Study of heat and mass transfer from sugarcane juice for evaporation

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Study of heat and mass transfer Corn sugarcane juice for evaporation

G.N. Tiwari*, Sanjeev &mar, Om Prakash

Centre for Energy Studies, Indian Institute of Technologv Delhi, Haus Khas, New Delhi I10016, India Fax: +91 (1I) 2686-2037; email: gntiwari@ces.iitdernet.in

Received 12 April 2002; accepted 31 January 2003

Abstract

The study of heat and mass transfer during natural convection heating for preparation of Jaggery was carried out for the open and closed conditions. An indoor experiment was conducted for shmdation of developed thermal model for heat and mass transfer for maximum evaporation. Evaporated water was condensed at the inner surface for the closed system as fresh water. The effect of different rates of heating (varying voltage) and heat capacity of sugar cane juice on heat and mass transfer were also carried out. It was observed that the evaporative heat transfer coefficient depends significantly on the rate of heating and heat capacity.

Keywords: Sugarcane juice heating; Convective and evaporative heat transfer

1. Introduction

The heat and mass transfer analysis from free water surface plays an important role in deter- mining the rate of evaporation. Dunkle [l] and Cooper [2] gave a relationship to determine the rate of evaporation for distillation under indoor conditions with the following limitations:

• operating temperature range of 50°C

• independent of cavity volume

• 15°C temperature difference between evaporative and condensing surfaces.

Later on, various authors have made an attempt to develop the model to determine the rate of evaporation without any limitations for indoor as well as for outdoor conditions. Tiwari et al. [3] and Kumar and Tiwari [4] have developed a model for heat and mass transfer for indoor and outdoor conditions by using regression analysis. They observed that the evaporative heat loss significantly depends on operating temperature, characteristic length and shape of condensing surface.

In this paper, an attempt has been made to study the behavior of heat and mass transfer

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82

relation during the preparation of jaggery for an open and closed system. The following temperature ranges were classified for preparation for the present study:

• natural convection boiling (19-90°C)

• pool/nucleate boiling (90-95°C)

• cooling with stirring.

An indoor experiment was conducted for natural convection boiling to measure various temperatures and mass evaporated at a regular time interval (10 min) for open as well as a closed system. It was found that the evaporative heat transfer coefficient significantly depends on operating temperature, conditions for heating and mass of sugarcane juice. Further, it is important to note that:

• the convective and evaporative heat transfer coefficient for sugar cane juice is lower in comparison to water due to the presence of sugar particulate;

• the convective and evaporative heat transfer coefficient is lower in the case of a closed system due to the smaller temperature difference between the evaporative and condensing cover.

2. Thermal modelling

The convective heat transfer coefftcient for evaporation can be determined by using the following relations [11:

Nu = — = C(GrPr)”

G.N. Tiwari et al. /Desalination 159 (2003) 81-96

Qe = 0.016hc[$)-yP(a)]

K or

Ji.

C(Grl-9)” (1)

The rate of heat utilized to evaporate moisture is given as

(2) (T, = Tl and T, = T6 used from Appendix II, Tables Al-A6).

On substituting h, from Eq. (I), Eq. (2) becomes

oe = O.O16;C(GrP$[I$)-yP(T,)] (3)

The moisture evaporated is determined by dividing Eq. (3) by the latent heat of vaporization (A) and multiplying the area of the pan (A,) and time interval (t).

X ' XX [P(Tc)-yP(Te)]Att

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Let

0.016-1 [P(TK c)-yP(Te)]tAt =

XX

- ^ = C(GrPr)m n (5)

Taking the logarithm of both sides of Eq. (5),

In

= lnC + nln(GrPr)

@a)

This is the form of a linear equation,

(6b) where

Y= ln ^tn. = n,X0 = ln(GrPr) and C, = lnC

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G.N. Tiwari et al. /Desalination 159 (2003) 81-96 83 Thus, C = e °. The values of m and C, in

Eq. (6b) can be obtained by using the regression method.

3. Experimental set-up and observations Several simulation experiments were carried out in the laboratory to determine convective heat transfer coefficients in the natural convective heating mode. The fresh sugarcane juice (pur- chased from the local market) in an aluminum cylindrical pot of 0.18 m in diameter and 0.065 m deep without a cover was heated using an electric hot plate (heater).

The experimental set-up (as shown in Fig. 1a) consists of a heater of 1000 W connected through a variac (to Icontrol the heating rate of the juice) and pot (capacity 1.25 L) with handle. The experiment was conducted under the following conditions:

• with variation of voltage

• with varying mass

• with water only for comparison.

