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Nucleate pool boiling heat transfer coefficient for methanol-salt mixture (LiBr.ZnBr2) solutions: Experimental studies
Solar & Wind Technology Vol. 4, No. 4, pp. 431-441, 1987 Printed in Great Britain.
0741--983X/87 $3.00+.00 Pergamon Journals Ltd.
NUCLEATE POOL BOILING HEAT TRANSFER COEFFICIENT FOR METHANOL-SALT MIXTURE (LiBr. ZnBr2) SOLUTIONS : EXPERIMENTAL STUDIES S. M. BIN GADrn,* R. S. AGARWALt a n d S. C. KAUSHIK:~ * Mechanical Engineering Department, College of Technology, Ma'alla, Aden, P.D.R., Yemen; t Mechanical Engineering Department, I.I.T., Delhi ; :~Centre of Energy Studies, I.I.T. Delhi, New Delhi, India
(Received 15 November 1986; accepted 20 December 1986) Abstract--This communication presents an experimental investigation on nucleate pool boiling heat transfer for methanol-LiBr. ZnBr2 mixtures to be used in an absorption refrigeration system. An experimental rig consisting of an insulated cylinder vessel with a horizontal test section, a condenser, a water chilling unit and a single U-tube manometer was used and measurements on various heat fluxes, temperatures, and system pressures were made for a selected range of salt concentrations in the methanol-LiBr. Zn. Br2 mixture. The heat transfer coefficient for the boiling of pure methanol and methanolLiBr. Zn. Br2 mixture was then obtained and presented in a graphical form and then correlated in an empirical form. It was found that the data on the heat transfer coefficient for pure methanol are in agreement with the data obtained by earlier authors, which supports the validity of experimental results presented here. The addition of LiBr. ZnBr2 to methanol causes a considerable loss in heat transfer capability of the pure methanol.
1. I N T R O D U C T I O N A N D LITERATURE REVIEW The main purpose of this work is to provide experimental pool boiling heat transfer coefficient data for the methanol-LiBr. ZnBr/mixture used for absorption refrigeration systems. The choice of this working fluid took place against the extensive absorption refrigeration system research, which is going on nowadays. Will [1] and Hainsworth [2] were first in suggesting the use of methanol as a working medium for the absorption system, proposing several salts as absorbents, among which LiBr was especially recommended. Aker, Squires and Albright [3] studied the vapour pressure and the viscosity of the mixed system with methanol, ethanol and LiBr, LiCI and ZnBr2. They found among all mixtures, that the methanol-LiBr. ZnBr2 mixture was the most appropriate in view of the strong vapour pressure lowering, along with a relatively low viscosity as compared to other methanol-salt mixtures. Uemura and Hasaba [4, 5, 6] have obtained the physical properties and performance of absorption refrigeration system using this working fluid. The suitability of CH3OH-LiBr. ZnBrz for an absorption system has also been well assessed by a number of investigators (Best [7], Smith [8], Olama [9], Stiemle [10] and Grosman [11]). Concerning the heat transfer studies in nucleate pool boiling for absorption refrigeration systems, several investigators have published some data. Filarkin 431
[12] studied the pool boiling heat transfer coefficient on a horizontal tube to a water-ammonia solution. Minchenko [ 13] also investigated the pool boiling heat transfer coefficient and presented the results of waterLiBr and Water-LiC1 solutions. Since no work has been carried out to find the heat transfer coefficient for the newly proposed mixtures of MethanolLiBr. ZnBr2, experimental studies have been carried out here to obtain data for the heat transfer coefficient for nucleate pool boiling for this mixture. The knowledge of boiling heat transfer over a range of heat flux, the system pressure and the useful range of salt concentration in methanol is of immediate application for the design of a generator of solar operated absorption refrigeration systems both for the single and the double effect absorption cycles. This paper presents an experimental study concerning the heat transfer rates to methanol and methanol-salt (LiBr. ZnBr2) solutions under nucleate pool boiling conditions on a horizontal copper tube of 31.6 mm dia. The tests were conducted for a range of values of heat flux q, pressure (vacuum) P and selected salt concentration X.
2. EXPERIMENTAL SET-UP
The experimental set-up used to measure the data for nucleate pool boiling of methanol and methanol-
432
S.M. B1N GADH! et al.
2
Pressure gouge E:~ Pressure cutout ® Hand valve U ~.n,Ene. rsion thermocquple ~ylinder service valve •~ -
~m
glass
dr~ L~ote vatve
-~-
Thermometer well
7
I
2. 3 4. 5. 6. 7 8. 9 I0.
