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366 • Renewable energy engineering and technology

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), several

attempts 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 of

collector 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 ºC can be obtained for such a box-type col-

lector. If the initial temperature of water is 30 ºC, the final water

temperature would be 50 ºC, which is quite adequate for bathing, etc. Such

Figure 6.25 Simple collector-cum-storage solar water heater

Solar thermal engineering • 367

box-type water heaters have been investigated in India at CAZRI (Central

Arid Zone Research Institute), Jodhpur, and at TER I.

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

pc c L p a = τα − −( ) ...(6.84)

where (MC)p is the mass-specific heat product of water in the pond, T

p is the

temperature of water at a given time t, Ac is the area of the pond exposed to

sunlight, and (τα) and UL are same as those in flat plate collectors. As fins and

Figure 6.26 Sectional view of shallow solar pond


fluid flow are not involved, F’ and FR are 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 ºC 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 λ of light, the transmission τ (λ, l) of a ray through a distance l in

water can be represented as

τ λδ λ

, expll( ) −

( )⎛

⎝⎜

⎞

⎠⎟ = ...(6.85)

where δ(λ) 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


ing from suspended particles. The higher the magnitude of δ(λ), the lower is

the penetration of radiation. Experimental values for distilled water show that

water is relatively transparent to the visible wavelength (0.4–0.7 µm), which

includes much of the solar spectrum (Hull, Nielsen, and Golding 1989).

Figure 6.28 Schematic diagram of a shallow solar pond based domestic solar water heaterSource Raman and Kishore (1992)

Figure 6.29 Storage tank temperatures of the SSPDHW system


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

kTT

= = =αν

π∆ 3 4274

657 5. ...(6.86)

where RT is the thermal Rayleigh number, g is the acceleration due to gravity, α

is the thermal expansion coefficient, ν is the kinematic viscosity, and kT is the

thermal 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

ρ = ρ0 [1 – C

T(T – T

0) + C

s(S – S

0)] ...(6.87)

where ρ0 corresponds to a reference state; C

S and C

T are 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.

∂∂

−ρ ρT

CT = 0 ...(6.88)

∂∂ρ ρS

Cs = 0 ...(6.89)

and

∂∂

∂∂

∂∂

∂∂

∂∂

ρ ρ ρx S

Sx T

Tx

= + ...(6.90)

where x is the vertical co-ordinate increasing downward. For densities to

remain stable, it is necessary that


∂∂

>ρx

0 ...(6.91)

Substituting from Equations 6.88 and 6.89 and re-arranging, we get

RC S

xC T

x

s

T

ρ = ∂

∂( )∂

∂( ) > 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 30–50 cm. The NCZ has a thickness of

1–1.5 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 m2 solar 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 6.30a Schematic diagram of the solar pond


Choosing a co-ordinate system with x = 0, corresponding to the surface of the

pond, the solar radiation at depth x is given by

G(x) = Gs g(x) ...(6.93)

where Gs is the radiation immediately below the surface and is given by

Gs = G

0 (1 – a) ...(6.94)

where Go is 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

ρCTt

kT

xGxp

∂∂

∂∂

− ∂∂

= 2

2 ...(6.95)

The initial condition can be taken as T = To at 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 m2 solar pond in BhujSource Kishore and Kumar (1996)

Month/Day


for G(x), Equation 6.95 can be solved using numerical techniques. One general

method of solving it is by applying the Crank–Nicolson 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 δT/δt = 0.

Equation 6.95 can then be written as

kd Tdx

ddx

G x2

2 = ( )( ) ...(6.96)

An energy balance for UCZ gives

Q G g x kdTdxs s

x x

= [ ( )]1 11

− +=

...(6.97)

where Qs is the sum of heat losses (convective, radiative, and evaporative)

from the surface and x1 is the depth of UCZ. A similar equation for LCZ can

be written as

Q G g x kdTdx

Qu sx x

b= ( )22

− −=

...(6.98)

where Qu is the useful heat extracted, Q

b is the bottom loss to the ground, and

x2 corresponds 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(τα) – U

t (T

b – T

s) – Q

b...(6.99)

where

τα( )−

∫=

g x dx

x xx

x

( )1

2

2 1

...(6.100)

and

Uk

x xt =2 1− ...(6.101)

Qs and Q

b can 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).


The attenuation function g(x) had been fitted to various functional

forms. The Rabl–Nielsen model is expressed as

g x r xi i ri

( ) exp sec= −( )∑=

µ θ1

4

...(6.102)

where ri and µ

i are the constants for a particular seawater and θ

r is the angle of

refraction.

Bryant and Colbeck proposed a simple two-parameter model

g(x) = a–b ln (x sec θr) ...(6.103)

The one-parameter model proposed by Hawlader and Brinkworth is

expressed as

g(x) = (1–F)exp[–µ(x–δ)secθr] ...(6.104)

where F is taken as 0.4 and δ 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 m2 solar 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 producing

electricity 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


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 collector to improve the concentration of the solar

radiation from below. The sealing of the glass to metal joint is the most

important 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


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 = k∆t/(g + 2p) ...(6.105)

where ql is 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 µm. 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 10–7 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 heat

transfer substantially.

The relative reduction in heat transfer as a function of the mean free

path can be derived from Equation 6.105

qq p g

vac

l

= 1

1 2+ / ...(6.106)

where ql is 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 Kreider

2000b).

q GAA

U T TAAu eff

tb

cL abs a

abs

c

= (τα)1 1

− −( ) ...(6.107)

where qu is the useful heat gain (W/m2) and G

eff is 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


coefficient (W/m2K), Tabs

is the absorber temperature (ºC), Ta is the ambient

temperature (ºC), 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).


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)

bo

Incident 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/m2K)

hfi

Fluid 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)


kT

Thermal diffusivity (m2/s)

K Extinction coefficient of the medium

KτaIncident 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)

qp–c

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 light

rpa

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/m2K)

UL

Overall heat loss coefficient (W/m2K)

Ut

Top 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

Φ Radiant flux (W)

θ Angle

.

.

.


τ Transmittance

τpa

Transmittance for the parallel component

τpp

Transmittance for the perpendicular component

ρ Reflectance

ρd

Diffuse reflectance

α Absorptance, thermal expansion coefficient

γ Wavelength (m)

β Collector tilt

δ Fin thickness (m)

δi

Thickness of the insulating material (m)

δc

Thickness of a copper plate (m)

η Efficiency

ηo

Optical efficiency

ν Kinematic viscosity (m2/s)

δ(λ) Characteristic wavelength-dependent attenuation length (m)

Ω Solid angle

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Cheaper alternatives to conventional solar water heatersodl.teriuniversity.ac.in/ren_en/pdf/week_40.pdf · Cheaper alternatives to conventional solar water heaters ... For a layer