel tubes which are attached to a black metal plate.

It is essential to have small thermal resistance between plate and tubes.

tube diameters ~ 2 cm, tube spacing ~20 cm, plate thickness ~ 0.3 cm

plate and tube enclosed within insulated sides and bottom, and top glass cover;

network diagram is similar to sheltered black bag, but steady flow open system

heated fluid may be used immediately , or stored and/or re-circulated.

volume of fluid in tubes is small so separate storage(100-200 litres) is required

pumping rate designed to give ΔTf ~ 5-10oC during daylight; shutdown at night

forced circulation systems are easily adaptable to existing water heater systems

usually higher η than passive systems due to higher circulation rate; better control


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Flat Plate Efficiency

Pnet = τcov.αp.Ap.G – [(Tp – Ta)]/RL=Ap[τcov.αp.G – UL(Tp – Ta)] = ηsp.ApG (4)

where ηsp is capture efficiency, UL is overall heat loss coefficient. Hence:

ηsp = τcov.αp – UL(Tp – Ta)/G (5)

Useful output, Pu, is energy transferred to fluid at temperature Tf :


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Pu = m’ c (T2- T1) where (m’) steady flow through collector

= ηpf . Pnet , where ηpf is the transfer efficiency(typically~0.85)

Defining a collector efficiency ηc : ηc = Pu/(Ap G)

ηc = ηpf × ηsp= ηpf [ τcov.αp – UL(Tp – Ta)/G]

Since Tp is usually not known, it is more convenient to use mean fluid temp T̅f:

ηc = ηpf [ τcov.αp – UL(T̅f – Ta)/G] (6)

ηc can be improved by:

i. reducing convective transfer between plate and outer glass cover; e.g. by inserting

extra glass cover, or vacuumizing

ii. reducing radiative loss from plate by using selective surface materials which are

strongly absorbing of short-wave radiation(λ ~0.5 μm) from sun(~6000 K) and

weakly emitting of long-wave radiation(λ~10 μm) from plate(~350 K). For

selective surfaces, α , ε in eqns are weighted average values of αλ , ελ over λ range.


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some semiconductors display αλ , ε which approach ideal selective surfaces

however they have poor mechanical strength, small k, and high costs

metals are mechanically strong, good conductors and relatively cheap, but poor α

Placing thin layer of semiconductor over metal, combines desirable characteristics.

Absorbed heat by semiconductor film is passed by conduction to underlying metal

Semiconductor thickness should be small to reduce conduction resistance, cost.


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4. Evacuated Collectors

A type of solar collector that can achieve high temperatures, in the range 77°C to

177°C and can, under the right set of circumstances, work very efficiently.

Evacuated-tube collectors are, however, quite expensive, with unit area costs

typically about twice that of flat-plate collectors. They are well-suited to

commercial and industrial heating applications and also for cooling applications

(by regenerating refrigeration cycles). They can also be an effective alternative to

flat-plate collectors for domestic space heating, especially in regions where it is

often cloudy. For domestic hot water heating, flat-plate collectors tend to offer a

cheaper and more reliable option. An evacuated-tube collector consists of parallel

rows of glass tubes connected to a header pipe. Each tube has the air removed from

it to eliminate heat loss through convection. Evacuated-tube collectors fall into two

main groups:

4.1 Direct-flow evacuated-tube collectors

These consist of a group of glass tubes inside each of which is a flat or curved

aluminum fin attached to a metal (usually copper) or glass absorber pipe. The fin is

covered with a selective coating that absorbs short wave solar radiation well but

inhibits long wave radiative heat loss. The heat transfer fluid is water and

circulates through the pipes, one for inlet fluid and the other for outlet fluid.

Direct-flow evacuated tube collectors come in several varieties distinguished by

the arrangement of these pipes:

4.1.1 Concentric fluid inlet and outlet (glass-metal).

These use a single glass tube. Inside this is a water flow pipe with attached fin.

This type of construction means that each single pipe can be easily rotated to allow

the absorber fin to be at the desired tilt angle even if the collector is mounted

horizontally. The glass-metal design is efficient but can suffer reliability problems.

The different heat expansion rates of the glass and metal tubes can cause the seal

between them to weaken and fail, resulting in a loss of vacuum. Without a vacuum,

the efficiency of an evacuated-tube collector is no better, and may be worse than,

that of a flat-plate collector.

4.1.2 Separated inlet and outlet pipes (glass-metal).

This is the traditional type of evacuated-tube collector. The absorber may be flat or

curved. As in the case of the concentric tube design, the efficiency can be very


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high, especially at relatively low working temperatures. The weakness again is the

potential loss of vacuum after a few years of operation.

