Energy Convers. Mgmt Vol. 26, No. 3/4, pp. 353-356, 1986 0196-8904/86 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright ~ 1986 Pergamon Journals Ltd

ANALYSIS OF A SOLAR WATER HEATING SYSTEM WITH n-TANKS IN SERIES

MADHURI and G. N. TIWARI Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India

(Received 13 December 1985)

Abstract--A straightforward analysis of a solar water heating system with n-tanks connected in series has been presented. The long-term performance of the system has also been studied. On the basis of numerical calculations made for four successive days, the following conclusions have been drawn:

(1) The fluctuation in temperature variation decreases with increase of the number of tanks connected in series.

(2) The variation becomes smooth after the second successive day, which is more desirable from the point of view of users.

Water heating system Sensible heat storage Solar energy

ACN C~v =

[: = f 4 =

n =

L = T,#= ~ = ~ = U L = ~ =

(~:o) =

NOMENCLATURE

Area of collectors (m 2) Specific heat of water (J/kg °C) Collector efficiency factor Solar intensity (W/m 2) Water flow rate at which water is collected from storage tank (kg/s) Water flow rate in collector loop (kg/s) Number of storage tanks Ambient temperature (°C) Inlet water temperature (°C) Water temperature in first tank (°C) Water temperature in n th tank (°C) Overall heat loss coefficient (W/m 2 °C) Thermal capacity of storage tank (J/°C) Absorption and transmittance product

INTRODUCTION

In various designs of solar water heating systems, hot water is usually withdrawn from the storage tanks by displacement with cold water from the mains. This causes the temperature of the outgoing water to decrease with time. In order to alleviate partially this undesirable feature, Robinovich and Fert [1] and Robinovich [2] have analysed a system of tanks in a solar collector loop without any outflow of water. Further, Sodha et al. [3] have analytically investigated the effect of the number of storage tanks on the temperature of the outlet water, assuming the flow of water to be the sole mechanism of heat exchange between the tanks. Also, a transient anal- ysis of n water tank heating systems connected in series with withdrawal of hot water at a constant flow rate has been studied by Sodha et al. [4].

In the present communication, a transient analysis of a water heating system with n storage tanks connected in series in a collector loop, as suggested by Robinovich and Fert [1] has been studied by

incorporating the effect of water flow in the tanks. Forced circulation between the collector and tanks has been assumed. Numerical calculations have been made for four successive days at Delhi.

It is concluded that connecting three or four stor- age tanks in series leads to a significant improvement of performance of a fixed number of collectors in parallel.

ANALYSIS

The energy balance equations for the water heating system with n storage tanks in series (Fig. I) may be written as follows:

(a) For the first storage tank:

W, d T z = Ou~ful- ~'IC,.(T] - Tin) , (1) n dt

where

~u~ru, = Ac:cFn~[(aozo)ll - UL (T , -- T~)]

r,_ox,,( F"~ = AcNUL I 61C,,. ./I"

(b) For the other tanks (perfectly insulated):

W, dT. = - ~ I C , , . ( T . - T,,_,) , n dt

where n = 2 , 3, 4 . . . n , (2)

with the boundary condition that

T , ,=T ,o at t = 0 .

Solving equation (I), one obtains

-~' I ' f ( t ) e u' dt + Tlo e -~', TI e do

353

354 MADHURI and TIWARI: SOLAR WATER HEATING SYSTEM

Fig.

Storage tanks connected in series

' , Collectors connected /

in parollal /

: / / i

1. Schematic representation system.

~ r h

of the solar heating

where

nMC.. a = - -

w,

O..~ru~ + YtC.,T,N f ( t ) = W,/n

Similarly, solving equation (2)

fo T , = e -°' N ( t ) e " ' d t + T , ~ e - ' ,

where

Y4C.,T._I N(t) = - -

W,/n

During off-sunshine hours, UL and I, are equal to zero.