Test vessel
Main condenser Vapour sampling vessel Liquid sampling vessel Liquid temp. sensor Manometer Measuring jar Temp. control ter Chit let Evaporator
II
12. [3. 14. 15. 16
Expansion valve Heater Compressor Chilling unit's condenser Receiver Water pump
Fig. 1. Schematic of the experimental facility.
salt mixtures for a range of values of heat flux, pressure and salt concentrations is shown in Figs 1 to 4. The test set-up essentially consists of an insulated vessel of 150 mm dia. and 300 mm in length having the horizontal test section, a condenser, a precisely temperature-controlled water chilling unit, a single U-tube manometer for pressure measurement and instruments for measurement of temperature and heat flux. 2.1. Test vessel The test vessel essentially consists of a cylindrical vessel of about 150 mm outside dia. and 300 mm in length, as shown in Fig. 2. It is fitted with sockets and checknuts to hold the horizontal test section along its axis. Inspection windows (38 mrn dia.) were provided diametrically on opposite sides of the vessel to allow the visual observation of the boiling of the test fluid. The test vessel was connected through copper tubes to the condenser and a manometer. The vessel has a provision to withdraw a liquid sample for measurement of concentration of test fluid. A precise platinum resistance temperature (Pt-100 sensor) probe was fitted at the bottom of the test vessel in such a way that
it was well dipped in the pool of test liquid to measure the liquid bulk temperature. The vessel was properly insulated with glass wool followed by a 50-ram-thick cylindrical thermocole layer. Thermocouptes were provided at the inner and outer surfaces of the insulation to estimate the energy loss. 2.2. Test section The test section, as shown in Fig. 3, consisted of 300-mm-long concentric copper tubes of 31.6 mm outside dia. and 4 mm thickness. The effective heat transfer surface length was 200 mm. This provided a total heating surface area of about 0.0199 m 2. The test section surface was turned smooth and rubbed with emery paper of well defined grain size to clean the minute scales and to make the surface smooth. Finally the surface was burnished with a clean dry cotton resulting in mean roughness of 0.3 #m at the start of the experiments. The inner copper tube was press fitted into the outer tube. On the outer surface of the inner tube, grooves were cut axially around the circumference for the passage of the nine iron-constanton thermocouples which were fixed at equal distance and equal circumferential angle. The
433
Heat transfer coefficient for methanol-salt mixtures I 2
3
4
56
7
8
9
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II
/
i 4" /
I I. 2. 3. 4. 5. 6. 7 8. 9.
Gloss wool insulation Sight glass flange Sight glass Teflon 0 ring Check nut Socket Test vessel Line to pressure relief valve and gauge Vopour outlet
//.d///
H I0. II. 12 13. 14. 15. 16. IZ 18.
///
15
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16 17
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18
Line to pressure cutout and manometer Heat transfer test surface Electrical lead Fe-K thermocouple lead Viewing port Liquid return Line Liquid temp sensor port Pf-ICX) sensor Line to liquid sampling vessel
19 20. 21. 22. 23. 24.
Asbestos cement Porcelain core Heating cement Watt therrnocouple Thermocote insulation Thermecouple for radial heat loss estimation
Fig. 2. Details of test vessel.
positions of thermocouples are shown in Fig. 3. The electric heater was made of nicrome wire of 14 gauge, wound over a porcelain tube and was inserted axially into the inner tube of the concentric heating tube. Both sides of the heating element were filled with glass wool and asbestos cement to prevent any heat loss from the ends of the test section. 2.3. Condenser A water-cooled condenser was used to condense the vapour generated from the test vessel. It is kept about 1500 mm above the test vessel to enable the return of condensate easily by gravity to the test vessel. It is basically a shell and tube type condenser with water flowing inside the tubes, while vapour condenses in the shell. 2.4. Water chilling unit This unit plays a very vital function in controlling the system pressure. It consists of a vapour compression refrigeration system, water chilling tank and a precision temperature regulator. When the temperature of the water inside the chilling water tank goes below the pre-set value, the precision temperature regulator unit receives a signal from the temperature sensing device and puts the heater 'ON'.
When the temperature increases above the set temperature, the regulating unit puts the heater ' O F F ' . An electric stirrer was used to keep the temperature uniform throughout the water tank. Two water pumps were connected to the chilling water tank with a bypass arrangement. Only one pump was used at a time to circulate the water in the condenser, while the other pump was on standby. 2.5. Instrumentation Iron--constantan thermocouples (30 gauge) calibrated over a wide range of temperatures were employed to measure the copper tube (test section) temperatures at four positions. The high precision platinum resistance thermometer was used to measure the bulk liquid temperature. The e.m.f, of the abovementioned thermocouples was fed to the digital temperature indicators of accuracy _ 0.1°C, through selector switches. A single phase, 50 C s - J A.C. supply, stabilized by an automatic stabilizer, was used. Power input to the electric heater in the test section was measured with the help of a Cambridge Watt-meter. The digital ammeter and the digital voltmeter of accuracy + 0.1 A and __+0.1 V, respectively, were also used to cross check the readings measured by the Watt-meter. The
434
S. M. BIN GADH1et al. D
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Thermocouple locations on the the test surface
Check nut Socket Teflon 0 ring Fe-K thermocoupte Leads Test surface outer tube 2-8 Fe-K thermocouple for walt temp measurement I end 9 for axial conduction estimation
G H I J. K L M
inner
tube of
Test surface inner tube Heating element Porcelain core Electrical. leads Glass wool Asbestos cement Thermocoupte groove
Fig. 3. Details of the heat transfer surface.
