Effect of size and material of a semi-cylindrical condensing cover on heat and mass transfer for distillation

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Effect of size and material of a semi-cylindrical condensing cover on heat and mass transfer for distillation

Rajesh Tripathi, G.N. Tiwari*

Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India Tel. +91 (I1) 2659-1258; Fax +91 (11) 2686-2037," gntiwari@ces.iitd.ernet.in

Received 3 February 2004; accepted 13 February 2004

Abstract

The rate of distillate depends mainly on operating temperature, shape and material of the condensing cover. Further, it is important to study the behaviour of heat and mass transfer relations as a function of operating temperature, shape and material. For the present study two sizes of semi-cylindrical condensing covers with characteristic dimensions of 0.14 cm and 0.07 cm were used. The materials most common for condensing covers for distillation used were aluminium and copper. The studies were carried out under controlled environmental conditions. The operating temperature kept during the experiments was between 40°C to 80°C for both forced as well as natural mode. It was observed that the convective and evaporative heat transfer coefficient depends strongly on operating temperatures. The following results at operating temperatures of 40°C to 80°C were obtained: (1) there is an increase of about 15% in the evaporative heat transfer coefficient due to the size of the condensing cover; and (2) there is an increase of about 7.5%

in the evaporative heat transfer coefficient due to a change in material.

Keywords: Distillation; Heat and mass transfer; Purification of brackish water

1. Introduction the indoor distillation unit and to commercialize

™ , . „ . , ,. ..,, .. ., ... the semi-cylindrical-shaped multi-effect distilla- The design of an indoor distillation unit with .^J , .^K , , ,

,. _, • 1 i , . - - tion system, there is a strong need to study the

a semi-cylindrical shaped condensing cover is , • , , ]r r . .

. . co ver , i s , basic heat and mass transfer for given semi- more convenient than one with a spherical shape . . . „ , . °

r i 1 T j . , ., ,. ..,, , , . - cylindrical sizes of the condensing cover with [1]. In order to enhance the distillate output from . . . . .. 6

different materials.

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232 R. TripathL G.N. Tiwari / Desalination 166(2004) 231-241

2. Design of the condensing cover and experi- mental set-up

Four semi-cylindrical covers made up of aluminium and copper were used for indoor distillation. The specifications of the condensing covers used for the present study are given in Table 1. A distillate channel with a " U " shape was fitted at the lower end of condensing covers from all sides as shown in Fig. l(a). A photograph of the two condensing covers with different sizes is shown in Fig. 1(b).

The experimental set-up consists of the following components:

• constant temperature bath

• semi-cylindrical condensing cover

• digital temperature indicator

• and thermocouples

The copper constantan thermocouples were cali- brated against a zeal thermometer. The effective evaporating surface area of the constant temperature bath is 36 cm x 26 cm (rectangular area). A photograph of the experimental set-up is shown in Fig. 2.

The water temperature inside the constant temperature bath, the inside and outside temperatures of the condensing cover and the ambient Table 1

Specifications of condensing covers Dimension

Shape Material Thickness,

gauge Length, cm Breadth, cm Height, cm Rivet, mm (dia.)

Size of large cover Semi-cylindrical Aluminium or copper 20 39 26 28 2

Size of small cover Semi-cylindrical Aluminium or copper 20 39 26 14 2

room temperature were measured with the help of copper constantan thermocouples and digital temperature indicator. Experiments were con-

pendensed droptet

Distiltat~ channet

Fig. la. Cross sectional view of a semi-cylindrical condensing cover.

Fig. lb. Photograph of the two condensing covers of different sizes.

Fig. 2. Photograph of the experimental set-up.

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R. Tripathi, G.N. Tiwari /Desalination 166(2004) 231-241 233

ducted from 40°C to 80°C at intervals of 2°C as suggested by Tiwari and Tripathi [1] under the conditions of no fan for a natural convection effect and with a fan for a forced convection effect.

