Energy Convers. Mgmt Vol. 26, No. 2, pp. 217-220, 1986 0196-8904/86 $3.00 + 0.00 Printed in Great Britain Pergamon Journals Ltd

THE EFFECT OF A BAFFLE PLATE ON THE TRANSIENT PERFORMANCE OF A SHALLOW

SOLAR POND WATER HEATER

M A D H U R I and G. N. TIWARI Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India

(Received 8 June 1985)

Abstraet--A straightforward transient analysis of a shallow solar pond (SSP) water heater fitted with a baffle plate has been presented. In order to study the performance of the system, numerical calculations have been made for a typical cold day in Delhi, viz. 18 Dec. 1984. It is concluded that the SSP can also be used as a built-in storage water heater, with better performance being achieved with the use of a baffle plate.

Solar energy Water heater Storage system

NOMENCLATURE of stationary water in the upper column, acts as

A = Area of baffle plate (m 2) insulation during the night. A ' = Vent-area in baffle plate (m 2) No theoretical and experimental study was made Cw = Specific heat of water (J/kg °C) by Van Straaten [1] on this aspect, it was later per- ht = Heat transfer coefficient between upper water formed by Rani [2] using a finite-difference technique.

column and ambient air (W/m2°C) Further, Tiwari and Dhiman [3] have studied its h 2 = Heat transfer coefficient between absorber plate

and upper water column (W/m 2 °C) different aspects by using a simple transient analysis h 3 = Heat transfer coefficient between upper and of the system.

lower water columns ( W / m E °C) In this communication, a baffle plate is used in a h b = Heat transfer coefficient between absorber plate shallow solar pond (SSP) water heater to make it

and lower water column (W/m 2 °C) possible to incline the system at an opt imum angle so h~, = Heat transfer coefficient between lower water

column and ambient air (W/m 2 °C) as to collect maximum solar radiation. By means of H s = Solar intensity ( W / m 2) the baffle plate, the bulging problem in the SSP water

Mwl = Heat capacity of water in upper column heater due to water pressure can be avoided. The (J/m 2 °C)

Mw2 = Heat capacity of water in lower column upper surface of the baffle plate is blackened, which (J/m 2 °C) acts as an absorber.

mw = Flow rate of water (kg/h) Comparat ive studies of different systems, viz. (i) a T a = Ambient temperature (°C) built-in storage water heater, (ii) a horizontal SSP Tb = Temperature of absorber plate (°C) water heater, (iii) an inclined SSP water heater and

Twt = Water temperature of upper water column (iv) an inclined SSP water heater with baffle plate (°c)

Tw2 = Water temperature of lower water column have been made. (°C) Numerical calculations have been made for a

(rgCtb) = Transmittivity of glass cover and absorptivity typical cold day, viz. 18 Dec. 1984, in Delhi. It is of absorber plate product concluded that the performance of the SSP water

heater with the baffle plate is better than that of the SSP water heater alone, because the SSP water cannot be positioned at the opt imum inclination to

INTRODUCTION receive maximum solar radiation due to the bulging effect. Also, the use of a baffle plate in the SSP water

Van Straaten [1] has suggested the use of an insulated heater is easier than with the built-in storage water baffle and a non-return valve in a built-in storage heater. tank instead of insulation on the top to reduce losses during the night. The baffle plate inside the storage tank divides the depth of the tank in a certain ratio. The plate has inlet and outlet vents to allow the ANALYSIS flow of water by convection from the upper water column to the lower column through the top vents The schematic configuration of an SSP water and vice versa. The baffle, together with the curtain heater with a baffle plate is given in Fig. 1. The energy

217

218 MADHURI and TIWARI: USE OF A BAFFLE PLATE IN SOLAR PONDS

b2 = - ~ 2 A h'b + th..,,C,,, + h3A'

o ° . . . °o,u m. : : . T= .u.,a°. B a f , , • , , , * , e

Lowercolumn~---------Ed-------'---i----'a/A " l r(tXb'~$) h2(A -- 2A ' .+ h l A T a ] ~ ,°,o,a,,o° f ( t ) = ~--~l L. ~ )H,

(a) and

• 1 -

x H, + (Ah~, + #twCw)T..

To solve equations (4) and (5), mult iply equation Glass cover (5) by ct and add to equat ion (4):

~ < ~ ~ B I ockenecl surface

~ Baffle plate d 4 5 ~ - - I n s u l a t i o n dt (Twl + txrw2) + (al + ~t bl)Twl

(b) + (a 2 + ~b2)rw2 = f ( / ) + o~g(l) Fig. 1. Schematic sketch of an SSP water heater with a baffle plate: (a) horizontal position; (b) inclined position, or

d

balance for the absorber plate and the upper and dt (Twl + aTw2) + CTwl + ¢tcTw2

lower water columns can be written as follows: = f ( t ) + atg(t), (6)

('~g~b)Hs = h2(T b -- Twl ) + hb(T b - T..,.,2), (1) where

c = aj + orb 1 dTwi (A - 2A ')h2(Tb - Twl) = Mwl ~-~ and

+ hl(T.l - Ta)A + h3A '(Twt - T.2 ) (2) ac = a2 + ctb2,

and which gives

(A - 2A ')hb(T b - Tw2 ) + h3A '(Twl - Tw2 ) = w2 "~ ~t± = (b2 - al) _ d ( a t - b2) 2 + 4bla2 •

+ h~(T~ 2 - Ta)A + rhwCw(Tw2 - Ti~). (3) Thus, equat ion (6) becomes

These equations can be rewritten as d d'-'t (Twl + ~± T~2) + c±(Twl + ~t± T'2)

dT,2 " + alTwi + a2rw2 = f ( t ) (4)

dt = f ( t ) + ¢t±g(t).

