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e w 7 - - ~ - ~ .s,,,-,7.-vwl

ELSEVIER Desalination 115 (1998) 121-128

DESALINATION

Experimental study of evaporation in distillation

° a *

G. N. Tlwarl

,

Md. Emran

K h a n b,

R.K. Goyal a

aCentre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India Tel. +91 (I1) 686-1977; Fax +91 (11) 686-2208; e-mail: gntiwari@ces.iitdernet.in

bJamia Millia Islamia University, New Delhi, India

Received 20 March 1997; accepted 27 February 1998

Abstract

In order to measure various internal heat transfer processes, namely convective and evaporative in a solar still, an indoor simulation experiment has been carried out over a typical operating temperature range. The condensing surface was maintained at three different environmental conditions: (a) by exposing it to ambient air temperature, (b) by exposing it to air conditioned surroundings, and (c) by keeping ice on the condensing surface. The temperature- dependent physical properties of enclosed vapour were considered. The constants (C and n) for the convective heat transfer coefficient were determined by using linear regression analysis. It was observed that the proposed model gives closure results with the experimental observation within an accuracy of 8%.

Keywords:

Solar still; Evaporative heat losses; Purification of water

1. Introduction

Numerous empirical relations for heat and mass transfer coefficients to predict the hourly and daily output for different designs of solar stills for different Grashof number ranges have been developed. An analytical expression for internal heat losses, mainly convective and

*Corresponding author.

evaporative, was developed by Dunkle [1] by using the well known expression:

h .d i C(Gr.p,.t

N u - , w _ ( 1 )

kj

The values o f C=0.075 and n = 1/3 on the basis o f simulation studies for 3.2×105>Gr>

3.2×105 was considered by Malik et al. [2].

However, the relation developed by him has the following limitations:

0011-9164/98/$09.50 © 1998 Elsevier Science B.V. All rights reserved PII S0011-9164(98)00031-9

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122 G.N. Tiwari et al. / Desalination 115 (1998) 121-128

• It is valid only for a mean operating temperature range of 120°F (50°C) and an equivalent temperature difference of 30°F (- 1 °C) [3-5].

• It is independent of cavity volume, i.e., the average spacing between the condensing and evaporating surfaces.

• It holds good for heat flow upwards in hori- zontally enclosed air space [6,7].

Another relation for evaporative heat loss was developed by Tiwari et al. [8] and Malik et al. [2]

using the Lewis relation [9]. Later on an expression for internal convective heat transfer was developed by Clark and Schrader [10] which was experimentally verified by Clark [11].

According to Clark [11], the value of C as considered by Dunkle [1] in Eq. (1) becomes half and reduces the evaporative heat loss. Recently Tiwari [12] reviewed the work on basic heat and mass transfer relations to study the performance of various solar stills given by researchers such as Adhikari et al. [13], Sharma and Malik [14]

and Tiwari and Lawrence [15], etc. It was observed that there is a strong need to develop new models for heat and mass transfer for a different operating temperature range.

In the present study, an attempt has been made to develop a new model under indoor-simulated conditions without any of the limitations mentioned earlier. The model was developed by using simple regression analysis. The values of C and n have again been used to find the theoretical output for validation of results. It has been observed that there is reasonable agreement within an accuracy of 8% between experimental and theoretical output. Experimental error in terms of percent uncertainty has also been calculated, which is less than 1%. Further, it was observed that the model presented by Dunkle [1]

and Tiwari and Lawrence [15] predicts results in better agreement with experimental observations.

2. Experimental set-up for indoor simulation The cross-sectional view of the solar still and its condensing chamber are shown in Figs. 1 a and lb. The experimental set-up consists of a constant temperature bath of 401 capacity and a condensing chamber (Fig. lb). The condensing chamber consists ofa PVC (4 mm) double-walled with a 5 mm air gap to have the one-dimensional heat flow in the condensing chamber. The one- dimensional heat flow is achieved by minimizing side losses which are about 5-8% in comparison to upward heat losses from the condensing cover.