Observations for temperatures for various locations, namelyjuice (T,), bottom (Q, pot side (T3) and ambient (&) temperatures were measured by calibrated copper-constantan ther- mocouples using a digital temperature indicator.

The temperature on the surface of the juice (T^s) was measured by infra-red thermometer. The relative hum.idity (Y) and temperature above juice surface (T,) were measured by a digital humidity/

temperature meter (with a least count of 0.1%

and 0.l °C, respectively). The different sets of heating of juice were obtained by varying the input power supply to the electric hot plate using variac for the open condition. For the closed system, the temperature of vapor (Ts) and condensing cover (T^J were measured by a copper-constantan thermocouple.

An electronic weighing machine with at least a count of 0..1 g was used to measure the mass of juice evaporated during preparation of the

Digito!

Balance lo 0 o

Fig. la. Experimental set-up of sugarcane juice heating/

boiling in the open system.

Condensing cover

Electric socket

Fig. lb. Experimental set-up of sugarcane juice heating/

boiling in the closed system.

Fig. lc. Photograph of sugarcane juice heating/boiling in the closed system.

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84 G.N. Tiwari etal. IDesalination J.59 QOO3~ 81 96 jaggery. The mass evaporated has been evaluated

by subtracting two consecutive readings for a given time interval.

The above experiment is generally referred as open system used for preparation of jaggery. In this case evaporated water from sugarcane juice is lost in the atmosphere. If the evaporated mass is allowed to condense, then the condensed water can be reutilized for human consumption or other uses. In order to collect evaporated water, the same experiments were conducted under the closed system (Fig. 1b). The photograph of the experimental set-up for the closed system is shown in Fig. lc.

The observations were recorded with regular and equal time interval (10 min), and the results are given in Appendix II (Tables AI-A6). The data in these tables were used to study the heat and mass transfer during the heating of juice in Eq. (6).

It is important to mention that the distillate output for the closed system was observed at a higher temperature (>90°C) for a higher value of voltage. This range is generally referred as pool/nucleate boiling conditions (Tables A2b- A6b). This range is preferred in the beginning for the preparation of jaggery.

4. Results and discussion

The convective mass transfer coefficient in the case of natural convection heating has been determined by using the data from Tables A l - A6. These data were used to plot the curve between In {mJT) and In (GrPr); the variation is shown in Fig. 2a, which has been used to evaluate constant C and n. The constants C and n can also be obtained by using Eq. (6b) and a regression analysis. The values of C and n during natural convection heating for different voltages and masses are reported in Table 1. After knowing the values of C and n, the values of the convective mass transfer coefficients were

1.6-]

1 . 4 • 1 . 2 •

5? 1-0- 1 0.8~

£ 0.6 - 0.4- 0.2- nn -

C = l.Z3and n~Q15

„ liJLjGJ. ——.-—."• ,,-.w^™-~ •.«»••

X

7.45 750 7.55 7.60 7.65 7 70 7.75 ln(G,P^t)

Fig. 2a. Variation of In(ni,,/Z) vs. In(GrPr) for the closed system (supply voltage = 100 V, sugarcane juice mass = 700 g).

164 - 16.2 - 160 • 15.8 - z ”25.6 - 15.4 \

15,2 •

15.0 14.8

3.4 3.8 4.2 4.6

GrPr(xW)

5.4

Fig. 2b. Variation of Nusselt number vs. (GrPr) for the closed system (supply voltage = 100 V, sugarcane juice mass = 700 g).

determined from Eq. (1). The results for the convective mass transfer coefficients are also given in Table 1 where it is noted that the value of the convective mass transfer coefficients depends significantly on the voltage and mass of juice. The increase of voltage means an increase of the rate of heating the sugar cane juice for faster evaporation for a given mass of sugar cane juice. As the mass of sugar cane juice increases for a given voltage (the rate of heating the juice), the convective mass transfer coefficient decreases, as expected. The variation of Nu vs.

(GrPr) is shown in Fig. 2b.