4.1.3 Two glass tubes fused together at one end (glass-glass).

The inner tube is coated with an integrated cylindrical metal absorber. Glass-glass

tubes are not generally as efficient as glass-metal tubes but are cheaper and tend to

be more reliable. For very high temperature applications, glass-glass tubes can

actually be more efficient than their glass-metal counterparts

4.2 Heat pipe evacuated-tube collectors

These consist of a metal (copper) heat pipe, to which is attached a black copper

absorber plate, inside a vacuum-sealed solar tube. The heat pipe is hollow and the

space inside, like that of the solar tube, is evacuated. The reason for evacuating the

heat pipe, however, is not insulation but to promote a change of state of the liquid

it contains. Inside the heat pipe is a small quantity of liquid, such as alcohol or

purified water plus special additives. The vacuum enables the liquid to boil (i.e.

turn from liquid to vapor) at a much lower temperature than it would at normal


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atmospheric pressure. When solar radiation falls the surface of the absorber, the

liquid within the heat tube quickly turns to hot vapor rises to the top of the pipe.

Water, or glycol, flows through a manifold and picks up the heat, while the fluid in

the heat pipe condenses and flows back down the tube for the process to be

repeated.

An advantage of heat pipes over direct-flow evacuated-tubes is the "dry"

connection between the absorber plate and the header, which makes installation

easier and also means that individual tubes can be exchanged without emptying the

entire system of its fluid.

Some heat pipe collectors are also supplied with a built in overheat protection –

when a programmed temperature has been reached, a "memory metal" spring

expands and pushes a plug against the neck of the heat pipe. This blocks the return

of the condensed fluid and stops the heat transfer.

A drawback of heat pipe collectors is that they must be mounted with a minimum

tilt angle of around 25° in order to allow the internal fluid of the heat pipe to return

to the hot absorber.


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Analysis of Evacuated Tube Collectors:

Convective losses can be reduced by double glazing or evacuating space

between plate and glass cover

Vacuum posses strong forces on structure and glass cover.

Outer tube is made of glass for transparency and strength; inner tube also

usually glass-tube because of its very low out-gassing rate.

Typically d = 4 cm and D=5 cm

Arrays of such tubes are connected.

Heat Balance of an evacuated collector

Ex3. Calculate loss resistance o f evacuated collector of Fig5.11(a) and estimate its

stagnation temperature. Take D=5 cm, d=4cm, length of tube 1.0m; long-wave

emittances: εp=0.10, εg=1.0; short wave(solar) absorptance of plate αp=0.85, short-


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wave transmittance of glass τg=0.90, G= 750 W/m2, Ta =20

oC, Tcov=Tg=40

oC;

Tp=100oC, u= 5 m/s.

Soln:

Treating tubes as 2 infinite parallel plates:

Taking characteristic internal area, Apg = π (.045m) (1.0 m) = 0.14 m2,

External area Ag = π ( 0.05 m) (1.0 m) = 0.157 m2

))((1 22

,

gpgp

gpgp

pggp

pgr

TTTTA

R

= 0.1288 W/K → Rpg = 7.7 K/W

From HT relations for v= 5 m/s we get hv,ga = 24.7 W/m2K

322

,

]2/)[(4))((1

gagaggagagag

gar

TTATTTTAR

=6.2 W/K

Combined radiation + convection resistance: Rga =1/[ (hv,gaAg)+1/Rr,ga]=0.21 K/W

Rpa = Rga + Rpg = 0.21 + 7.7 = 7.9 K/W.

It is seen that Rpg is the dominant resistance term, since convection is absent.

Conducting a heat balance in absence of heat removal by fluid flow(to get Tmax):

τg αp G d (1.0 m) = (Tp,max – Ta) / Rpa → Tp,max = 200oC.

0.5


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5. Air Heaters

Mainly used for space heating and crop drying.

Similar to solar water heaters; air is warmed by contact with a radiation

absorbing surface

Does not contain heavy fluids so can be built of light, cheap materials

Pu = ρ c Q(T2 –T1)

Volume flow rate Q is much larger than for water heaters

Since kair << kwater , rate of heat transfer from plate to fluid is reduced

Roughened or grooved plates are employed in Fig6.1a designs to increase the

surface area and turbulence(to increase

h) in order to improve rate of heat

transfer.

Alternatively contact area is increased

using porous or grid collectors,Fig6.1b

Same molecules carry useful heat and

convection losses, Fig 6.2

Coupling ignored as a first approx. to

simplify analysis.

If component of solar irradiance incident

perpendicular to collector is Gc on area A,

heat absorbed by air is difference

between heat absorbed by plate and heat

losses from plate, multiplied by collection

factor f:

Pu = f [A Gc τcov αp – Uc A (Tp – Ta)]

and collector efficiency is

ηc =Pu /(GcA) = ρ c Q (T2 – T1)/(GcA)


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FlatPlate With Evacuated Tubes(1)

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