The overall efficiency of the system can be written /

as

q = fo fllVlC.,(T.- Tm)dt + Wr ( T ' . - TIN )

n

fo Acu It dt

NUMERICAL RESULTS AND DISCUSSIONS

The following relevant parameters have been used for the numerical calculations:

and

(~0z0) = 0.81 C.,=4.19 x 103 J/kg°C F ' = 0.77 UL = 8.0 W/m 2 °C

ACN = 7.5 m E W, = 2.6875 x 106 J/°C /~=1 n = l , 2, 3, a n d 4

rh = 20 kg/h • : / = 10, 20, 30, 40 and 50 kg/h

T,N= To.

The hourly values of solar intensity on the collectors and ambient air temperature are shown in Fig. 2.

Figure 3 represents the hourly variation of the outlet temperature from the last storage tank for four consecutive days for different numbers of tanks connected in series with a flow rate 20 kg/h.

~ 30 =

~ 20 > - 0

E

It

h

4 8 12 16 20 24 iA.M. Time (in hrs}

Fig. 2. Hourly variation of solar intensity and ambient air temperature.

1200

1000

800 E

600 >"

t.00 ,_

200

MADHURI and TIWARI: SOLAR WATER HEATING SYSTEM 355

,50

4 0

30

2 0

1 0 ~P

0 0 ,~ 0

E

5O

o

40

I One tank I"x7

rl Two tanks TIT

TIT Three ranks { I Four Tanks ' ' ~ ~

I

I I 1VI I J J I I I I I I 4 8 12 16 20 24 28 32 36 4 0 4 4 48

20

]I I

i o

o i i i i i f i P I i i i 49 .53 57 61 65 69 73 ?T 81 85 89 93 96

T i m e (h )

Fig. 3. Hourly variation of outlet temperature for different numbers of storage tanks. A;/(t )= 20 kg/h.

.~ 3C

.o_ 20

10 0

Flow rate = 20 Kg/hr

0 I I I I I

0 I 2 3 4 5 No. of tanks

Fig. 4. Dependence of efficiency of the system on the number of tanks.

50

40

u ;= 3C

o

c~ 2(3

10

No. of tanks = 4

~ f

I I I I I I

10 20 30 40 50 60

Flow rate (w i thdmwal ) (Kg /h r )

Fig. 5. Dependence of efficiency of the system on the flow rate.

The dependance of the efficiency of the system on the number of tanks and flow rate are shown in Figs 4 and 5, respectively.

On the basis of the numerical results, it is con- eluded that

(1) The outlet water temperatures, with an in- crease in the number of tanks connected in series, becomes almost constant after 24h for constant withdrawal of water. Here, the total collector area and the total heat capacity of the water in the tanks is kept constant.

(2) The overall efficiency of the system for a partic- ular flow rate decreases with the number of storage

tanks connected in series and saturates for n > 3. Therefore, there is the optimum number of tanks to be connected in series.

(3) The overall efficiency of the system for a fixed number of tanks (four) increases with outlet flow rate. This is explained by the fact that, at higher flow rates, the outlet water temperatures decrease, and hence, the thermal losses are reduced to a minimum.

Acknowledgements--The authors are grateful to Prof. H. P. Garg for various help during preparation of the paper. One of the authors, Madhuri, is grateful to CSIR for financial support.

356 MADHURI and TIWARI: SOLAR WATER HEATING SYSTEM

REFERENCES

1. M. O. Robinovich and A. R. Fert, Geliotekhnika 16(2), 39 (1980).

2. M. O. Robinovich, Algorithm for calculation and investigating solar hot water systems in collection; engineering equipment for settled areas, dwelling units

and public buildings, Moscow, Report No. 2 (1979) (in Russian).

3. M. S. Sodha, S. N. Shukla and G. N. Tiwari, Solar Energy 31(2), 291 (1984).

4. M. S. Sodha, V. S. V. Bapeshwara Rao and G. N. Tiwari, Energy Res. (in press).