power supply to the test section heater was varied by a dimmesstat. A mercury single U-tube manometer was used to measure the system pressure. 3. EXPERIMENTAL PROCEDURE
A number of steps were taken to clean the apparatus before starting the series of experimental runs. The compressed carbon dioxide gas was admitted into the test vessel to remove all the traces of the previous fluid from it. The test surface was also cleaned with distilled water and acetone. Both the test surface and the test vessel were rinsed with the test fluid, methanol. After cleaning and rinsing, the experimental rig was tested at a pressure of about 15 bar to check against leakage in the set-up. The set-up was left at this pressure for 24 h. Similarly the set-up was tested under vacuum. It was ensured that there was no leakage in the system. Finally, electrical insulation of the test section heater was tested. 3.1. Chargin # process The system was evacuated with the help of a precision vacuum pump before charging the test fluid in
the system. First, experiments were conducted on pure methanol, in this case pure methanol was charged into the test vessel up to a certain level above the test section, making use of the atmospheric pressure to drive methanol into the evacuated test vessel. For the mixtures experiment, a mixture of an appropriate concentration (highest salt concentration 54%) was first prepared in the charging cylinder by measuring the mass of individual components on a precision balance. The mixture was then transferred to the test vessel purely by gravity and slight heating. The mixtures and lower concentration were prepared by diluting the concentrated solutions (highest concentration 54% salt) already charged into the system, by adding the requiste amount of methanol to give the required concentration. 3.2. Data recordin9 procedure The boiling heat transfer for pure methanol and methanol-salt mixture were measured by varying the pressure from a lower (270 mbar) to a higher value (530 mbar) and the heat flux from 8432 W/m 2to 17750 W/m 2. The experiment was started by switching on the test section heater and increasing the voltage
Heat transfer coefficient for methanol-salt mixtures
435
Fig. 4. Photographic view of experimental set-up for pool boiling data measurement.
gradually to the maximum value. The liquid in the test vesssel was kept in the boiling condition for several hours at the saturation condition. The liquid and wall thermocouple readings were recorded only when the steady state was achieved. These steps were repeated several times to attain the stability of the test section. Only after obtaining good reproducibility of observation for certain conditions of heat flux and pressure, was the test section used for actual runs, assuming that the test section surface was stabilized. During a particular experimental run the required system pressure was first obtained by circulating water from a water chilling unit in the condenser. The system pressure was maintained by controlling the water temperature with the help of an automatic temperature regulator and with the refrigeration unit. After attaining the required pressure the test section heater was switched on and the voltage was gradually increased to the required value with the help of an auto-transformer. At steady state conditions, the readings of the ammeter, volt-meter and watt-meter, the liquid and the heating surface temperatures and the system pressure were recorded. The system pressure was varied to the next highest value by increasing the temperature of the condenser
water, while the heat flux was kept the same. It took nearly 2-3 h to attain the next steady state condition. The uniformity of concentration was maintained constant as far as practicable during the period of experimentation. At the steady state condition, a liquid sample was drawn from the test vessel into the sampling unit, and its saturation pressure was tested by measuring the vapour and pressure data. At each steady state condition, it was confirmed through liquid sampling test that the concentration was maintained in the test vessel, within + 1%.
3.3. Reproducibility and consistency of experimental
data The experimental data were checked for their reproducibility by conducting the experiments at different times under the same operating conditions. Further, the reproducibility was ascertained by conducting the experiments on pure methanol, and comparing the data obtained with the available data of Cryder et aL [14], Borishanskii [15] and Sharma et al. [16] (Fig. 5). It was found that the data were within the moderate experimental error limits. The range of operating parameters used in this investigation is given in Table 1.
436
S. M. BIN GADHI et al. 3
Table 2. Experimental data for boiling heat transfer from a horizontal tube to the pool of pure methanol Run no.
• J2"/'0mbarJSharma,Gul:¢~~ Var~ney(~ b × f~
! ,o 8 I
P (mbar)
I
6
I
I I
[
IO
2
7 8 9
I
3
Heot fLUXq X10-3 , W/m2 Fig. 5. Comparison of heat transfer coefficient during pool boiling methanol by different investigators. zO I
"J
Pr~sure,mb x 525
~q~
x
ATw(°C) ~ ( W m -2 K)
1 2 3 4
280 328 450 525
q = 9175W/m 2 35.0 10.08 36.9 9.01 43.8 9.24 47.5 10.19
910 1018 993 900
5 6 7 8
270 350 447 525
q = l1481W/m 2 35.0 11.82 37.7 11.51 43.8 10.49 47.9 10.07
971 987 1094 1140
9 10 II 12
260 336 448 525
q = 14026W/m ~ 35.0 12.49 38.1 12.0I 44.6 12.36 48.6 12.30
1123 1167 1135 1t40
13 14 15 16
283 315 480 525
q = 16847W/m ~ 35.0 14.55 38.2 14.20 44.3 1[.75 47.3 10.04
1158 1186 1434 1678
17 18 19 20
265 328 456 525
q = 18656W/m: 35.0 12.07 38.1 11.80 44.5 11.90 47.6 10.65
1546 1581 1568 1752
6
5
TL(°C)
9
z
5 5
I
I
I
6
7
8
1
I
I
9 IO" ZO Heat ftux q x I0 3,W/rn z
3O
while Tables 2-5 tabulate the experimental data o f the present work. The average heat transfer coefficient, was calculated from the values o f heat flux, q and the average values o f wall superheat, AT~ by using the following expression
Fig. 6. Heat transfer to boiling pure methanol at different pressures.