The distillate output was measured with the help of a transparent beaker and a balance with a sensitivity of 0.1 g. The yield was taken at 10- min time intervals. The characteristic dimension (Lv) was taken as half the vertical height of the condensing cover, i.e., 0.14 m for the larger cover and 0.07 m for the smaller cover.

The temperatures and yield under natural and forced modes of operation for operating temperatures ranging from 40°C to 80°C were recorded for both aluminium and copper covers.

Different precautionary measures such as use of proper adhesive at the joints from four sides of the condensing cover and the use of sponge rubber gaskets were taken to avoid vapour leakage before starting the experiment.

(2a) where C and n can be obtained by using the data from Tables 2a-h for different conditions as suggested by Tiwari and Tripathi [1].

After knowing C and n for each case, hc~, can be evaluated from Eq. (2a). For comparison of the proposed model with Dunkle's [2] relation, the following formula has also been used to evaluate convective heat transfer coefficient (h~w):

= 0-884 T -T.+

W CI

1/3

2--6-~,9x-1-~-~-~ 273) The evaporative heat transfer coefficient is calculated by the following relation:

^ = 0

^'

01623 ^ C{GrPrY\^A

⁽³⁾

^ v I K^lci)

3. Methodology

Following Tiwari and Tripathi [1], the rate of convective heat transfer for a given evaporative surface area 'A' was described by the general equation

(1) where hew is the convective heat transfer coefficient. The convective heat transfer coefficient mainly depends on the following parameters:

• operating temperature range

• geometry of the condensing cover

• physical properties of the fluid at the operating temperature

• flow characteristics of the liquid.

The internal natural convective heat transfer coefficient can be evaluated by

4. Results and discussion

The values of convective (hew) and evaporative heat transfer (hew) coefficients were calculated, as suggested by Tiwari and Tripathi [ 1 ], for different operating temperature ranges for different sizes and materials of semi-cylindrical condensing covers (Tables 2a-h). The results are given in Figs. 3 to 6 under natural and forced modes of operation.

The variation of the convective and evaporative heat transfer coefficient under natural and forced modes of operation for different operating temperature ranges are indicated as the present model (PM). For a comparison, the results obtained by Dunkle's relation [2] for the convective and evaporative heat transfer coefficients have also been indicated in the same figures as Dunkle model (DM).

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234 R. TripathL G.N. Tiwari / Desalination 166(2004) 231-241 Table 2a

Various measured temperatures and yield under the natural mode for a large aluminium condensing cover for the operating temperature range of 40°C to 80°C

Table 2c

Various measured temperatures and yield under natural mode for small aluminium condensing cover for the operating temperature range of 40°C to 80°C

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

40.0 41.7 43.3 45.4 46.9 48.0 49.5 51.4 53.3 55.3 57.1 59.4 61.1 63.0 64.8 67.3 68.9 71.1 72.8 74.6 76.6

30.0 30.8 31.7 32.6 33.6 34.6 35.9 37.2 38.6 39.7 41.0 42.4 43.7 45.7 47.7 50.2 52.4 54.0 56.0 58.1 60.1

0.0035 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.0115 0.013 0.015 0.017 0.019 0.021 0.023 0.025 0.027 0.029 0.031 0.034 0.038

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

T~ °C 39.0 40.5 42.0 43.5 45.2 46.9 48.6 50.4 52.2 54.0 55.8 57.7 59.6 61.5 63.5 65.5 67.5 69.5 71.4 73.5 75.5

T~g, °C 30.4 31.3 32.3 33.3 34.3 35.4 36.7 38.0 39.4 41.0 42.6 44.4 46.3 48.2 50.1 52.0 53.8 55.8 57.7 59.7 61.7

m ~ , k g 0.0025 0.003 0.0035 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.0145 0.016 0.0175 0.0195 0.0215 0.0235 0.0255 0.0275

Table 2b

Various measured temperatures and yield under forced mode for a large aluminium condensing cover for the operating temperature range of 40°C to 80°C

Table 2d

Various measured temperatures and yield under forced mode for a small aluminium condensing cover for the operating temperature range of 40°C to 80°C