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G.N. Tiwari et al. 1Desalination 159 (2003) 81-96 85 Table la

Values of constants (C and n) and convective and evaporative mass transfer coefficients for different voltages and weights of sugar cane juice in the open and closed conditions

SUPPlY voltage, V

100 120 130 140 150

wt. of juice, g

700 800 1000 800 1000

Open condition h,, W/mz °C

1.87-8.72 5.31-8.01 3.25-4.14 3.57-4.97 5.35-7.21

h,, W/mz °C 11.2-150^s 31.9-127.9 21.0-64.75 30.9-61.98 33.3-144.9

C 2.65

1.82 1.03 0.82 0.64

« 0.15 0.18 0.16 0.17 0.24

Closed condition h,, W/mzoC 2.76-3.04 4.24-4.97 5.29-6.22 8.0-9.48 8.47-10.2

he, W/m2 OC 46.9-72.0 75.9-132.0 118.6-148.9 127.0-228.5 175.0-312.0

C 1.23 0.95 0.79 0.60 0.68

n 0.14 0.18 0.20 0.25 0.24 Table lb

Values of constants (C and n) and convective and evaporative mass transfer coefficients for different voltages and weights of water in the open and closed conditions

SUPPlY wt. of Open condition voltage, V water, g

Closed condition

h,,W/m^’,“C h,,W/m2,“C C ², ‘C h,, W/m^’, ‘C C

100 ⁷⁰⁰ 4.48-8.6 24.9-91.9 ^{0.40 0.42} 6.41-7.0 80.0-120 1.00 0.21

Table 2

Total mass evaporated for different cases in open condition and closed conditions SuPPlY

voltage, V

100 120 130 140 150

wt. of water, g

700 800 1000 800 1000

Open condition Duration of heating, h 4.20 2.50 0.30 0.30 0.30

Evaporated ma.=, g 486.7 504.7 24.4

63.3 48.7

Evaporated mass, % 69.52 63.08 2.44 7.91 4.87

Closed condition Duration of heating, h 4.10 3.50 3.20 2.30 2.30

Evaporated mass, g 441.3 487.9 436.1 487.3 477.8

Evaporated mass, % 63.04 60.9 47.5 55.13 47.78

Figs. 3 and 4 show the variation of convective and evaporative heat transfer coefficients for open and closed system. The convective and evaporative heat transfer coefficients for water have also been evaluated for comparison

purposes. It was inferred that the heat transfer coefficient for sugarcane juice is lower (Fig. 3a) in comparison to water (Fig. 3b) for the open as well as the closed condition. This may be due to the fact that the water is pure in comparison with

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86 G.N. Tiwari et al. /Desalination 159 (2003) 81-96

Qi

O 10-i

"re 5 6-

o Closed xOpen

40 50 60 70 a0 90 100 Sugarcane juice temperature (“C)

Fig. 3a. Variation of convective heat transfer coefficient vs. sugarcane juice temperature for the open and closed conditions (supply voltage = 100 V, sugarcane juice mass

= 700 g).

10 -

g p 6 -

I 0

o Closed x Open

40 45 50 55 60 65 70 75 a0 a5 90 Water temperature (‘C)

Fig. 3b. Variation of evaporative heat transfer coeffkient vs. water temperature for open and closed conditions (supply voltage = 100 V, water mass = 700 g).

140 120- 1 0 0 - 8 0 - 60 40 • 2 0 - 0 -

o closed

xOpen ^X

X j S ^

* x ^ ^

X J ^ K- o

^ * ^ X

40 50 60 70 60 90 Sugarcane juice temperature (“C)

100

Fig. 4a. Variation of evaporative heat transfer coefficient vs. sugarcane juice temperature for the open and closed conditions (supply voltage = 100 V, sugarcane juice mass

= 700 g).

50 60 70 80 90

Sugarcane juice temperature (‘C)

100 110

Fig. 5a. Variation of convective heat transfer coefficient vs. sugarcane juice temperature for open and closed conditions (supply voltage = 120 V, sugarcane juice mass

= 800 g).

50 ^{60 70 80}

Water temperature (“C)

90 ¹⁰⁰

Fig. 4b. Variation of evaporative heat transfer coefficient vs. water temperature for open and closed conditions (supply voltage = 100 V, water mass = 700 g).

140- 120- lOO- 80- 60- 40- 20-

n -u — 40

x open^x o

o closed x /

50 60 70 a0 9c 100 1 Sugarcane juice temperature (“C)

Fig. 5b. Variation of evaporative heat transfer coefficient vs. sugarcane juice temperature for open and closed conditions (supply voltage = 120 V, sugarcane juice mass

= 700g).

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14- 12- 10- 8- 6 4 2-i 0

oVMOO

A V = 1 3 0

»V»140 o VM50

G.N. Tiwari et al. /Desalination 159 (2003) 81-96 350-

3 0 0'

81

80 85 so 95 loo 105 Sugarcane jutce te4nperature {“c)

110

Fig. 6a. Variation of convective heat transfer coefftcient vs. sugarcane juice temperature for different voltages and juice mass in tie closed condition.