The arrangement o f double walled with air cavity is shown in Fig. lb. A 3 m m glass cover was fixed on the vertical wall o f the double-walled chamber as a condensing cover with the help of the adhesive known as araldite TM. In order to keep ice cubes on the glass cover, the outer vertical wails are extended 5 cm above the cover on all sides. The glass cover and all distillate channels have been carefully sealed to ensure no water or vapour leakage. The temperatures of the water and condensing cover were measured by calibrated copper constantan thermocouples with an accuracy of 0.1 °C with the help of a digital thermometer available locally. A graduated measuring flask was used to measure the half- hourly distillate output. The experiments were conducted for two operating temperature ranges of 43°C and 67°C, respectively, which are normally the operating temperature range for solar distillation systems. Observations were recorded for water temperature, condensing cover temperature and distillate output. The experiment was carried out for a given operating temperature several times in a steady-state condition for the following conditions:

• by exposing it to ambient air temperature

• byexposingittoair-conditionedsurroundings

• by keeping the ice on the condensing cover The results for each case are given in Table 1.

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G.N. Tiwari et al. / Desalination 115 (1998) 121-128 123

d| ÷ d w = constant

D r = h e i g h t of ¢ n c l o s u r ¢ = d f ' . -b tan 2

Fig. la. Cross sectional view of the solar still.

Extension to keep ice

Double walled chamber Glass cover

DrainagG system

X ..

Drainage ~ot distillate

Fig. lb. View of the condensing chamber.

Table 1

2 h)

SI. no. Operating Temperature, °C condition

Water (Tw) Glass cover (Tg)

Jacob &

Gupta model

Graf & Dunkle Tiwari & Exp.

Held model Lawrence output

model model

2

Normal 43.6 26.6 555.2

condition 64.1 36.6 2305.0

Air 43.9 22.4 690.1

conditioned 67.1 33.2 3113.0

3 lce on con- 42.0 2.4

densing cover 65.3 2.8

396.7 331.8 226.3 275.2

1647.0 1422.4 1107.7 1120.0

683.5 410.2 336.3 330.0

3265.0 1916.0 1470.0 1442.2

985.0 720.0 571.6 466.3 540.0

4000.0 2945.0 2381.0 1875.0 2059.0

3. Calibration of thermocouples

C o p p e r - c o n s t a n t a n t h e r m o c o u p l e s are used with a digital t e m p e r a t u r e indicator to record the w a t e r and c o n d e n s i n g c o v e r temperatures. These t h e r m o - c o u p l e s o v e r a prolonged usage period tend to deviate f r o m the actual data. Therefore, it b e c o m e s n e c e s s a r y to c a l i b r a t e t h e s e t h e r m o c o u p l e s with respect to a standard

t h e r m o m e t e r , the Z E A L t h e r m o m e t e r , which gives accurate temperature readings.

4. Evaporative heat transfer in distillation In a solar distillation process, the internal thermal e n e r g y losses, n a m e l y c o n v e c t i v e and evaporative, are important in evaluating the

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124

G.A( Tiwari et al. / Desalination 115 (1998) 121-128

performance of the system. The convective and

evaporative losses are strongly dependent on each other. Hence, various heat and mass transfer relations are discussed in this section.

4.1. Convective heat transfer coefficient (h~w)

The heat transfer across the humid air inside distillation units occurs by natural convection.

The rate of heat transfer from water surface to the glass cover by convection through humid air in the upward direction is given by

(¢c~ = hew(T- T) (2)

Now, h~w can be predicted from Eq. (1) where C and n are the constants depending upon the range of the Grashof number [13]. Further, the Grashof number and Prandtl number depend on the temperature-dependent physical properties of water vapour, volume of the enclosure and the temperature difference between the water and glass cover. The expressions for the Grashof and Prandtl numbers are given by [2,6]

G r -

~2

and

g13' pZ d] h T

(3)

P r -

(4)

where

(Pw-Pg)(T+273)

A T = ( T - T ) + (268.9× 1 0 3 - P )

ranges. These values of C and n and their corresponding Grashof number range are given by Adhikari et al. [13]. According to Dunkle [1], C=0.075 and n= 1/3 for 3.2x 105<Gr< 107.

