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Cheaper alternatives to conventional solar water heaters
As conventional solar water heaters have higher initial costs as compared to
commercial fuel-based water heaters (for example, electric geysers), severalattempts have been made to design cheaper systems. Some of these are
discussed below.
Collector-cum-storage water heater
This is a rectangular or cylindrical metal box (usually galvanized iron or mild
steel to keep the cost low), one side of which is painted black. The metal box is
kept inside a wooden enclosure (or a similar low-cost enclosure) with one side
open for fixing a cover glass (Figure 6.25).
If the height of the metal box is 50 mm, it can hold 50 litres/m2
ofcollector area. On the basis of a rough calculation for a 24-hour average
radiation level of 200 W/m2 and an average collector efficiency of 25%, a
temperature rise of about 20 C can be obtained for such a box-type col-
lector. If the initial temperature of water is 30 C, the final water
temperature would be 50 C, which is quite adequate for bathing, etc. Such
Figure 6.25 Simple collector-cum-storage solar water heater
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Solar thermal engineering 367
box-type water heaters have been investigated in India at CAZRI (Central
Arid Zone Research Institute), Jodhpur, and at TERI.
Shallow solar ponds
SSPs (shallow solar ponds) have long been considered potential alternatives for
conventional flat plate collectors. One of the earlier applications of SSPs was
in desalination (Hodge, Thompson, Groh, et al. 1966). An SSP prototype
facility was built and operated to supply hot water to the Sohio Uranium Mill
near Grants, New Mexico (Dickinson, Clark, and Iantuore 1976). A compact
SSP for hot water preparation for military and recreation purposes was
reported by Kudish and Wolf (1979).
SSP consists of a shallow bed of water contained within two plastic layers
black plastic layer at the bottom and transparent layer at the top with
suitable insulation and container box, and another glazing to reduce heat
losses (Figure 6.26).
The temperature build-up over the day can be obtained by solving the
equation
( ) ( )MCdT
dtA G A U T Tp
p
c c L p a = ( ) ...(6.84)
where (MC)pis the mass-specific heat product of water in the pond, Tpis the
temperature of water at a given time t, Ac is the area of the pond exposed to
sunlight, and () and ULare same as those in flat plate collectors. As fins and
Figure 6.26 Sectional view of shallow solar pond
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368 Renewable energy engineering and technology
fluid flow are not involved, Fand FRare unity. A theoretical and experimental
investigation of SSPs with continuous heat extraction has been proposed
(Kishore, Gandhi, and Rao 1986). A domestic solar water heater based on SSP
with a heat pipe heat exchanger, shown in Figure 6.27, has been studied experi-
mentally (Gandhi and Kishore 1983).
A portable SSP water heater has also been proposed (Kishore, Ranga
Rao, and Raman 1987). Temperature increments of up to 30 C over the day
have been reported. An SSP-DHW (shallow solar pond based domestic hot
water) system, where the hot water can be drained down into an insulated stor-
age tank, has been tested for long-term performance in Delhi (Raman and
Kishore 1992) (Figures 6.28 and 6.29).
Salinity gradient solar ponds
When sunlight falls on a water body such as a pond or a lake, part of the en-ergy is reflected from the surface and the rest is transmitted. For a given
wavelength of light, the transmission (, l) of a ray through a distance l in
water can be represented as
, expll
( )
( )
= ...(6.85)
where () is the characteristic wavelength-dependent attenuation length.
Attenuation of light results from absorption, molecular scattering, and scatter-
Figure 6.27 Shallow solar pond based domestic solar water heater
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370 Renewable energy engineering and technology
Due to the absorption of radiation, the temperature of a given layer of
water increases and the heated water tends to rise to the surface through
convection. For a layer of thickness l and temperature difference between the
top and bottom layer temperatures T, Rayleigh showed that convection does
not set in until T reaches a critical value given by the following equation
Rg T l
kT
T
= = =
3 4274
657 5. ...(6.86)
where RTis the thermal Rayleigh number, g is the acceleration due to gravity,
is the thermal expansion coefficient, is the kinematic viscosity, and kTis thethermal diffusivity.
In normal circumstances, convection would set in depending on the
magnitude of the Rayleigh number, but if one can create a density gradient,
in which the bottom portion of the layer has higher density than the top,
convection can be suppressed even if T is higher than the critical value. If
convection is suppressed, the solar energy entering the pond is trapped,
resulting in higher temperatures of the lower layers of water in the pond, from
which heat can be extracted for useful purposes. This is the principle of
operation of a solar pond. The pond thus becomes a solar collector with
built-in storage, and as no expensive metals are used, it is potentially cheaper.