85 90 95 100 105 Sugarcane juice temperature (*C)

110

Fig. 6b. Variation of evaporative heat transfer coefficient vs. sugarcane juice temperature for different voltages and juice mass in the closed condition.

sugarcane juice. Further, the heat transfer coeffl- cient for closed system for water as well as juice is higher in open condition due to large difference in temperature between evaporative surface to ambient for ,a given temperature of evaporation.

The same results for supply voltage 120 V has been shown in Fig. 5.

The effect of the supply voltage on the convective and evaporative heat transfer coefft- cients have been shown in Fig. 6. It can be concluded that convective and evaporative heat transfer coefficient increase with increase of supply voltage as expected.

5. Conclusions and recommendations

On the basis of the present study, the following conclusions have been made:

1. The value of convective and evaporative heat transfer coefficients in the case of water is more at the lower value of temperature in comparison to sugar cane juice (Figs. 3 and 4) due to purity of water.

2. The convective and evaporative heat transfer coefficients are significantly increased

with an increase of voltage (the rate of heating), as expected.

3. The present study will be helpful to design a distillation cum jaggery system.

6. Symbols A, - C —

c,, -

g - Gr —

K -

Kv — mev — n — Nu — Pr — P{T) — Qe -

Area of pan, m

Experimental constant Specific heat, J/kg “C

Acceleration due to gravity, m/s2

Grashof number = pgx’ pf AP/p,2

Convective heat transfer coefficient, W/m’, “C

Thermal conductivity, W/m “C Rate of mass evaporated, kg Experimental constant Nusselt number = h, x/K, Prandtl number = p&/K, Partial vapor pressure, N/m2

Rate of heat utilized to evaporate moisture, J/m2 s

t — Time, s

Effective temperature difference, “C Weight of sugarcane juice, g

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G.N. Tiwari et al. /Desalination 1.59 (2003) 81-96

w2

W X

Greek

Y

a X

|i^v pv

Weight of empty pot, g Total weight, (w, + w2) Characteristic dimension, m

Relative humidity Surface tension, N/m

Latent heat of vaporization, J/kg Dynamic viscosity, kg/m Density, kg/m3

Acknowledgements

The financial assistance provided by the Indian Council of Agricultural Research (ICAR), New Delhi, in the form of a sponsored research project is gratefully acknowledged. The authors

are also thankful to Dr. S.1. Anwar and Dr. R.D.

Singh, Indian Institute of Sugar Cane Research (IISR), Lucknow, for their kind help and support during the experiment at various stages.

— Coefficient of volumetric expansion, References

[l] R.V. Dunkle, Solar water distillation; The roof type still and multiple effect diffusion still, International Development in Heat Transfer, ASME, Proc.

International Heat transfer, Part V, University of Colorado, 1961, p. 895.

[2] P.I. Cooper, The transient analysis of glass cover solar stills, PhD Thesis, University of Western Aus- tralia, 1970.

[3] G.N. Tiwari, A. Minocha P.B. Sharma and M.E.

Khan, Energy Convers. Mgmt, 38(8) (1997) 761.

[4] S. Kumar and G.N. Tiwari, Estimation of convective mass transfer in solar distillation system, Solar Energy, 57(6) (1996) 459.

[S] G.N. Tiwari and S. Suneja., Solar thermal engineer- ing systems. Narosa Publishing, New Delhi, 1997.

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Appendix I

G.N. Tiwari et al. /Desalination 159 (2003) 81-96

KY = 0.0244 + 0.6773 x 1O-4 Ti

-96

The following expressions were used for calculating values of the physical properties such as specific heat ( CJ , thermal conductivity (IQ, density (p,,) and viscosity (py) and partial vapor pressure P(I’): [51:

C,, = 999.2 + 0.143 TI + 1.101 x 1O-4 T2

- 6.7581 ~1O-8T;

pv = 353.44 (T, +273.15)

p,= 1.718 x l o- ’ 4.620

25.317- 5144 Vt + 273.15)

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90

Appendix II

G.N. Tiwari et al. /Desalination I59 (2003) S/--96

Table Ala

Observations for heating the sugarcane juice in the open condition (supply voltage = 100 V. w, = 700 g, w2 = 187 g) Timi

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

e interval (min) T,, ‘C 26.4 43.1 60.8 70.7 74.8 77.5 78.1 78.1 77.1 77.2 75.9 75.6 74.6 74.2 71.9 71.8 69.5 70.7 70.4 69.0 69.0 66.0 63.0 66.4 72.2 78.0 89.2

T,,“C 26.7 44.0 63.5 74.5 78.1 80.6 81.0 79.7 79.1 78.5 77.8 76.9 76.0 76.6 75.4 72.0 72.2 74.4 72.0 72.0 72.3 71.7 72.0 74.1 78.6 87.2 93.7