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

T~,*C 39.6 41.4 42.9 44.6 46.8 48.7 50.6 52.6 54.2 56.2 58.2 60.2 62.4 64.3 66.5 67.7 69.5 71.6 73.7 75.7 77.6

T~i, °C 30.6 31.6 32.6 33.6 34.5 35.5 36.8 37.8 38.8 40.2 41.1 43.1 45.0 46.8 48.8 49.6 51.6 53.6 55.3 57.5 59.8

0.003 0.004 0.005 0.006 0.007 0.0085 0.01 0.0115 0.0135 0.0155 0.0175 0.0195 0.0215 0.024 0.0265 0.029 0.0315 0.034 0.037 0.041 0.0465

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Tw,°C 39.9 41.4 43.1 44.8 46.5 48.2 49.9 51.6 53.3 55.0 56.7 58.4 60.2 62.1 64.0 65.9 67.9 69.9 71.9 73.9 76.1

T °C 30.3 3I.1 31.9 32.9 33.9 35.2 36.6 38.0 39.4 40.8 42.5 44.2 45.9 47.7 49.5 51.4 53.4 55.4 57.4 59.4 61.4

>»e»» kg 0.003 0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095 0.0105 0.0115 0.0125 0.0135 0.015 0.0165 0.018 0.0195 0.0215 0.0235 0.026 0.0285 0.031

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R. Tripathi, G.N. Tiwari /Desalination 166(2004)231-241 ²³⁵ Table 2e

Various measured temperatures and yield under natural mode for a large copper condensing cover for the operating temperature range of 40°C to 80°C

Table 2g

Various measured temperatures and yield under natural mode for small a copper condensing cover for the operating temperature range if 40°C to80°C

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Tw,°C 41.0 42.6 44.2 45.7 47.0 48.5 50.5 52.2 53.9 55.7 57.5 59.7 61.5 63.3 65,3 67.6 69.2 71.4 73.2 75.0 76.9

T °C 30.9 31.5 32.2 33.0 33.9 34.9 36.2 37.4 38.7 40.0 41.3 42.7 43.9 45.9 48.2 50.7 52.7 54.2 56.2 58.3 60.5

0.0035 0.0045 0.0055 0.0065 0.0075 0.0085 0.0095 0.011 0.0125 0.014 0.0155 0.0175 0.0195 0.0215 0.0235 0.0255 0.0275 0,0295 0.0315 0.0345 0.04

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

T °C 37.5 38.7 40.0 42.5 44.2 46.1 48.0 50.1 51.9 54.0 56.1 58.1 60.1 62.1 64.2 66.1 68.2 70.0 71.8 73.8 75.8

T °C 28.0 28.7 29.4 30.3 31.4 32.7 34.6 36.5 38.4 40.2 41.9 43.9 46.0 48.0 50.0 52.0 54,0 56.0 58.0 60.0 62.0

mew, kg 0.0025 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.01|

0.0125 0.014 0.0155 0.017 0.0185 0.02 0.022 0.024 0.026 0.028 0.03

Table 2f

Various measured temperatures and yield under forced mode for a large copper condensing cover for the operating temperature range of 40°C to 80°C

Table 2h

Various measured temperatures and yield under forced mode for a small copper condensing cover for the operating temperature range of 40°C to 80°C

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

41.1 42.5 44.0 45.5 47.2 48.9 50.7 52.6 54.6 56.6 58.6 60.5 62.8 64.6 66.0 68.0 69.8 71.9 74.1 76.1 77.9

T °C 30.4 31.3 32.3 33.3 34.3 35.4 36.4 37.5 38.8 40.1 41.4 43.4 45.2 47.2 49.2 50.1 51.9 53.8 55.5 57.7 60.2

ni~, kg 0.004 0.005 0.006 0.007 0.008 0.009 0.0105 0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.0265 0,0295 0.0325 0.0355 0.0385 0.0425 0.0485

S. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Tw,°C 39.8 41.4 43.0 44.7 46.4 48.1 50.0 51.7 53.4 55.2 57.0 58.9 60.7 62.5 64.3 66.2 68.1 70.0 71.9 74.0 75.9