Practical solar ponds are based on the fact that saline water has higher density
as compared to pure water. The density of a salt solution can be represented as
= 0[1 C
T(T T
0) + C
s(S S
0)] ...(6.87)
where 0corresponds to a reference state; C
Sand C
Tare coefficients; and S is
the salinity expressed as concentration or percentage of salt in the saline solu-
tion. The change in density can be calculated as follows.
T
CT= 0 ...(6.88)
S
Cs= 0 ...(6.89)
and
x S
S
x T
T
x= + ...(6.90)
where x is the vertical co-ordinate increasing downward. For densities to
remain stable, it is necessary that
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Solar thermal engineering 371
>
x0 ...(6.91)
Substituting from Equations 6.88 and 6.89 and re-arranging, we get
RC S x
C T x
s
T
=
( )
( ) > 1 ...(6.92)
This is the criterion for static stability and provides the salinity gradient
values for a given temperature gradient. In real ponds, there is another
criterion called dynamic stability criteria, in which both thermal and mass
diffusivity are considered in the double-diffusive system (Hull, Nielsen, and
Golding 1989).
In real solar ponds, there are three distinct zones: UCZ (upper
convective zone) or the surface zone, NCZ (non-convective zone) or the
gradient zone, and LCZ (lower convective zone) or the storage zone. A sche-
matic diagram of the solar pond is shown in Figure 6.30 (a).
The UCZ is formed due to wind effects, evaporation, etc., and can be
maintained at a thickness of about 3050 cm. The NCZ has a thickness of
11.5 m and the LCZ has a thickness of about 1.5 m. The density gradient
can be created artificially using a diffuser method (Kishore and Kumar
1996). Temperatures in LCZ and NCZ build up rapidly once the salinity gra-dient is established in a clear pond. The rise of temperature in the LCZ for
the 6000 m2solar pond of Bhuj is shown in Figure 6.30 (b).
With convection suppressed, NCZ can be treated as a transparent con-
ducting solid with a heat generating source (solar radiation absorbed).
Figure 6.30aSchematic diagram of the solar pond
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372 Renewable energy engineering and technology
Choosing a co-ordinate system with x = 0, corresponding to the surface of thepond, the solar radiation at depth x is given by
G(x) = Gsg(x) ...(6.93)
where Gsis the radiation immediately below the surface and is given by
Gs= G
0(1 a) ...(6.94)
where Gois the global radiation on a horizontal surface and a is the albedo of
the surface, which depends on the incident angle.
The one-dimensional unsteady heat conduction equation for the NCZ is
CT
tk
T
x
G
xp
=
2
2 ...(6.95)
The initial condition can be taken as T = Toat the start-up of the pond.
The two boundary conditions required to solve the above equation are
obtained by heat balance on UCZ and NCZ. With a suitable functional form
Figure 6.30(b)Temperature history of the storage zone for the 6000 m 2solar pond in BhujSource Kishore and Kumar (1996)
Month/Day
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Solar thermal engineering 373
for G(x), Equation 6.95 can be solved using numerical techniques. One general
method of solving it is by applying the CrankNicolson method (Joshi and
Kishore 1985a; Joshi, Kishore, and Rao 1984).
A useful expression for obtaining the efficiency of the solar pond can
be derived by assuming pseudo-steady state conditions in which T/t = 0.
Equation 6.95 can then be written as
kd T
dx
d
dxG x
2
2= ( )( ) ...(6.96)
An energy balance for UCZ gives
Q G g x kdT
dxs s
x x
= [ ( )]1 11
+
=
...(6.97)
where Qs is the sum of heat losses (convective, radiative, and evaporative)
from the surface and x1is the depth of UCZ. A similar equation for LCZ can
be written as
Q G g x kdT
dxQu s
x x
b= ( )22
=
...(6.98)
where Quis the useful heat extracted, Q
bis the bottom loss to the ground, and
x2corresponds to the interface between NCZ and LCZ. Equation 6.96 can be
solved using the boundary conditions of Equations 6.96 and 6.98 (Kishore and
Joshi 1984; Kooi 1979).
Qu= G
s() U
t(T
b T
s) Q
b...(6.99)
where
( )
=
g x dx
x x
x
x
( )1
2
2 1
...(6.100)
and
Uk
x xt =
2 1...(6.101)
Qsand Q
bcan be related to the ambient and ground conditions, respec-
tively. Taking assumed or measured profiles for g(x), thermal efficiencies of
solar ponds can be obtained. However, such results are applicable only for
yearly average performance (Joshi and Kishore 1986).