T °f"1

26.4 32.6 57.1 67.3 70.5 73.1 73.8 73.5 73.6 71.9 72.0 69.9 68.6 68.0 70.7 69.0 70.8 70.9 70.5 71.5 70.7 71.9 72.0 73.8 73.9 79.8 88.4

26.0 26.5 26.6 27.0 27.0 27.0 26.7 26.7 27.9 26.9 27.3 27.5 27.3 27.2 27.2 27.3 26.9 27.2 27.1 27.0 26.8 27.3 27.0 26.8 26.9 26.7 26.6

T ,,“C 23.5 36.0 59.0 60.5 64.0 66.0 67.0 67.5 66.0 66.5 67.0 65.5 65.5 64.5 65.0 65.0 65.0 65.5 66.0 64.0 64.0 64.5 65.0 66.5 68.0 69.5 76.0

T,,“C 23.0 25.3 26.8 27.2 27.5 29.7 31.0 31.2 31.1 31.2 31.4 31.4 31.4 32.0 31.2 31.2 32.2 31.2 31.0 31.2 30 30.5 31.4 31.0 30.5 29.8 30.8

Y, %

55.5 58.6 57.0 78.0 82.7 86.0 88.0 87.0 96.0 93.0 98.0 96.0 99.0 100.0 100.0 102.0 100.0 98.0 100.0 100.0 99.0 98.0 87.0 84.0 86.0 83.0 81.0

w, g 887.0 886.0 881.6 872.2 855.4 834.6 815.1 793.0 769.4 745.2 722.6 700.1 678.1 654.9 630.9 610.7 588.6 566.2 543.2 522.4 501.4 483.2 464.2 448.3 432.2 414.6 400.3

1.0 4.4 9.4 16.8 20.8 19.5 22.1 24.0 23.8 22.6 22.5 22.0 23.2 24.0 20.2 22.1 22.4 23.0 20.8 21.0 18.2 19.0 15.9 16.1 17.6 14.3

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G.N. Tiwari et al. /Desalination 159 (2003) 81-96 91 Table Alb

Observations for heating the sugarcane juice in closed condition (supply voltage=100 v, w,= 700 g, w2 = 175 g) Time interval

(min) ___

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T,,“C Juice temp.

36.9 54.1 66.6 77.9 85.7 88.3 89.3 89.0 89.1 89.0 89.1 89.2 89.4 89.4 89.3 90.4 90.0 88.5 88.6 87.0 88.0 87.5 87.0 90.5 92.3 99.0

Pot bottom temp.

38.7 56.5 69.5 80.1 85.6 88.7 90.8 91.6 93.4 93.5 93.2 93.5 93.6 93.6 93.6 93.9 94.0 94.4 95.0 94.9 94.7 97.1 97.6 98.5 99.7 102.0

T,, “C Pot side temp 40.8 50.6 59.1 66.8 71.2 74.7 77.2 78.3 79.3 80.0 79.7 80.0 80.3 80.6 80.7 81.1 81.4 81.8 82.6 83.4 84.0 85.3 86.4 87.0 88.0 89.3

T,,“C Ambient temp.

32.6 32.9 33.0 32.7 32.8 32.8 32.8 32.7 32.8 32.8 33.0 32.8 32.8 32.9 32.9 32.9 32.9 32.9 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0

Vapor temp.

32.6 32.9 33.0 32.7 32.8 32.8 32.8 32.7 32.8 32.8 33.0 32.8 32.8 32.9 32.9 32.9 32.9 32.9 33.0 33.0 33.0 33.0 33.0 33.0 33.0 33.0

T,,“C Condensing cover temp.

33.5 34.0 35.0 35.5 36.0 36.0 36.5 37.5 37.0 37.0 37.5 37.0 37.0 37.0 37.0 37.0 37.0 38.0 36.5 37.5 37.0 37.5 37.5 37.5 37.0 37.2

—

— 0.28 0.70 14.8 16.1 19.1 22.2 20.8 20.6 21.4 20.9 21.1 23.7 22.7 20.1 21.3 24.2 23.5 22.8 24.8 24.2 24.2 23.0

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92 G.N. Tiwari et al. /Desalination 159 (2003) 81-96 Table A2a

Observations for heating the sugarcane juice in open condition (supply voltage = 120 V, w, = 800 g, w² = 163 g, W= 963 g) Time, min

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T,,“C 27.4 43.3 65.4 81.5 86.9 91.9 87.4 84.5 83.0 84.2 81.3 81.3 80.8 79.8 84.0 78.5 78.9 81.8