The Grashof number can be calculated using the standard equation and temperature-dependent physical properties of humid air [16]. The heat transfer relation used at Eq. (1) is only valid for horizontal condensing surfaces. Hence, Tiwari and Lawrence [ 15] have suggested a new relation incorporating the inclination angle (13) of the condensing surface, similar to that used for a flat plate collector [ 17].

4.2. Evaporative heat transfer coefficient (h~w)

The evaporative heat transfer coefficient is determined using the expression given below [8]:

O.O16Xh~w(Pw-Pg )

:

5. Evaluation of distillate output

The rate of heat loss due to evaporation can be evaluated by the following expression [2]:

(l~q = O.Ol6xh~w×(Pw-Pg)

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The expected hourly distillate output per m 2 from a distiller can be evaluated as

l~lw

_ O~w _ O . O 1 6 h c w ( P w - P g ) × 3 6 0 0 (7)

It is seen from Eq. (1) that the value of h~w depends on the values of two constants, namely C and n. Various authors have proposed different values of C and n for different Grashof number

The above equation, with the help of Eq. (1), can be arranged in the terms of constants C and n

a s :

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G . N .

Tiwari et al. / Desalination 115 (1998) 121-128

125

_ O.O16(Pw-Pg)kf.C(Gr.Pr)".3600

1 ~ I w -

Therefore,

(8)

w =C(Ra)"

(9)

R where

R= O'O16(Pw-eg)'kv3600 df.L

and

Ra = Gr.Pr

Table 2

Values of X and Y used in regression analysis

SN X Y

1 16.83 2.85

2 17.40 3.00

3 17.08 2.89

4 17.63 3.03

5 17.76 3.25

6 18.26 3.25

The values o f X a n d Yused in the determina- tion o f constant a and b from Eqs. (11) and (12) are given in Table 2. After knowing the values o f constants a and b, the values o f C and n were calculated using Eq. (10a).

Taking the logarithm o f both sides o f Eq. (9), it reduces into a equation o f straight line:

In - ~ ) =lnC+nln(Ra) (lO)

It has an analogy o f a straight line represented by

Y=aX+b

where Y=ln (M,/R), a=n, X = ln(Ra) and b = In C.

Eq. (1) for different sets o f observation has been solved using a linear regression technique as mentioned below:

6. Experimental uncertainty

The experimental method used is an indirect approach for estimating the convective heat transfer coefficient based on the mass o f distillate collected from the still. This indirect approach will certainly have a considerable degree o f experimental uncertainty in the estimation o f convective heat transfer coefficients. An estimate o f internal uncertainty [I 8] was carried out for experimental observations. For these data, an estimate of individual uncertainties o f the sample values of each set were calculated by taking the square roots of the sum o f each sample standard deviation divided by the square root o f the number o f the samples.

a= N ~ X Y - E X E Y

NE X2- Z ;O

and

b = E r E x2 - E x E x r

NE X2-O2 ;O 2

(11)

(12)

6.1. Internal uncertainty

An estimate of internal uncertainty (UI) is given as [ 18]

~/-~2 2 2

U/= 1 +02 + '"ON (13)

N

(6)

126 G.N. 73wari et al. / Desalination 115 (1998) I21-128

where o is the SD which is given as

No

w h e r e X - X i s the deviation from the mean and N O is the number o f observations taken to find the mean.

