Solar Water Heating Theory
R T Dobson
Senior Lecturer
rtd@sun.ac.za
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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The
Objective
of this talk is to present the
basic theory
on which solar water heaters work.
We will consider
flat plate solar water heaters
(both thermosyphon and pumped)
as well as
evacuated tube solar water heaters
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Contents
How do we?:
•Collect the heat
•Transport the heat
•Store the transferred heat
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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A little about myself
1970-1980 Nuclear Energy
1980-1985 Solar Energy
1985-1988 Missile Manufacture Management
1988-2008 Heat Transfer Lecturer
My research philosophy is:
Adaptive engineering
were we try and engineer our heat transfer systems to make
exclusive use of
natural forces
such as gravity, surface tension density gradients and buoyancy
to do the job for us
without the use of any mechanically moving parts such as pumps
and mechanical activators and active electronic and mechanical
controls and switches
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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We used the roof and the car park as our solar water heater
test laboratory at Kwikot LTD, Edinburg Road, Benoni
Solar panels
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Integral Solar water heaters
South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Thelma (Kwikot Factory Personal manager) cooking pap along
side Benoni Lake in 1983
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Front and back-page of our “Frost Resistance” Panel
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Solar water heater
configurations
• Integral
• Thermosyphon
• Pumped
• Close-coupled
• Swimming pool
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Integral solar water heater
W
Co
lle
at
ct
er
or
sto
ra
ge
Solar collector and Water Storage all in one unit
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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r
Co
lle
ct
o
Thermosyphon
solar water
heater
Water
storage
Solar collector below
water Storage and
water flows by
thermosyphonic action
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Pumped solar water heater
Solar collector
below water
storage. Water is
pumped
Co
l
lec
to
r
Water
storage
Water Pump
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Close-coupled Thermosypon
solar water heater
Solar collector and
water storage
separated but on a
common integrated
support platform to
look like a single unit
Ro
o
Co
l
lec
to
r
f
Water
storage
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Close-coupled Indirect Tank-in-Tank
Thermosyphon solar water heater
Thermosyphon (or natural circulation
indirect solar water heating system
Water
storage
tank
Tank-in-tank
heat exchanger
Solar
collector
Circulation loop
containing anti-freeze
and water solution
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Swimming pool solar water
heater
Water pumped from
pool up to solar
collectors on roof
Solar
collector
“High-pressure” pump
Open water tank
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Swimming
pool solar
water heating
system
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Thermosyphon solar water heating system
How does it work?
Fhot = ρhotgH
H
The density of the hot
fluid is less than the
density of the cold fluid.
The force of attraction to
the earth of the hot fluid
is less than for the cold
fluid. As a result of this
force imbalance cold
fluid sinks and the hot
Fcold = ρcoldgH fluid rises and the fluid
circulates around the
loop. The denser or
heavier fluid package
will sinks and pushes the
less-dense or lighter fluid
up
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Thermosyphon solar water heating system
Glass cover
Hot
Hot water
rises
Cold
Insulation
Cold
Cold
water
water
sinks
sinks
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Basic theory: Divide the system into control volumes and
apply the conservation of mass, momentum and energy
m& out
∆x
m& vout
Pout
m& hout
m& in
Conservation of mass:
m& vin
∆m
= m& in − m& out
∆t
Pin
mg
τ℘∆x
m& hin
Q& heat transfer
Conservation of momentum:
Thot − Tcold
=
∆mv
R
= m& vin − m& vout − mg − τ℘∆x − ( Pout − Pin ) A
∆t
∆U
= m& hin − m& hout + Q& heat transfer
Conservation of energy and heat transfer:
∆t
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Basic heat transfer theory:
Thot − Tcold
&
[W] Q&
Heat transfer equation: Q =
R
Hot
Conduction:
Convection:
R=
R=
∆x
[°C/W]
kA
∆x
Cold
Q&
1
[°C/W]
hA
Cold
Hot
Fluid
Radiation:
R=
(
1
)
εAσ (T1 + 273) + (T2 + 273) ((T1 + 273) + (T2 + 273) )
2
2
Q&
Hot
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vacuum
Cold
South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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[
Basic theory: Effect of glazing (glass)
longwave
Q& radiation
shortwave
Q& solar