T,,“C 27.2 47.3 71.0 85.8 91.0 95.4 89.6 86.9 86.1 87.4 85.0 85.5 85.0 86.0 87.5 86.9 89.7 95.6

T^it°C 27.0 46.9 66.8 79.9 83.9 86.4 82.4 79.5 79.5 80.5 80.6 80.4 81.1 81.5 79.9 81.5 81.2 84.7

T4, “C 25.3 25.9 26.2 26.4 26.4 26.5 26.6 26.6 26.7 26.8 26.8 26.9 26.9 27.0 27.0 27.0 27.1 27.1

T^$,°C 23.0 39.0 54.0 66.0 74.0 78.0 79.0 76.0 77.0 76.0 76.0 79.0 90.0 90.0 96.0 100.0 102.0 106.0

T °f

1 6' ^

22.5 24.5 28.0 28.5 29.5 30.0 30.5 31.5 33.4 34.5 35.5 35.8 35.8 35.8 32.1 34.5 35.0 36.0

Y, % 56.0 56.0 69.2 89.2 93.0 93.8 93.3 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

w,g 963.0 960.0 952.9 931.5 905.3 877.1 837.4 797.4 757.2 715.7 678.7 645.1 611.7 579.1 545.1 510.4 482.9 458.3

m^m __

0.0 7.1 2 : . : 26^:2 28.2 39.7 40.0 40.2 41.5 37.0 33.6 33.4 32.6 34.0 34.7 27.5 24.6 Table A2b

Observations for heating the sugarcane juice in closed condition (supply voltage =120 V, w, = 800 g, w² = 183.5 g) Time interval, min

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

Tlt°C 31.7 561 70.1 82.8 86.2 91.6 92.6 94.5 95.6 95.7 95.5 94.6 93.4 91.2 90.0 86.5 87.6 88.4 91.0 95.5 98.6 99.1 103.2

T²,°C 32.4 60.1 68.1 70.6 83.2 85.2 87.5 88.0 87.6 88.2 87.3 87.3 87.1 87.5 87.5 87.6 88.5 88.4 86.4 87.4 87.7 91.2 102.0

r

³

,°c

33.9 53.7 69.0 73.1 82.0 86.4 88.4 90.0 90.0 90.6 90.7 91.7 90.6 91.2 91.9 92.2 91.3 91.8 92.8 93.3 94.1 95.2 101.0

r

⁴

,°c

33.6 33.5 33.4 33.3 33.1 33.1 33.0 33.1 33.1 33.2 33.0 33.1 33.2 33.1 33.1 33.2 33.2 33.3 33.2 33.1 33.2 33.2 33.2

r

^5;o

c

31.3 55.7 80.0 83.5 88.9 90.6 92.2 93.6 93.4 93.8 94.0 94.6 94.4 94.5 94.7 95.8 97.6 98.1 98.7 99.9 102.1 105.9 131.9

T,,“C 34.5 35.0 37.5 38.5 38.5 39.0 39.5 40.0 40.0 40.0 40.0 40.0 40.5 40.5 40.5 40.5 40.5 40.2 39.7 39.5 38.5 38.5 38.5

mmg

—

— 0.2 16.0 21.6 23.9 25.2 25.1 25.0 32.0 31.0 33.6 32.6 31.4 33.0 30.7 28.4 33.4 31.4 35.5 28.7

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G.N. Tiwari et al. /Desalination 159 (2003) 81-96 93 Table A3a

Observations ,foor heating the sugarcane juice in the open condition (supply voltage = 130 V, w, =177.4 g, w2= 1000 g) Time, min

10 10 10

18.9 49.6 71.1 84.6

T,,“C 26.2 66.1 83.1 93.6

r

³

,°c

23.4 54.3 72.8 79.2

7*4, ° C 26.2 26.4 26.8 27.0

T,, ‘C 19.0 44.0 58.0 65.0

T,,“C 23.2 24.8 26.1 35.3

y,%

52 56 61 65

W,g

1177.4 1180.0 1170.6 1153.0

»»„> g 2.6 9.4 17.6

Table A3b

Observations for heating the sugarcane juice in closed condition (supply voltage =130 V, w, = 1000 g, w¹ = 171.5 g) Time, min

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T,,“C 33.1 53.4 71.8 85.8 95.3 96.6 98.3 98.4 98.4 98.6 98.7 98.8 99.0 99.0 98.2 98.8 98.8 96.8 102.9 107.6