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374 Renewable energy engineering and technology
The attenuation function g(x) had been fitted to various functional
forms. The RablNielsen model is expressed as
g x r xi i ri
( ) exp sec= ( )=
1
4
...(6.102)
where riand
iare the constants for a particular seawater and
ris the angle of
refraction.
Bryant and Colbeck proposed a simple two-parameter model
g(x) = ab ln (x secr) ...(6.103)
The one-parameter model proposed by Hawlader and Brinkworth is
expressed as
g(x) = (1F)exp[(x)secr] ...(6.104)
where F is taken as 0.4 and as 0.06 m. The effect of using different attenua-
tion models on performance predictions has been studied by Joshi and
Kishore (1985b).
Considerable work on solar ponds has been done worldwide, including
India (Rao, Kishore, and Vaja 1990). The largest solar pond in Asia, the
6000 m2solar pond at Bhuj, India, operated in an industrial environment and
supplied process hot water to the Kuchch dairy for more than two years
(Kishore and Kumar 1996). The solar pond at Pondicherry is producingelectricity since 2004. A very large number of applications, including
desalination, bromine recovery, manufacture of magnesium chloride,
improved salt production, and so on have been identified for coastal areas in
India.
Evacuated tube collectors
Evacuated or vacuum tube collectors are fast becoming popular in the world
market. Emmett first proposed the concept of an evacuated tube collector
in 1909. With recent advances in vacuum and sealing technology and the
development of selective coating on glass surfaces, the evacuated tube
collectors are now mass-produced in various countries.
Essentially, these are based on the Dewar vacuum flask concept, wherein
the convective losses from the collector surface are reduced by providing
vacuum around the absorber. There are two major design configurations in
evacuated tube collectors
Single-glass tube
Double-glass tube
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Solar thermal engineering 375
Figure 6.31 Evacuated tube collector designsSource Goswami, Kreith, and Kreider (2000)
Single-glass tube evacuated collectors
In single-glass tube collectors, either a heat pipe is used to extract heat from
the collector or a simple U-tube with fin is provided to circulate the fluid
(Figure 6.31 a, b). The metal tube or heat pipe tube and the glass tube covering
it are hermetically sealed to form a vacuum tight joint. The air between
the gap is extracted from the other end using a vacuum pump and then the
end is sealed. Activated barium getter is provided to absorb the gases, which
can diffuse through the glass tube. Sometimes a small ripple reflector is pro-
vided below the col lector to improve the concentration of the solar
radiation from below. The sealing of the glass to metal joint is the mostimportant area in these collectors. These types of collectors have a few advan-
tages as listed below.
Higher heat transfer efficiencies.
No fluid present inside the glass collectors.
Easy to use as an indirect heating element, especially when the outside
conditions are freezing or hard water is to be heated.
Double-glass tube evacuated collectors
Double-glass tube collectors (Figure 6.31c) are easy to manufacture but are
less efficient than single-glass tube collectors. They have two glass tubes
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376 Renewable energy engineering and technology
attached to each other at one end while the other end of both the tubes is
closed. The space between them is evacuated and a selective absorbing coating
is applied on the outer surface of the inner tube. They can be used directly to
heat water stored in the inner tube and are commonly used in domestic water
heating systems. Domestic solar water heating systems based on double-glass
tube collectors are now commonly available in the Indian market.
Evacuated tube collector thermal analysis
Conductive heat transfer between two surfaces having low-pressure gas in the
interim space is given by the following equation (Goswami 2006).
ql= kt/(g + 2p) ...(6.105)
where qlis the heat loss, k is the constant, t is the temperature gradient, g is
the gap between surfaces, and p is the mean free path of molecules.
For air, the mean free path at atmospheric temperature and pressure is
about 70 m. If 99% air is removed from a tubular collector, the mean free
path increases to 7 mm, and conduction heat transfer is almost unaffected.
However, the mean free path increases to 7 cm at 107 torr, which is
substantially greater than the heat transfer path length (gap between the glass
tubes), which is of the order of 20 mm. This reduces the conductive heattransfer substantially.
The relative reduction in heat transfer as a function of the mean free
path can be derived from Equation 6.105
q
q p gvac
l
=1
1 2+ / ...(6.106)
where qlis the conductive heat transfer if convection is suppressed and q
vac is
the conductive heat transfer under vacuum.