incident
Q& reflected
Q& convection
shortwave
Q& solar
incident
longwave
Q& radiation
Q& convection
Q& reflected
Glass
longwave
Q& conductionQ& radiation
Absorber
Insulation
Absorber
Insulation
Q& conduction ≈ 0
Q& conduction ≈ 0
(a) No glass cover
plate
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(b) With glass cover plate
South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Evacuated-tube solar water
Hot
heaters
Hot water
water
Vapour
Cold water
glass
Black paint
Vacuum
Evacuated
double walled
SAHPA® glass tube
Condensate
Evacuated
double walled
glass tube
+
heat pipe
South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Typical domestic evacuated-tube
solar water heater installation
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Typical pumped indirect solar
water heating system
Heat exchanger
Water
storage
tank
Pump Expansion tank
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Basic theory: Heat collection
Q& solar
Q& reflected = (1 − τα )Q& solar
Heat storage
Q& water−out
= m& cTwater−out
Q& in = ταQ& solar
Q& lost
(
Q& water−into tank
= m& cTwater−in
Q& water−in = m& cTwater−in
)
= U Tcollector − Tsurrounding air
Q& into water
Water
storage
tank
(
Q& into collector = ταQ& solar − U Tcollector − Tsurrounding air
)
Q& in − Q& lost = Q& absorbedby water
& c(Twaterout − Twaterin )
ταQ& solar - U(Tcollector − Tsurrounding air ) = m
Q& water−in = m& cTwater−in
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Typical solar water heater collector characteristics
100
Collector efficiency, η (%)
80
Solar collector thermal perfofmance characteristic is :
η = a + b(Tc − Ta )
60
where solar colloector efficiency η =
&
Q
τ α ⋅ Q&
input
a= &
= & solar = τ α , and
Qsolar
Qsolar
heat input factor
40
20
0
Evacuated glass tube
Black
paint
Black paint
+ Glass
(
heat collected τ α - U Tcollector − Tsurrounding air
=
&
&
Q
Q
solar
solar
& c(Twater out − Twater in )
heat into water m
=
=
&
&
Q
Q
solar
solar
heat loss factor b =
Selective coating
+ Glass
100
200
Temperature difference, Tc – Ta (°C)
where Tc ≈
&
Q
collected
&
Q
input
300
Twaterin + Twater out
2
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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)
My rules!@#$%^&*()?:
Up to 40% electricity savings
50 % efficient
500 W/m2 over an 8 hour period
Overheating??
Expansion relief??
Air bubbles??
Thanks
Pressure??
Corrosion??
Gas loaded heat pipe
temperature control??
Automatic air relief??
Freezing??
Reverse thermosyphoning??
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Typical pumped indirect solar
water heating system
Heat exchanger
Water
storage
tank
Pump Expansion tank
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Theoretical modeling
Consider a hollow pipe with a variable diameter
and fashioned into a closed loop and also
containing a working fluid
Expansion
tank
z
∆z
g
Divide the loop up into a number of smaller control
volumes, apply the equations of change to each
control volume, and integrate around the loop!
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Theoretical modeling (cont.)
Conservation of Mass
∆m
Single phase flow
= 0 = m& in − m& out
∆t
∆m
≠ 0 = m& in − m& out but mass enters the
Two-phase flow
∆t
expansion tank instantaneously
Assumptions:
* One-dimensional flow m& = ρVA
* Both liquid and vapour phases are incompressible
* Density (pressure) waves occur instantaneously, ie speed of
sound >> m&
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Theoretical modeling (cont.)
Conservation of Energy
Single phase flow for the ith control volume with the
temperature T expressed explicitly:
Heat transfer rate
t + ∆t
Ti
t
= Ti
m = ρ A∆z
∆t &
t
+ t (Qin,out + m& iin − m& iout )
mi c
i = enthalpy
c = specific heat
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Theoretical modeling (cont.)
Conservation of Energy
Two-phase flow for the ith control volume with the
temperature T expressed explicitly:
uit + ∆t
=
uit
∆t &
+ t (Qin,out + m& iin − m& iout )
mi c
t +∆t
If ut+∆t < uf then Thp
= ut +∆t cv and xt+∆t = 0
t +∆t
If u t+∆t > uf then Thp
= Tsat and
xt+∆t = ut+∆t − utf+∆t utfg+∆t , where uhp = uf + xufg ,
i = if + xifg , uf = cvThp and if = cpThp .
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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Theoretical modeling (cont.)
Conservation of Momentum applied to heat pipe control
volumes to determine the mass flow rate
Buoyancy driving term
Frictional-resistance term
C f ,l o,kφ l o,k L k + Lf,equiv,k 2
m&
2
∑ ρ k L k g sin φ k k∑=1 ρ r
Ax, k
d m&
k i, hp
k =1
=−
−
Nk L
Nk L
dt
k
∑
∑ k
k =1 Ax, k
k =1 Ax, k
Nk
Nk
Assumptions:
* Quasi-eqilibrium
* Both liquid and vapour phases are incompressible
* Homogeneous two-phase flow model
* Hydrostatic pressure at a point (Archimedes and
Boussinesq ‘s approximation)
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South African Heat Pipe Association Solar Water Heating Theory, 24 Oct 2008, Stias, Stellenbosch
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