q a =
_ - :. AT~
(1)
4. RESULTS AND DISCUSSION
4.1. Effect of heat flux on boilin 9 heat transfer
Table 1 gives the range o f operating p a r a m e t e r s o f pure m e t h a n o l and m e t h a n o l - L i B r . ZnBr2 mixtures,
Figures 6 to 9 show the effect o f heat flux, q, on average heat transfer coefficient, c~, on a log-log plot
coefficient
Table 1. Values of operating parameters Boiling fluid
Heat flux (W m 2)
Pressure (mbar)
Pure methanol
9175, 11481, 14026, 16847, 18656
270, 330,460, 525
Methanol-LiBr. ZnBr2
7700, 9850, 12389, 14637,
270, 330, 460, 525
16754
Salt concentration (Wt%)
40, 48, 54
437
Heat transfer coefficient for methanol-salt mixtures Table 3. Experimental data for boiling heat transfer from a horizontal tube to the pool ofmethanol-LiBr. ZnBr2 mixture at 40% salt concentration
Runno.
P(mbar)
TL(°C) AT~(°C) a(Wm-2K)
Table 4. Experimental data for boiling heat transfer from a horizontal tube to the pool ofmethanol-LiBr. ZnBr2 mixture at 48% salt concentration Runno.
P(mbar)
TL(°C) AT.(°C) a ( W m - 2 K )
1 2 3 4
272 337 446 525
q = 8042W/m 2 44.6 24.09 48.0 20.45 55.0 19.70 61.0 16,95
334 393 408 474
1 2 3 4
265 325 464 538
q = 7626W/m 2 51.0 24.73 54.1 22.55 61.0 22.13 64.2 18.27
308 338 345 417
5 6 7 8
280 336 443 540
q = lO182W/m 2 44.7 23.30 49.2 23.68 55.0 21.55 60.5 21.25
437 432 472 479
5 6 7 8
265 325 479 535
q = 9847W/m 2 50.9 24.98 54.0 23.08 61.2 22.75 64.0 22.15
394 427 433 445
9 10 11 12
275 332 444 525
q = 12606W]m 2 44.5 26.35 48.8 30.05 55.9 30.57 60.0 21.86
479 420 412 577
9 10 11 12
265 333 462 525
q = 12192W/m 2 51.0 25.71 54.2 24.21 61.0 23.16 63.8 22.68
474 504 526 538
13 14 15 16
246 332 444 522
q = 14505W/m 2 44.7 30.61 47.7 28.25 57.0 34.88 60.0 22.83
474 513 415 635
13 14 15 16
266 325 476 536
q = 14830W/m 2 51.0 26.43 54.0 24.81 61.3 24.66 64.0 24.66
561 598 601 601
17 18 19 20
279 356 451 531
q = 16967W/m 2 45.2 26.41 50.3 25.54 56.1 24.01 59.2 22.08
642 664 707 768
17 18 19 20
260 335 462 520
q = 16567W/m 2 50.8 26.72 54.8 25.49 60.7 24.44 63.7 23.29
620 650 678 711
with pressure as a parameter. F r o m the figures, the following features can be seen : (a) The values of heat transfer coefficient changes with the heat flux linearly at a fixed value of pressure. (b) The value o f the heat transfer coefficient increases with the rise in pressure. On both cases it can be reasoned out as the flux and or the pressure increases, the number of bubbles per unit area of heating surface increases, thereby the turbulence due to bubble dynamics also increases. This is in fact, responsible for increasing the value of the heat transfer coefficient with heat flux and pressure. It may be added that the heat transfer coefficient is also affected by the heating surface characteristics. 4.2. Heat transfer for the methanol-salt mixture As anticipated, the heat transfer from the heating surface to the boiling methanol-salt mixtures would depend upon the parameters, namely, nature o f the salt, its concentration, heat flux, pressure and heating surface characteristics. 4.2.1. The effect of salts and their concentration on the boiling heat transfer coefficient. The m e t h a n o l salt mixtures exhibit boiling point increases depending
upon the nature of the salts, their concentration and pressure. This in fact results in an increased boiling point of the mixtures over the boiling point of pure methanol at a given pressure. This in turn, is likely to make the heat transfer coefficient of the mixture lower than that of pure methanol on a given heating surface for a given heat flux and pressure. Keeping the above in view, Figs 7-9 were drawn for ~ vs heat flux, q at different pressures for the boiling of m e t h a n o l - L i B r . ZnBr2 mixtures (salt concentration 40, 48 and 54%). The following characteristic features emerge from the plots : (a) F o r the boiling of the mixtures investigated, the value o f ~ decreases with the increase in salt concentration for a given pressure. (b) F o r a given concentration, with the fall in pressure on the mixture, the values o f ~ decrease. (c) F o r a given concentration and pressure the values of ~ increase with the increase in heat flux, q. 5. EMPIRICAL CORRELATIONS
Empirical correlations have been developed for heat transfer coefficients in terms of significant parameters,
438
S. M. BIN GADH1 et aL I0
Table 5. Experimental data for boiling heat transfer from a horizontal tube to the pool of m e t h a n o l - L i B r . ZnBL, mixture at 54% salt concentrations R u n no.