T~s, °C 30.3 31.1 31.9 32.8 33.9 35.1 36.5 37.9 39.3 40.7 42.1 43.8 45.6 47.4 49.2 51.0 53.0 55.0 56.9 59.0 61.0

rhea, kg 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.0115 0.0125 0.014 0.0155 0.017 0.0185 0.02 0.022 0.024 0.026 0.0285 0.031 0.0335

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236 R. Tripathi, G.N. Tiwari /Desalination 166(2004) 231-241

AIB(PM),hc,v AIB-Big Aluminlum condensing cover AIB(DM),hcw /UsSmeU Aluminium condensing cover

PM-Pmsent ~model DM-Dunkle model

A IBp M ) , h AIB(DM),h Als(PM),h~

AJs(DM).h

40 55 60 65

Temperature (°C)

Fig. 3a. Variation of convective and evaporative heat transfer coefficient with temperature in natural mode.

A IB( P M ) , hc w A IB- B i g Aluminium condensing cover

!CJ A IB( D M ) , hc w A Is- S m a l l Aluminium condensing c o v A Is( P M ) , hc w PM-Present model

DM-Dunkle model

45 50 55 60 6J5

Temperature (°C)

70

AIB(DM),hew .

A Is (P M) ,hew ~2 0

Als(DM),he w |

t : 10

75 80 Fig. 3b. Variation of convective and evaporative heat transfer coefficient with temperature in forced mode.

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R. Tripathi, G.N. Tiwari / Desalination 166(2004) 231-241 111

4.5 . p

CD

"a

....O- CUs(PM),hcw CUB-Big Copper condensing co~er B C UB (D M)I I IC W CUg-Small Copper condensing co\er

PM-PP=sent model DM-Dunkle model Cus(DM),h

O

3 . 5 -

60 '615 Temperature (°C)

.110 Q- . _O_ CUB(PM),he w CUB-Big Copper condensing cover

"c 4 5 - ~ CUB(DM),hcw CuB-Small Copper condensing cover

< | " ^ _ C Us( P i ) , hc w PM-Present model c

'o 4 -

Cus(DM),hcw

hcw

DM.Dunkl~ modej

100 o

4'5

4) O

O

&

a>

>

LU>

50 5'5 60 65

Temperature (°C)

;0 75 810

Fig. 4b. Variation of convective and evaporative heat transfer coefficient with temperature in forced mode.

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238 R. Tripathi, G.N. Tiwari / Desalination 166 (2004) 231-241

o

E

I

>

AIB-Big Atuminium condensing cover CUB-Big Copper condensing cover P M ) , h c w model

DM-Dunkle model

40 50 55 60 65

Temperature (°C)

70 75 8010

p

"g 4.5 -

- -e-

AIB-BIg Aluminium condensing cover CUB-Big Copper condensing cover PM-Present model

DM-Dunkle model

40 ^{55 60 65}

Temperature (°C)

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R. Tripathi, G,N. Tiwari /Desalination 166(2004)231-241 239 4.5

p

6

1

o_o o

to 0)

3.5

i i 100

-O-

AIs-Small Aluminium ccndensing cover Cus-Small Copper condensing cov~

PM-Present model DM-Ounkle model

40 45 ...L

50 55 60 65 70

Temperature (%)

4.5

p

o a5

3.5

AIs(PM),hc w AIs-Small Aluminium condensing cmer [] A Is (D M) ,h c w Cus-Small Copper condensing cov~r

4, Cus(PM),hc w PM-Present model Cus(DM),hc w DM-Dunkle model

45 50 55 60 6

Temperature (°C)

70 75 80

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240 R. Tripathi, G.N. Tiwari / Desalination 166 (2004) 231-241 Table 3

Variations (%) in convective heat transfer coefficient for different sizes and materials of condensing covers Conditions

Natural mode Forced mode

Condensing covers Low operating

temperature

High operating temperature

Low operating temperature

High operating temperature Large copper and large aluminium 7.37

Large copper and small copper 12.44 Small copper and small aluminium 0.41 Large aluminium and small aluminium 18.59