and The solution of the above equat ion can be written

dTw2 as - - + blTwi + b2rw2 =- g(t), (5)

dt T~, + ~t± T~2 = A± e x p ( - c±t)

,Io where + e x p ( - c±t e×p(c± t)

1 [ + h2hb ( A - 2 A ' ) ] al = ~ hlA + h3A" h2 + hb ' x [ f ( t ) + a±g(t)]dt. (7)

1 [ hzhb ( A - 2 A ' ) ] The constant A± can be obtained by using a2 = - - ~ h3A" + h - - ~ ' the initial condition, viz. for t = 0, Tw~ = T0~ and

T.2 = To2, to get b l = ~ [h3A '+ . hbh2 ( A - 2 A ' ) ] ,

w2L ~/2 "~- hb A± = Tol + 0t± To2-

MADHURI and TIWARI: USE OF A BAFFLE PLATE IN SOLAR PONDS 219

From equation (7), one has temperature for a typical winter day, 18 Dec. 1984, l in Delhi. The different relevant parameters used for

T.~ = - the calculations are 0~+ - - <Z_

A' = 0.05 m 2, f

x ~at+A_ e x p ( - c t) - -_A+ exp(--c+t) A = 1.0 m 2, L Cw =- 4190.0 J/kg °C,

exp(_c_t)]f(t) + ~_g(t) hi = 6.115 W/m 2 °C, + ¢{+ [1 c_ h 2 = 135.0 W/m 2 °C, h 3 = 534.5 W/m 2 °C (during the day),

- ~_[1 - exp ( - c+ t ) ] f(t) +o~+g(t)~ (8) = 0.0 W/m 2 °C (during the night), c+ j h b = 0.692 W/m 2 °C,

and h~, = 1.6 W/m e °C,

1 and

=+ - ~_ ~b~ = 0.85.

The hourly variation of water temperature in the x A+ e x p ( - c + t ) - A_ exp(- -c_t ) built-in storage and horizontal and inclined (hypo-

+ [1 -exp(-c+t)] f(t) +~+g(t) thetical) SSP water heaters is shown in Fig. 2. Figure 3 shows the hourly variation of water

c+ temperature with and without the baffle plate in an exp(_c_t)]f(t) + ~,_g(t)'l~, SSP water heater for no withdrawal of water from

[1 c_ )" (9) the pond, along with the hourly variation of solar intensity and ambient air temperature.

The efficiency of utilization of solar energy is given The effect of flow rate on the efficiency of the

by system is shown in Fig. 4.

flrhwCw(Tw 2 _ T~n)dt Referring to Figs 2--4, the following conclusions may be drawn:

r1=

fo A H,dt (i) A baffle plate can be used in an SSP water heater by keeping it in an inclined position.

(ii) The performance of the SSP water heater with a baffle plate has been improved (to almost NUMERICAL RESULTS AND

DISCUSSION equal that of the inclined built-in storage water heater) by keeping it in an inclined

Numerical calculations have been carried out for position). the water temperature as a function of time using the (iii) The efficiency of the system increases with an hourly variations of solar radiation and ambient increase in flow rate.

-X - -X- Inclined shallow solar pond water heater

Bu i l t - in storage water heater 60 . . . . Horizontal shallow solar pond

water heater

50 x~X.~x. .o .X.~x ,o . .

-'~ 40 ~ f . ~ . . . . ~ ~ - x'°'x-o.x.o.x.o.x.=.x.o. 2

30 xr // ~ ~ x-o-x~, x

E J /-" - - - _ _ r.

~ 2 0

1 0

I t I I t I I I I I I I 3 5 7 9 11 13 15 17 19 21 23 25

T i m e ( h )

Fig. 2. Hourly variation of water temperature for (i) a built-in storage water heater; (ii) a horizontal SSP water heater; and (iii) a hypothetically inclined SSP water heater.

220 MADHURI and TIWARI: USE OF A BAFFLE PLATE IN SOLAR PONDS

6O

11oo

9 0 0

4 0 8 0 0 (,)

* 700

3o ~ r~ 60o

500

E 20 ...._... -.-.-. T 1 400 E

10' ) 2 0 0

O0

l I l l I 3 5 7 9 11 13 15 17 19 21 25 25

T i m e ( h i

Fig. 3. Hourly variation of water temperature with and without (upper and lower water columns) a baffle plate and solar intensity and ambient air temperature.

(iv) The water heater , i.e. SSP and buil t- in s torage 60 with baffle plate, will no t funct ion in a hori-

50 - ~ zontal posi t ion. Hence, in the hor izonta l pos- ition, the only solut ion to reduce the night losses is movable insulat ion.

4 0

*~ ~ Acknowledgements - -The authors are grateful to Professor

~ 3o H.P . Garg for help during the preparation of this paper. Madhuri is grateful to acknowledge the CSIR for financial

i--- support. 2 0

I.d

REFERENCES 10

I. J. P. Van Straaten, Proc. 2rid Southeastern Conf. on I M I I J J Application o f Solar Energy, Baton Rouge, La (1976). 5 lO 15 20 z5 3o 2. U. Rani, Analysis and optimization of solar collections

Flow rote (kg/h} for heating of fluids. IIT, New Delhi (1981). 3. G. N. Tiwari and N. K. Dhiman, Energy Convers.

Fig. 4. Effect of flow rate on the efficiency of the system. M g m t 23, 151 (1983).