P (mbar)
TI
(:C)
9
, x 5~
!
2u46o
|
/ / J 3 4
ATw ('C) ~(W m 2 K)
bo 1 2 3 4
290 342 450 527
q = 7434 W/rn: 61.2 21.86 65.0 20.10 72.0 20.90 73.8 19.06
5 6 7 8
290 340 450 536
q = 9523W/m 2 61.2 22,3 65.0 19.8 72.0 17.1 74.0 17.2
9 10 11 12
283 342 450 525
q = 12368W/m: 60.8 22.80 65.0 24.83 72.0 24.30 74.7 24.71
13 14 15 16
286 342 453 526
17 18 19 20
288 336 453 526
x
340 370 356 390 427 481 497 495
a/
{o I 2
q
q
=
=
542 498 509 501
14576W/m ~ 61.1 27.0 65.0 26.18 72.0 26.30 75.0 26.16
540 557 554 557
16727W/m 2 61.0 27.34 64.8 24.39 72.0 24.66 75.0 25.73
612 686 678 650
I
525
x
/
/
/
6
7'
8
9 I0
20
50
Fig. 8. Heat transfer to boiling methanol LiBr. ZnBr, mixture at 48% salt concentration and different pressures.
Y
I0
Pressure, mb
,~ 6 -
-
|
~,-/
-
I
I
.
/
2= ~ 3 • 25
~9
5
Hoot flux q x 10-3,W/m 2
Pressure, mb I0
:¢
/
z
/
5
6
7
8
9
10
20
30
Heot ftux q x l O -3 , W / m 2 x 6
Fig. 9. Heat transfer to boiling m e t h a n o l - L i B r . ZnBr2 mixture at 54% salt concentration and different pressures.
7
4
I 2
5
I
I
I
I
6
5'
8
9 I0
I
I 20
30
T h e v a l u e s o f c o n s t a n t C a n d e x p o n e n t s n, a n d n2 are given in T a b l e 6, f o r p u r e m e t h a n o l a n d methanol--salt m i x t u r e s . Similarly, t h e h e a t t r a n s f e r coefficients, cL f o r m e t h a n o l - L i B r . Z n B r 2 m i x t u r e s are c o r r e l a t e d by t h e f o l l o w i n g e m p i r i c a l c o r r e l a t i o n in t e r m s o f salt c o n c e n t r a t i o n , X a n d h e a t flux q.
He(:R flux q x l O - 3 , W / m z
Fig. 7. Heat transfer to boiling methanol LiBr. ZnBr2 mixture at 40% salt concentration and different pressures.
viz p r e s s u r e a n d h e a t flux f o r p u r e M e t h a n o l as well as m e t h a n o l - s a l t m i x t u r e s . = Cp",q"~.
(2)
(3)
~2 = C ~ X " ~ q "4.
T h e v a l u e s o f c o n s t a n t C, a n d e x p o n e n t s n3 a n d n 4 are given below : C , = 0.4976,
n3 = - 0 . 0 3 8 3 9 ,
n4 = 0.7337.