0.90 1.59 8.10 8.84

8.45 14.34 1.17 6.66

1.24 9.15 4.91 13.11 Table 4

Variations (%) in evaporative heat transfer coefficient for different sizes and materials of condensing covers Conditions

Natural mode Forced mode

Condensing covers Low operating

temperature

High operating temperature

Low operating temperature

High operating temperature Large copper and large aluminium 1.09

Large copper and small copper 31.19 Small copper and small aluminium 10.23 Large aluminium and small aluminium 20.31

2.22 1.1 9.25 8.06

12.12 18.3 1.05 6.62

2.55 12.24 3.57 13.37

Fig. 3a and b show the variations of convective and evaporative heat transfer coefficients under the natural and forced modes of operation for larger and smaller aluminium condensing covers. The results for the copper condensing cover under similar conditions are depicted in Fig. 4a and b. The effect of aluminium and copper on convective and evaporative heat transfer coefficients for larger and smaller condensing covers is shown in Figs. 5 and 6.

From Figs. 3-6 it is observed that the results obtained from the present model (PM) deviate significantly from the results obtained by Dunkle model (DM). The percentage deviation for convective and evaporative heat transfer coefficients at low and high operating temperatures for

different sizes and materials of condensing covers obtained from Figs. 3-6 are summarized in Tables 3 and 4, respectively.

It is inferred from Table 3 that the convective heat transfer coefficient depends mainly on shape, material, mode of operation and operating temperature, unlike the model for the convective heat transfer coefficient [Eq. 2(b)] presented by Dunkle. The values of the convective heat transfer coefficient obtained by the present model are very close to the values as obtained by the Dunkle model at operating temperatures of 50- 55°C (Figs. 3-6). The values deviate significantly below and above the operating temperature of 50-55°C.

From Table 4 it is inferred that:

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R. Tripathi, G.N. Tiwari / Desalination 166(2004) 231-241 241

• There is 6--18% variation in the evaporative heat transfer coefficient under the forced mode of operation, except for smaller copper and aluminium condensing covers at a low operating temperature range, which is due to fast heat loss from the condensing cover.

• There is about a 20-30% variation in the evaporative heat transfer coefficient under the natural mode of operation due to the effect of size of the condensing covers at a low operating temperature range, as expected.

• There is about a 12-13% variation in the evaporative heat transfer coefficient under the forced mode of operation due to the effect of size of condensing covers at a high operating temperature range, as expected.

• Except for a few cases, the evaporative heat transfer coefficient has minimum variation of 6% due to material and size of the condensing covers for a given operating temperature.

These variations are significant due to more heat loss either due to size and material of condensing covers or due to mode of operation.

5. Symbols

A — Surface area, m2

Aw — Area of water surface, m2

C — Unknown constant in the Nusselt number expression

GF — Grashof number

hew — Convective heat transfer coefficient from water to condensing cover, W/m2oC

hew — Evaporative heat transfer coefficient, W/m2°C

Kv — Thermal conductivity of the humid air,W/m2°C

L — Latent heat of vaporization of water, J/kg

L^v — Characteristic dimension of the condensing cover, m

mew — Distillate output

n — Unknown constant in Nusselt num- ber expression

Pei — Partial saturated vapor pressure at condensing cover temperature, N/m2

Pr — Prandtl number

Pw — Partial saturated vapor pressure at water temperature, N/m2

Q — Rate of heat transfer by convection, W

4ew — Rate of evaporative heat transfer, W/m2

t — Time, s

To; — Inner temperature of condensing cover, °C

rs — Evaporative surface temperature, °C Tw — Water temperature, °C

To — Temperature of the boundary layer away from the evaporating surface,

°C

References

[1] G.N. Tiwari and R. Tripathi, Study of heat and mass transfer in indoor conditions for distillation, Desalination, 154(2003) 161-169.

[2] R.V. Dunkle, Solar water distillation, the roof type still and a multiple effect diffusion still, International Developments in Heat Transfer, ASME, Proc.

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