T,,‘C 33.5 63.8 76.8 89.9 98.5 98.6 97.8 94.8 94.4 94.9 94.1 94.4 94.3 94.4 94.3 94.2 94.3 96.1 98.8 106.5

r

³⁾

°c

33.7 52.9 64.2 76.1 91.3 93.6 95.1 94.3 97.5 98.3 98.8 97.6 99.0 99.4 99.0 92.5 92.6 99.8 100.0 100.5

4>

34.1 34.3 34.2 34.1 34.0 34.0 33.8 33.9 33.8 33.7 33.7 33.7 33.6 33.6 33.5 33.5 33.5 33.5 33.5 33.6

T °C*

33.3 55.4 69.2 84.2 94.2 95.0 98.0 97.5 97.8 97.8 98.0 98.4 98.7 99.3 99.6 100.3 100.4 102.4 103.0 111.3

T Of1

34.5 35.0 36.5 37.5 40.2 40.5 41.2 41.5 41.5 41.7 42.3 42.5 42.5 42.5 42.5 42.5 42.5 42.5 42.0 42.0

—

— 26.2 28.5 32.1 37.0 35.0 33.1 34.2 36.5 34.1 32.9 30.1 29.9 24.4 31.6 29.8 24.1

(14)

94 G.N. Tiwari et al. /Desalination 159 (2003) 81-96 Table A4a

Observations for heating and boiling the sugarcane juice in open condition (supply voltage = 140 V, w, = 800 g, w2

199.4 g) Time, min __

10 10 10

T,,“C 27.5 46.1 67.5 90.0

7*2, °C 28.5 52.6 71.5 92.0

7-3, °C 27.4 51.5 69.8 84.5

T O P 14, V-

25.0 25.4 25.5 25.5

T,,“C 24.0 42.0 56.0 74.0

T,, “C 22.0 26.0 29.0 30.0

y, % 40.2 48.0 67.0 90.0

w,

^g

999.4 995.0 974.4 936.1

wcv, g

4.0 21.0 38.3

Table A4b

Observations for heating the sugarcane juice in closed surface (supply voltage = 140 V, w, = 994.4 g, w2 = 194.4 g) Time, min

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

7\,°C 46.8 69.0 83.3 95.1 96.2 96.1 96.3 96.2 96.6 96.8 97.5 97.2 96.8 97.0 98.0 102.7

7-2, °C 48.2 72.1 82.1 96.2 97.6 96.8 96.8 96.9 97.2 97.4 98.0 97.5 97.9 99.3 98.7 102.6

r

³

,°c

50.4 73.0 83.0 96.0 97.1 97.5 97.7 97.8 98.8 99.0 100.1 100.1 101.8 103.2 104.9 112.2

7-4, °C 32.6 32.8 32.8 32.8 32.9 32.8 32.9 32.9 32.9 32.9 32.9 33.0 32.9 32.8 32.7 32.8

7-5,°C 43.7 64.6 75.6 87.6 93.9 94.4 94.3 88.1 92.5 94.9 95.4 94.1 96.6 98.0 98.5 101.5

T6, °C 34.0 34.0 35.5 36.3 38.5 38.5 38.5 38.7 39.5 39.7 40.2 41.0 40.7 40.5 40.3 39.5

-—

16.0 28.0 34.0 32.0 31.0 26.6 32.8 38.1 35.8 36.0 34.0 34.3 31.5 30.9

(15)

G.N. Tiwari et al. /Desalination 159 (2003) 81-96 95 Table A5a

Observation for heating of sugarcane juice in the open condition [supply voltage = 150 V, w, = 1000 g, w² (wt. of pot + asbestos sheet) = 731.9 g]

Time, min

10 10 10

T,,“C 23.6 32.1 59.6 79.5

T,, ‘C 21.8 31.1 59.0 79.0

7-3, °C 23.3 35.2 58.0 76.7

r

^4)o

c

24.3 24.4 24.3 24.4

T,,OC 17 28.0 49.0 72.0

T6,OC 20.7 21.0 23.5 26.5

y,%

58.0 62.5 72.0 78.0

W,g 1731.9 1727.7 1704.7 1683.2

<,g

— 4.2 23.0 40.3

Table A5b

Observations for heating the sugarcane juice in the closed condition (supply voltage = 150 V, w, = 1000 g, w² = 176.3 g) Time, min

— 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T °C 37.1 66.4 84.2 95.1 96.4 97.3 98.1 98.6 99.1 99.4 99.3 99.6 99.7 99.4 100.5 107.9

T,,“C 39.2 68.4 90.1 95.1 94.9 90.3 95.0 94.1 93.7 94.0 94.2 94.6 95.3 96.8 99.2 109.8

T °ri

39.3 68.3 80.7 99.0 99.7 104.1 99.7 99.9 100.1 100.5 100.9 101.3 102.1 103.2 105.0 114.6