T h e R M S e r r o r is a b o u t 8 % . A n e r r o r a n a l y s i s h a s also b e e n c a r r i e d o u t for all
439
Heat transfer coefficient for methanol-salt mixtures Table 6. Values of constants for finding out heat transfer coefficient in eqn 2 Solution salt concentration, Wt%
C
nt
n2
RMS error %
Pure methanol 40 48 54
0.488 0.250 0.0646 0.510
0.192 0.277 0.195 -0.00113
0.700 0.632 0.830 0.735
8.6 13.0 3.8 5.7
the experimental data and it has been observed that the order o f magnitude o f error is about _ 6%. The detailed error analysis calculation is given in Appendix A.2. 6. CONCLUSIONS Based on the results obtained from this investigation the following conclusions may be drawn : 1. The data for the heat transfer coefficient for pure methanol obtained from a horizontal tube are in agreement with the data obtained by different authors. This indicates reliability in the data obtained from the present work. 2. The addition of LiBr. ZnBr2 salt into methanol causes a considerable loss in boiling heat transfer capability of methanol. The magnitude of this loss depends upon the salt concentration. 3. The boiling heat transfer coefficient for the metha n o l - L i B r . Z n B r 2 mixture increases with the increase o f heat flux and with the increase in pressure at a fixed level o f salt concentration. 4. The heat transfer coefficient for the boiling of m e t h a n o l - L i B r . Z n B r 2 mixture can also be obtained by using the empirical correlation (~ = ClXtl3qn4
8. I. E. Smith, lnt. Advanced Course on Heat Pump Fundamentals, NATO Advanced Study Institute Programme. Espinho, Portugal (1980). 9. M. A. Olama, Evaluation of some methanol-salt solutions for absorption refrigeration, Ph.D. thesis, King's College, London (1980). 10. F. Stiemle and M. Renz, Absorptions-W/irmepumppenTheorie und Praxis. VDI Berichte 427, 37 (1981). 11. E.R. Grosman, Methanol as a working medium in sorption type thermal converters. LLR. Congress of Refrigeration, Paris 9, 359 (1983). 12. V. N. Filarkin, Boiling heat transfer to water-ammonia mixtures. Problems of Heat Transfer and Hydraulics of two-Phase Media (a symposium edited in Russian and translated by O. M. Blunn). Pergamon Press (1969). 13. F. P. Minchenko and E. V. Firsova, Heat transfer to water and water-lithium salt solutions in nucleate pool boiling. Problems of Heat Transfer and Hydraulics of Two-Phase Media (a symposium edited in Russian by S. S. Kutatetedze and translated by O. M. Blunn). Pergamon Press (1969). 14. D. S. Cryder and A. C. Finalborgo, Heat transmission from metal surface to boiling liquids: Effect of temperature of the liquid on the liquid film coefficient. Trans. Am. Inst. Chem. Engrs 33, 346 (1937). 15. V. M. Borishanskii, Problems of Heat Transfer and Hydraulics of Two-Phase Media, S. S. Kutateladze, Ed. Pergamon Press, Oxford (1969). 16. P. R. Sharma, P. Kumar, S. C. Gupta and B. S. Varshney, Nucleate pool boiling of liquids on horizontal cylinders at subatmospheric pressure. 4th National Heat and Mass Transfer Conference (1981).
which gives ~ at a given salt concentration, x and heat flux, q, with an R M S error of 8%. Acknowledgements--The authors gratefully acknowledge the help and cooperation of Mr S. Dorairaj during the experimental observations and fruitful discussions.
REFERENCES
1. W. Will, Z. ges. Kiilteind. 47, 65 (1940). 2. W. R. Hainsworth, Refrigng Engng 48, 97, 201 (1944). 3. J. E. Aker, R. G. Squires and L. F. Albright, A S H R A E Trans. 71, 14 (1965). 4. T. Uemura and S. Hasaba, Rie-to 43, 784 (1968). 5. T. Uemura and S. Hasaba, Rie-to 44, 502 (1969). 6. T. Uemura, Rie-to 51, 590, 1027 (1976). 7. R. Best, Proc. 1st Int. Conf. on Solar Building Technique 2, 54, 436. R.I.B.A., London (1977).
APPENDIX A.1. SAMPLE CALCULATIONS FOR COMPUTATION OF HEAT TRANSFER COEFFICIENT The heat transfer coefficient was calculated as the quotient of heat flux to the temperature difference between the outer surface temperature of the test section and the bulk liquid temperature. General data used for heat transfer coefficient calculation : Outside dia. of heating surface, do = 0.03165 m. Inside dia. of heating surface, ~ = 0.02505 m. Length of heating surface, L = 0.200 m. W Thermal conductivity of heating surface, 2 = 383 m-I(" (copper material)
440
S. M. BIN GADH! et al.
A. 1.1. Heating surface area.
corrected surface temperature of the heating test section tube.
Area of heating surface, A = nd,,L = 3.14 × 0.03165 × 0.20 = 0.01989428 m ~'. From Table 2 for boiling of pure methanol input data is selected here to demonstrate the calculation procedure. Data corresponding to run number 1 l are reproduced below :
AT,,, = Tw~- ire = 56.85--44.6 = 12.2Y~C; AT\,, = T ~ - T ~ . = 59.65-44.6 = 15.0YC: AT,,~ = T,,~
Voltage, V = 191V
AT,~ = T , . - T ~ = 5 2 . 5 5 - 4 4 . 6 = 7.95'C.