Thus, percent uncertainty could be determined using the following expression:

% uncertainty :

v,

xlO0

Average o f total number of observations

6.2. External uncertainty

External uncertainty is evaluated by taking into account the errors which occurred in taking the measurements for distillate output, tempera- tures o f water and glass, etc. It has been considered by taking the least count o f the measuring instruments:

• % error in measuring water temp. 0.1%

• % error in measuring glass temp. 0.1%

• Error in measuring yield: 1%

• Total % external uncertainty: 1.2%

• Total % uncertainty=internal

+external 1.54%

Sample calculations of experimental uncer- tainties are given in Table 3. Using values from this table, U 1 is calculated as

19.76 U, - - - - 3.29

6

• /

2 2 2

fl=

t3"1 + 0 2 + . . . 0"6

6

% uncertainty - 3.29×100

1153 .28 = 0.34%

Table 3

Sample calculation of experimental uncertainties

7. Results and discussion

The experiment was conducted at the water temperature of 43 °C and 65°C, respectively. A number o f observations were taken, and average values for each operating temperature range are reported in Table 1.

A simple regression analysis was carried out to find the modified values o f C and n for the following condensing chamber parameters:

A = 0.37 x 0.26 m2; [3 = 8.5°; df = 0.22 m

SN Operating condition Water temperature X Y,(X-X) 2 o

1 Normal condition 43.6 275.2 1139.06 6.75

64.1 1120.0 420.25 4.10

2 Air conditioned 43.9 330.0 4879.02 13.97

67.1 1442.2 1459.24 7.64

3 Ice on condensing cover 42.0 540.0 444.36 4.21

65.3 2059.0 1421.29 7.54

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G.N. Tiwari et al. / Desalination 115 (1998) 121-128 127 Table 4

Computed values ofh~v and he~ and percent deviation between experimental and theoretical distillate output for modified values of C and n (modified value ofC = 0.0294, n = 0.376; Grashofrange: 2.9×108 < Gr < 1.2×109)

SI. no. Experimental distillate Theoretical distillate h .... he, ~

output (g/m 2 h) output (g/m 2 h) W/m 2 ,°C W/m 2, °C

% deviation between exp. and theor, output

1 275.2 264.0 2.06 7.45 3.90

2 1120.0 1129.0 2.67 14.47 -0.87

3 1411.0 1442.0 2.25 7.66 -2.12

4 1442.2 1542.0 2.91 15.74 - 6.52

5 540.0 499.0 2.82 6.79 8.17

6 2059.0 2055.0 3.52 14.14 o. 18

The measured distillate output for different operating conditions is given in Table 1. The Yiwari and Lawrence [I 5] model gives closure prediction to the experimental observations at 43 °C and 65 °C. This is due to the fact that this model has incorporated the effect o f inclination (13) o f the condensing surface. Further, Dunkle's [1] model comes next to that o f Yiwari and Lawrence's [15] model. The prediction of the other models, namely Jacob and Gupta [19] and Grafand Held [20] deviate substantially from the experimental observations for the same water temperatures.

The regression analysis [Eqs. (11) and (12)]

was carried out to find modified values of C and n for the experimental operation. The values of C and n and given in Table 4. These values have been used to calculate the theoretical output of distillate (Table 4). The deviation between experimental and theoretical output is about 8%.

Experimental error in terms o f percent uncer- tainty [Eq. (13)] is calculated to predict precisely the values o f C and n. This error has been less than 2% as experiments were conducted under indoor simulation conditions.

8. Conclusions

On the basis o f modified values o f C and n, the result obtained for theoretical output was in

better agreement with the Tiwari and Lawrence model [15] as this model does not have any limitations. The results are also in good agreement with Dunkle's model [1] at a low operating temperature range. In particular, claims made by Clark [11] regarding convective heat loss are not consistent with the present experi- mental observation at a low operating temperature range.

The proposed model can be used for any design o f condensing cover without any limitation o f cavity volume, inclination of condensing cover and operating temperature.