7-4)°C 33.0 33.5 33.4 33.5 33.7 33.5 33.7 33.5 33.3 33.5 33.5 33.5 33.4 33.4 33.4 33.4

i-5, ‘C 35.3 62.4 73.4 94.1 94.0 94.7 94.6 95.5 96.0 96.9 97.0 98.5 100.1 101.7 103.8 106.5

34.0 34.5 37.4 39.5 40.0 41.0 41.0 41.0 41.0 41.2 41.5 41.7 41.7 41.5 41.5 41.2

—

— 18.7 25.3 33.2 33.1 44.1 46.8 45.6 42.3 40.6 38.4 35.6 36.7 35.1

(16)

96 G.N. Tiwari et al. / Desalination I59 (2003) 81-96 Table A6a

Observation for water heating in open condition (supply voltage = 100 V, wt. of water = 700 g, I++ = 186.4 g) Time, min

— 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T,,“C 25.4 34.9 49.5 62.1 68.8 71.5 71.5 71.8 71.4 71.6 71.0 70.5 69.7 69.7 70.9 68.7 68.8 69.1 70.0 69.9

T2, “C 23.1 33.0 45.5 56.2 62.4 65.1 66.6 66.5 67.3 68.0 67.4 67.1 67.9 67.0 67.4 66.4 66.2 66.1 67.2 66.3

T °C 24.6 35.7 47.3 58.6 64.1 65.5 66.0 66.3 66.1 67.8 67.1 65.4 65.4 65.5 65.2 64.4 64.7 65.6 65.5 64.2

r

^4)o

c

25.7 26.2 26.5 26.3 26.3 26.3 26.3 26.4 26.6 26.3 26.4 26.4 26.4 26.3 26.4 26.4 26.4 26.4 26.5 26.4

T,, “C 21 29 43 53 60 64 64 64 65 65 64 65 64 65 65 64 64 64 65 65

T,,“C 22.9 23.7 25.0 25.6 28.5 28.5 28.5 28.8 30.3 30.2 31.0 29.0 28.5 28.5 31.0 32.0 29.0 31.5 31.4 31.4

y, % 53.2 55.5 63.7 66.4 91.6 92.5 94.4 91.5 100.0 100.0 100.0 95.0 96.2 97.2 98.4 100.0 100.0 100.0 100.0 100.0

w, 887.0 885.6 878.2 872.5 853.4 837.5 820.4 793.7 782.2 755.7 732.2 711.5 683.0 663.7 650.3 626.4 603.1 583.0 565.2 550.0

mcv, g __

1.4 7.4 5.7 19.1 15.9 17.1 26.7 11.5 26.5 23.5 20.7 28.5 19.3 13.4 23.9 23.3 20.1 17.8 15.2

Table A6b

Observations for heating the water in the closed condition (supply voltage = 150 V, W, = 163.1 g, wt. of water = 700 g) Time, min

10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

T,,“C 31.5 46.0 67.0 74.2 79.3 81.3 83.6 84.7 85.1 85.3 84.9 85.1 85.0 85.0 84.8 83.7 82.7 80.2 80.1 79.9 79.4 78.9 78.9

Tz,‘C

32.2 47.1 68.8 74.8 80.9 82.7 85.1 86.4 87.0 87.0 86.6 86.8 86.9 87.1 86.8 86.6 86.1 86.0 85.6 84.6 84.2 84.0 84.2

r

^3;

°c

32.0 48.6 68.4 74.3 79.8 81.8 84.1 85.4 86.0 86.8 85.5 85.7 85.8 86.2 86.7 87.0 86.9 87.0 87.0 87.3 87.2 87.2 87.2

T,, “C 32.7 32.8 33.3 33.1 32.9 33.0 33.0 33.1 33.4 33.2 33.1 33.2 33.2 33.2 33.2 33.2 33.2 33.1 33.2 33.1 33.2 33.1 33.1

7"5,°C 32.1 45.3 59.5 65.1 70.6 73.1 75.8 77.4 78.4 86.0 78.5 78.4 78.7 79.0 79.4 79.7 79.7 79.7 79.7 79.3 78.8 79.1 79.0

T °C*

35.0 34.0 34.0 34.5 35.7 36.5 36.5 37.2 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0

— 0.3 0.7 14.0 16.0 21.2 25.1 28.7 31.8 31.2 33.0 32.2 35.3 34.1 36.2 38.2 33.2 31.1 31.2 29.1 27.0