Current, l = 1.62A
_
Heatflux, q
T~ = 57.0 T2 = 59.8 T 3 = 58.9 T4 = 52.7 T~ = 44.6.
d,
6T~=--ln-, 22w c/~
-
(A. 1.2)
A.I.5. Heat loss to surroundings. There is always some heat loss from the test vessel to the surroundings. The heat loss can be classified into two types. (i) Radial heat loss through wall insulation. (ii) Axial heat loss, Radial Heat: The radial heat loss can be calculated by using the following expression [16]: QR = H L R = 2n2iL
d~ = 0.02505 m. Substituting the values of q, du, 2w and d~ in eqn (A. 1.1), the 6T~ can be obtained 15553.4 x 0.03165 0.03165 2x383 ln0~02~0~ = 0.15'C.
Therefore, the corrected surface temperatures of the test section are calculated using the following equation
rw~--6T~
where subscript r denotes the recorded surface temperature. Hence
T~,, = T~,,-~T~ = 57.0-0.15 = 56.85'C; T,~ = T,r~-bTw = 59.8-0.15 = 59.6Y'C;
where, 2~ represents the thermal conductivity of the test vessel's insulation 2i = 0.029 W/mK. L represents the test vessel's insulation length = 0.500 m; Do represents the test vessel's insulation outer diameter: Do = 0.33 m ; D~ represents the test vessel's inner diameter : D~ = 0.18 m ; T, represents the test vessel's inner surface temperature: T~ = 48. I'~C : To represents the vessel's insulation outer surface temperature : To = 24.1°C. Substituting the values of 2~, L, Do, D~, T, and 7',, from (A.1.5) in eqn 3, we get QR=HLR=
2 x 3.14 x 0 029 x 0 500 " " × (48.1-24.1)=3.6l W. 1 /0.33~
Axial heat loss : The axial heat loss can be calculated using the following expression [16]: }'c7~
2
2
A.1.4. Calculation of average wall superheat. The values of local wall superheat at the circumferential position of the heating surface are calculated by subtracting the values of liquid bulk temperature from the corresponding values of
'
'
QA = HLA = ~ (do -d~ ) [(Tw: T~,)/I, + (Tw~-- 7w~)//2l
T,,~ = T~3--fTw = 58.9~0.15 = 58.75:C;
T~, = T,,.,.--fTw = 52.7-0.15 = 52.55 C.
(A.I.3)
Di
(A.I.I)
where, d~ represents the outer diameter of the inner copper tube
=
4
= 12.35 'C.
QM _ 309.42 _ 15553.4W/m2 A 0.01989428
T,,
-
12.25+ 12.05+ 14.15+7.95
A.I.3. Calculation of corrected surface temperature, Tw. The corrected temperatures of the heating surface were calculated by subtracting the temperatures drop across the thickness of the heating tube surface from the recorded values of surface temperatures. The temperature drop across the wall thickness of heating surface is obtained by using the following equation [161:
fir~ =
~
=
191 x 1.62 = 309.42W.
qdo
-
4
A.1.2. Calculation of heat flux, q. Power input to heating surface : QM - V x l =
ATw,+ATw,+AT,,+ATw,
AT,,.=
= 310W
Temperature, C :
44.6 = 14.15 (':
The values of local wall superheat are averaged linearly by means of the following equation to get the value of the average wall superheat :
Pressure, P = 448 mb
Watt, W
T~ = 58.75
(A.l.4) where )~¢ represents the copper tube thermal conductivity : ).~ = 383 W / m K where do and di are defined in eqn A. 1.1. T,~,, T,,:, T~ and T~., are the temperatures recorded by the
441
Heat transfer coefficient for methanol-salt mixtures thermocouples, nos. 1, 2, 3, and 4, respectively as shown in Fig. 3. lj represents the distance between the thermocouples 1 and 2; l~ = 0.098 m. 12 represents the distance between the thermocouples 8 and 9; 12 = 0.09 m. Substituting the values of 2c, do, a~, Two, T,~, Tw¢ Twv l~ and 12 in eqn (A. 1.4), we get HLA
heater, wall and liquid temperatures. In fact the instruments used for measuring these quantities each had their respective accuracies. Consequently, an error results in the calculation of the heat transfer coefficient. In order to find out the size of the error, an error analysis for the experimental data of this investigation was carded out. A typical calculation of error analysis is given below. The experimental error is the absolute value of the maximum expected deviation from the reported experimental results and is given by :
383 x 3.14 [(0 03165) 2 - (0.02505) 2] 4 x
F. /a~
(A.2.1)
[(57 - 4 8 . I)/0.098 + (52.7-48.1)/0.09] = 25.86 W.
A. 1.6. Computation of net heat supplied to the test fluid. The net heat load QN supplied to the test fluid is computed by subtracting the axial heat loss and radial heat loss from the power heat input to the test section. Hence, QN = QM - - (HER + HLA) = QM - (QR + QA) QN = [309.42- (3.61 + 25.86)] = 279.95 W.