9. Symbols C

c , -

4 - -

g G r

h~w w

Constant

Specific heat capacity o f humid air, J/kg K

Minimum spacing between water surface and glass cover (character- istics length), m

Acceleration due to gravity, m/s 2 Grashof number

Convective heat transfer coefficient from water surface to glass cover, W/m 2 K

Evaporative heat transfer coeffi- cient from water surface to the condensing surface, W/m 2 K

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128 G.N. Tiwari et al. / Desalination 115 (1998) 121-128 I(t)

Mw

n

N N u Pg Pw P r qew

L re

L rw

Greek

1.

g P

- - Solar flux, W / m 2

-- Thermal conductivity o f humid air, W/m, K

-- Mass flow rate per unit area, kg/m 2 h

Constant

- - N u m b e r o f observations

-- Nusselt number

-- Saturated vapour pressure o f water at Tg, N/m 2

Saturated vapour pressure o f water at Tw, N / m 2

Prandtl number

-- Rate o f heat loss due to evapora- tion, W / m 2

-- Ambient air temperature, K

-- Temperature o f condensing (glass) cover, K

- - Temperature o f sky, K

-- Temperature o f water, K

- - Fraction o f thermal energy ab- sorbed by the basin

-- Fraction o f thermal energy ab- sorbed b y the glass cover

- - Fraction o f thermal energy ab- sorbed b y the water mass

-- Inclination o f glass cover with the horizontal, °

- - Thermal expansion coefficient, 1/k m Latent heat o f humid air, J/kg

-- D y n a m i c viscosity o f humid air, kg/ms

Density o f humid air, kg/m 3

References

[1] R.V. Dunkle, Proc., ASME International Heat Transfer, Part V, University of Colorado, 1961, p. 895.

[2] M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S.

Sodha, Solar Distillation, Pergamon Press, UK, 1982.

[3] V.A. Baum and R. Balramov, Solar Energy, 8(3) (1964) 78.

[4] P.I. Cooper, Presented at First Australian Conference on Heat and Mass Transfer, 1973, Melbourne, Australia.

[5] J. Rheinlander, Solar Energy, 28 (1982) 173.

[6] P.I. Cooper, Ph.D. Thesis, University of Western Australia, 1970, p. 69.

[7] M. Jakob, Heat Transfer, Vol. 1, Wiley, New York, 1949.

[8] G.N. Tiwari, A. Kumar and M.S. Sodha, Energy Conversion and Management, 22 (1982) 143.

[9] W.K. Lewis, Trans. ASME, J. Solar Energy Engi- neering, 44 (1922) 325.

[10] J.A. Clark and J.A. Schrader, ASME Paper No. 85- WA/SOL-2, Miami Beach, FL, 1985, p. 1.

[11] J.A. Clark, Solar Energy, 44 (1990) 43.

[12] G.N. Tiwari, Recent Advances in Solar Distillation, Wiley Eastern, New Delhi, 1992, p. 32.

[13] R.S. Adhikari, A. Kumar and A. Kumar, Int. J.

Energy Res., 14 (1990) 636.

[14] U.B. Sharma and S.C. Malik, Trans. ASME, J. Solar Energy Engineering, 113 (1990) 36.

[15] G.N. Tiwari and S.A. Lawrence, Energy Conversion and Management, 31 (1991) 201.

[16] S. Toyama, T. Aragaki, H.M. Saleh, K. Marase and M. Sando, J. Chem. Eng. Japan, 20 (1967) 473.

[17] J.A. Duffle and W.A. Beckman, Solar Engineering of Thermal Processes, Wiley, New York, 1991.

[18] B.C. Nakra and K.K. Choudhary, Instrumentation Measurements and Analysis, 1st ed., Tata McGraw Hill, New Delhi, 1985, p. 33.

[19] M. Jacob and P. Gupta, Chemical Engineering Progress Symposium, Series 9, 50 (1954) 15.

[20] J.G.A. De Graf and E.F.M. Vander Held, Applied Science Research Section A, 3 (1953) 393.

References

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