The effective heat gain of the evacuated tubular collector based on
the aperture area can be expressed as follows (Goswami, Kreith, and Kreider2000b).
q G A
AU T T
A
Au eff
tb
c
L abs a abs
c
= ()1 1
( ) ...(6.107)
where quis the useful heat gain (W/m2) and G
effis the effective solar radiation,
both intercepted directly and after reflection from the back reflector
(reflected radiation is typically 10%) (W/m2); Atb
is the projected tube
area (m2), Ac1
is the total collector area (m2), UL is the overall heat loss
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Solar thermal engineering 377
coefficient (W/m2K), Tabs
is the absorber temperature (C), Ta is the ambient
temperature (C), and Aabs
is the projected area of the absorber (m2).
Bekey and Mather have shown that a tube spacing of one diameter apart
maximizes the energy output (Goswami, Kreith, and Kreider 2000).
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392 Renewable energy engineering and technology
Nomenclature
a Albedo of the surface
A Aperture area of the cooker (m2)
Ac
Area of the collector (m2)
Ar
Receiver area (m2)
Ac1
Total collector area (m2)
Atb
Projected tube area (m2)
Aabs
Projected area of the absorber (m2)
A1/A
2Area ratio
b Width (m)b
oIncident angle modifier coefficient
B Radiance (W)
C Concentration ratio
Cb
Bond conductance (W/m)
Cr
Ratio of (MC)w
/(MC)w
d Diameter (m)
De
Equivalent diameter (m)
Di
Inside tube diameter (m)
E2/E
1Flux concentration ratio
f Factor
F Fin efficiency
F Collector efficiency factor
g Gravitational acceleration (m/s2)
Go
Global radiation on a horizontal surface (W/m2)
Gs
Radiation immediately below the surface (W/m2)
Gs,c
Solar constant
Geff
Effective solar radiation (W/m2)
Gsun
Radiosity
h1, h
2Convective heat transfer coefficient (W/m2K)
hbf
Convective heat transfer coefficient from the bottom plate to the air
(W/m2
K)h
fiFluid heat transfer coefficient (W/m2K)
hpf
Convective heat transfer coefficient between the plate and the fluid
(W/m2K)
hr,pb
Radiative heat transfer coefficient between the collector plate and the
bottom plate (W/m2K) in air heater
I Irradiance, W/m2
k Equivalent number of velocity heads lost by the flow in passing through
bends, thermal conductivity (W/mK)
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Solar thermal engineering 393
kT
Thermal diffusivity (m2/s)
K Extinction coefficient of the medium
Ka
Incident angle modifier
l Thickness of water layer (m), length, m
L Length of the collector plate (m)
L Cover plate thickness (m)
m Fluid flow rate for a single tube (kg/s)
MC Mass-specific heat product of water in the pond (J/K)
n1, n
2Refractive indices of the media
Nu Nusselt number
p Mean free path molecule (m)
q1
Conductive heat transfer if convection is suppressed (W)
qu
Useful heat gain (W)
qpc
Heat loss, W
qload
Useful energy supplied to the load from the storage (W)
qvac
Conductive heat transfer under vacuum (W)
Qb
Bottom loss to the ground (W)
QL
Heat lost (W)
Qs
Sum of heat losses (W)
Qu
Useful heat (W)
r Reflectance of unpolarized lightrpa
Parallel component of the unpolarized light
rpp
Perpendicular component of the unpolarized light
Re Reynolds number
RT
Thermal Rayleigh number
S Salinity (kg/m3)
S Solar radiation absorbed by the fin (W/m2)
t Time (s)
T Temperature
u Velocity (m/s)
Ub
Heat loss coefficient from the bottom of the collector (W/m 2K)
UL Overall heat loss coefficient (W/m2K)U
tTop loss coefficient (W/m2K)
(UA)tank
Product of the overall heat transfer coefficient and the surface area of
the tank (W/K)
x x-coordinate
y y-coordinate
Radiant flux (W)
Angle
.
.
.
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394 Renewable energy engineering and technology
Transmittance
pa
Transmittance for the parallel component
pp
Transmittance for the perpendicular component
Reflectance
d
Diffuse reflectance
Absorptance, thermal expansion coefficient
Wavelength (m)
Collector tilt
Fin thickness (m)
i
Thickness of the insulating material (m)
c
Thickness of a copper plate (m)
Efficiency
o
Optical efficiency
Kinematic viscosity (m2/s)
() Characteristic wavelength-dependent attenuation length (m)
Solid angle
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