Ch.3 solar water

SOLAR WATER
HEATING−AN PPLICATION OF
SOLAR ENERGY
Arranged by Prof. Dr. Asad Naeem Shah

SOLAR WATER HEATING
 A very common use of solar energy is found in water heating as
hot water is frequently used by the people of cold climates for
their washing and other domestic purposes. For example,
about 30% of the UK’s energy consumption is beneficial for
heat in buildings and of Australia’s energy consumption, about
20% is used for heating fluids to low temperatures (< 100℃).
 Collector is the main part of a solar heating system on which
solar radiation is absorbed and energy is transferred to the
fluid.
 Collectors which do not concentrate the solar irradiance by
mirrors or lenses are known as non-focusing type, and are
further classified either as flat plate or as evacuated collectors.

SOLAR WATER HEATING Cont.
 However, focusing collectors concentrate or focus the
irradiance. The scope of study is restricted here only to non-
focusing type collectors which can absorb both beam and
diffuse radiation, and therefore still function when beam
radiation is cut off by cloud. This advantage, together with
their ease of operation and favorable cost means that non-
focusing collectors are generally preferred for heating fluids to
temperatures (< 80℃).
 The difference between simpler & refined collectors is that
simpler collectors hold all the water that is to be heated. The
more refined collectors, however, heat only a little water. The
heated water is then accumulated in a separate storage tank
through a heat exchanger (Fig. 1)

SOLAR WATER HEATING Cont.
Fig. 2: Collector coupled to a separate
storage tank by a pump.

HEAT BALANCE OF A SOLAR
COLLECTOR
 In the tube and plate collector ( Fig. 1), water is confined in
parallel tubes which are attached to a black metal plate. It is
essential to have small thermal resistance between the plate
and the tube, and across the plate between the tubes.
 Typically specifications are: the tube diameter is ∼2cm, the
tube spacing ∼20cm and the plate thickness ∼0.3cm.
Fig.1: Metal tube and plate collectors.

COLLECTOR Cont.
 Let the radiant flux striking the plate (an absorbing surface) be:
𝑞1 = 𝜏 𝑐𝑜𝑣 𝛼 𝑝 𝐴 𝑝 𝐺 → (1)
where 𝜏 𝑐𝑜𝑣= transmittance of a transparent cover (as shown in Fig. 2);
G = the irradiance on the collector; 𝐴 𝑝 = exposed area of the plate;
& 𝛼 𝑝 = absorptance of the plate.
 Since the plate is hotter than its surroundings, it loses heat at a rate:
𝑞2 =
𝑇𝑝−𝑇𝑎
𝑅 𝐿
→ (2)
where 𝑅 𝐿 = the resistance to heat loss from the plate temperature
(𝑇𝑝) to the outside environment temperature (𝑇𝑎).
Fig. 2: Heat transfer from solar
radiation to a fluid in a collector

COLLECTOR Cont.
 The net heat flow into the plate is (by eqns. 1 & 2):
𝑃𝑛𝑒𝑡 = 𝜏 𝑐𝑜𝑣 𝛼 𝑝 𝐴 𝑝 𝐺 −
(𝑇𝑝 − 𝑇𝑎)
𝑅 𝐿
𝑃𝑛𝑒𝑡 = 𝐴 𝑝[𝜏 𝑐𝑜𝑣 𝛼 𝑝 𝐺 − 𝑈𝐿(𝑇𝑃 − 𝑇𝑎)] → (3)
 Capturing efficiency of the plate is:
η 𝑐𝑝 =
𝑃𝑛𝑒𝑡
𝑃𝑖𝑛𝑐.
=
𝑃𝑛𝑒𝑡
𝐴 𝑝 𝐺
η 𝑐𝑝 = 𝜏 𝑐𝑜𝑣 𝛼 𝑝 −
𝑈𝐿 𝑇𝑝 − 𝑇𝑎
𝐺
→ (4)
 Now plate to fluid transfer efficiency is given as:
η 𝑝𝑓 =
𝑃𝑢
𝑃𝑛𝑒𝑡
→ (5)
 But, useful o/p power from collector is:
𝑃𝑢 = 𝑚𝑐
𝑑𝑇 𝑓
𝑑𝑡
for static mass of fluid being heated, &
𝑃𝑢 = 𝑚 𝑐 𝑇𝑓2 − 𝑇𝑓1 = 𝜌𝑄𝑐 𝑇𝑓2 − 𝑇𝑓1 for moving fluid.

COLLECTOR Cont.
 COLLECTOR EFFICIENCY (𝜼 𝒄): It is defined as the product of the
capture efficiency and the transfer efficiency, i.e.
𝜂 𝑐 = 𝜂 𝑐𝑝 × 𝜂 𝑝𝑓 → (6)
 From eqns. (4) & (6), we get
𝜂 𝑐 = 𝜂 𝑝𝑓 𝜏 𝑐𝑜𝑣 𝛼 𝑝 −
𝑈𝐿 𝑇𝑝 − 𝑇𝑎
𝐺
→ (7)
 As the plate temperature (𝑇𝑝) in an operating collector is not usually
known , it is more convenient to relate the useful energy gain (𝑃𝑢) to
the mean fluid temperature (𝑇𝑓), so that
𝜂 𝑐 = 𝜂 𝑝𝑓 𝜏 𝑐𝑜𝑣 𝛼 𝑝 −
𝑈𝐿 𝑇𝑓 − 𝑇𝑎
𝐺
→ (8)
 Typically 𝜂 𝑝𝑓 = 0.85, however for well designed collector it may be
taken equal to 1.

COLLECTOR Cont.
KEY FINDINGS:
a) Eqn. (4) shows that as the plate gets hotter, the losses increase
until 𝛈 𝐜𝐩 decreases to zero at the equilibrium temperature or
stagnation temperature (𝑻 𝒑
(𝒎)
).
b) Collector efficiency 𝜼 𝒄 (i.e. eqn. (8)) can be improved by the
following two methods:
1) By reducing the convective losses b/w plate & outer glass cover by
inserting an extra glass cover. This method is used for low-temperature
collectors.
2) By reducing the radiative losses from the plate making its surface not
simply black but selective i.e. strongly absorbing but weakly emitting
(e.g. semiconductors, silicon), as shown in Fig. 2. This method is
preferred for high-temperature collectors.

COLLECTOR Cont.
Fig. 2: Typical efficiency curves of single-glazed flat plate collectors.

PASSIVE SWH WITH THERMOSYPHON
CIRCULATION
 Thermosyphon refers to a method of passive heat exchange based on
natural convection which circulates liquid without the necessity of a
mechanical pump.
 This is basically a heat induced circulation of liquid. Its operation is
based on the simplest fact that hot water will rise to settle above a
quantity of cooler water, pushing it down and out of the bottom.
 This combination of the water storage with the collector in one unit
at roof height without any need of external pump, is common for
domestic use in countries with a generally hot climate, e.g. Africa and
Australia.
 The water circulation in such a thermosyphon system is caused by
the density difference between hot and cold water (Fig. 1).

CIRCULATION Cont.
Fig. 1: Collector and storage tank with thermosyphon circulation. (a) Physical
diagram. (b) Temperature distribution

CIRCULATION Cont.
 CALCULATION OF
THERMOSYPHON HEAD:
 Consider the simple system (Fig. 2), a
closed vertical loop of pipe filled with
fluid.
 At the section 𝑎𝑎,
𝜌0
𝑏
𝑎 (𝐿)
𝑔𝑑𝑧 − 𝜌𝑔𝑑𝑧 > 0
𝑏
𝑎 𝑅
 The left column of fluid is exerting a
greater pressure at 𝑎𝑎 than the right
column, thus setting the whole loop of
fluid in motion, where as 𝜌0 is any
convenient (reference) density.
∆𝑃 = − 𝜌 − 𝜌0 𝑔𝑑𝑧
𝑏
𝑎
Also
∆𝑃 = −𝜌0 𝑔∆𝑧 → (2)
Fig. 2: Principle of thermosyphon flow.
∆𝑃 = − 𝜌 − 𝜌0 𝑔𝑑𝑧 → 1 (𝑓𝑜𝑟 𝑡𝑕𝑒 𝑙𝑜𝑜𝑝)

CIRCULATION Cont.
 Comparing eqns. (1) & (2):
−𝜌0 𝑔∆𝑧 = − 𝜌 − 𝜌0 𝑔𝑑𝑧
∆𝑧 =
𝜌
𝜌0
− 1 𝑑𝑧 = 𝐻𝑡𝑕 → (3)
 But the expansion coefficient (𝜷) is given as:
𝛽 = −
1
𝜌0
𝜌 − 𝜌0
𝑇 − 𝑇0
− 𝛽 𝑇 − 𝑇0 =
𝜌
𝜌0
− 1 → (4)
 From eqns. (3) & (4):
𝐻𝑡𝑕 = −𝛽 𝑇 − 𝑇0 𝑑𝑧 = −𝛽𝑰 𝑻 → (5)
where 𝑰 𝑻 = 𝑻 − 𝑻 𝟎 𝒅𝒛 & 𝑻 𝟎 = 𝒂 𝒓𝒆𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒕𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆.

PROBLEM
A flat plate collector measuring 2𝑚 × 0.8𝑚 has a loss resistance
𝑟𝐿 = 0.13 𝑚2
𝐾𝑊−1
and a plate transfer efficiency 𝜂 𝑝𝑓 = 0.85. The
glass cover has transmittance 𝜏 𝑐𝑜𝑣 = 0.9 and the absorptance of the
plate is 𝛼 𝑝 = 0.9. Water enters at a temperature 𝑇1 = 40℃. The
ambient temperature is 𝑇𝑎 = 20℃ and the irradiance in the plane of
the collector is 𝐺 = 750 𝑊𝑚−2. Assuming the mean temperature of
the fluid and taking 𝜌 𝑤 = 1000 𝑘𝑔𝑚−3
& 𝑐 = 4.184
𝑘𝐽
𝑘𝑔.℃
;
1. Calculate the flow rate needed to produce a temperature rise 4℃.
2. Suppose the pump continues to pump at night, when 𝐺 = 0; what
will be the temperature fall in each passage through the collector?
(Assume 𝑇𝑝 = 38℃ & 𝑇𝑎 = 20℃)

SOLUTION
Hints: Take the plate temperature as the mean temperature
of the fluid.
o As we have useful power per unit area:
𝒒 𝒖 = (𝝆𝑸𝒄/𝑨 𝒑) 𝑻 𝒇𝟐 − 𝑻 𝒇𝟏 = 𝜼 𝒑𝒇 𝝉 𝒄𝒐𝒗 𝜶 𝒑 𝑮 −
(𝑻 𝒑−𝑻 𝒂)
𝒓 𝑳
𝑸 = 𝟑. 𝟓 × 𝟏𝟎−𝟓 𝒎 𝟑 𝒔−𝟏 = 𝟏𝟑𝟎𝑳𝒉−𝟏
o Also, putting G = 0 & keeping the same Q in above eqn. we
have;
𝑻 𝒇𝟐 − 𝑻 𝒇𝟏 = ∆𝑻 = −𝟏. 𝟑℃

Ch.3 solar water

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