(A.I.S)
A. 1.7. Calculation of the average heat transfer coefficient, ~. The value of the average heat transfer coefficient is calculated by :
QNIA = ~
k~7 °~
e~ = L,~/~.e=,j j
279.95 12.385 x 0.01989428
1138.2W/m2K. (A. 1.6)
A.2. ERROR ANALYSIS
The present investigation involved the measurement of quantities like heating surface area, electric power to the
where E~ represents the error in the measurement of the heat transfer coefficient and z~ represents any of the n variables affecting this coefficient, since QN 07 = A(Tw -- Tr)"
(A.2.2)
Thus the overall uncertainty in the average heat transfer coefficient can be obtained by partial differentiation of eqn A.2.2 which becomes the following :
Pl
EQs ~2 f
+(
Qs" EA
e,.-,, y
A~)#
(
'~2
+ k ~ }
ylO,
1 " (A.2.3)
A typical calculation of error analysis of run number 11 in Table 2 was carded out using the above method with the help of a computer. An average error of the order of 6% was found for the set of parameters taken in this paper.
0741--983X/87 $3.00+.00 Pergamon Journals Ltd.
NUCLEATE POOL BOILING HEAT TRANSFER COEFFICIENT FOR METHANOL-SALT MIXTURE (LiBr. ZnBr2) SOLUTIONS : EXPERIMENTAL STUDIES S. M. BIN GADrn,* R. S. AGARWALt a n d S. C. KAUSHIK:~ * Mechanical Engineering Department, College of Technology, Ma'alla, Aden, P.D.R., Yemen; t Mechanical Engineering Department, I.I.T., Delhi ; :~Centre of Energy Studies, I.I.T. Delhi, New Delhi, India
(Received 15 November 1986; accepted 20 December 1986) Abstract--This communication presents an experimental investigation on nucleate pool boiling heat transfer for methanol-LiBr. ZnBr2 mixtures to be used in an absorption refrigeration system. An experimental rig consisting of an insulated cylinder vessel with a horizontal test section, a condenser, a water chilling unit and a single U-tube manometer was used and measurements on various heat fluxes, temperatures, and system pressures were made for a selected range of salt concentrations in the methanol-LiBr. Zn. Br2 mixture. The heat transfer coefficient for the boiling of pure methanol and methanolLiBr. Zn. Br2 mixture was then obtained and presented in a graphical form and then correlated in an empirical form. It was found that the data on the heat transfer coefficient for pure methanol are in agreement with the data obtained by earlier authors, which supports the validity of experimental results presented here. The addition of LiBr. ZnBr2 to methanol causes a considerable loss in heat transfer capability of the pure methanol.
1. I N T R O D U C T I O N A N D LITERATURE REVIEW The main purpose of this work is to provide experimental pool boiling heat transfer coefficient data for the methanol-LiBr. ZnBr/mixture used for absorption refrigeration systems. The choice of this working fluid took place against the extensive absorption refrigeration system research, which is going on nowadays. Will [1] and Hainsworth [2] were first in suggesting the use of methanol as a working medium for the absorption system, proposing several salts as absorbents, among which LiBr was especially recommended. Aker, Squires and Albright [3] studied the vapour pressure and the viscosity of the mixed system with methanol, ethanol and LiBr, LiCI and ZnBr2. They found among all mixtures, that the methanol-LiBr. ZnBr2 mixture was the most appropriate in view of the strong vapour pressure lowering, along with a relatively low viscosity as compared to other methanol-salt mixtures. Uemura and Hasaba [4, 5, 6] have obtained the physical properties and performance of absorption refrigeration system using this working fluid. The suitability of CH3OH-LiBr. ZnBrz for an absorption system has also been well assessed by a number of investigators (Best [7], Smith [8], Olama [9], Stiemle [10] and Grosman [11]). Concerning the heat transfer studies in nucleate pool boiling for absorption refrigeration systems, several investigators have published some data. Filarkin 431
[12] studied the pool boiling heat transfer coefficient on a horizontal tube to a water-ammonia solution. Minchenko [ 13] also investigated the pool boiling heat transfer coefficient and presented the results of waterLiBr and Water-LiC1 solutions. Since no work has been carried out to find the heat transfer coefficient for the newly proposed mixtures of MethanolLiBr. ZnBr2, experimental studies have been carried out here to obtain data for the heat transfer coefficient for nucleate pool boiling for this mixture. The knowledge of boiling heat transfer over a range of heat flux, the system pressure and the useful range of salt concentration in methanol is of immediate application for the design of a generator of solar operated absorption refrigeration systems both for the single and the double effect absorption cycles. This paper presents an experimental study concerning the heat transfer rates to methanol and methanol-salt (LiBr. ZnBr2) solutions under nucleate pool boiling conditions on a horizontal copper tube of 31.6 mm dia. The tests were conducted for a range of values of heat flux q, pressure (vacuum) P and selected salt concentration X.
2. EXPERIMENTAL SET-UP
The experimental set-up used to measure the data for nucleate pool boiling of methanol and methanol-
432
S.M. B1N GADH! et al.
2
Pressure gouge E:~ Pressure cutout ® Hand valve U ~.n,Ene. rsion thermocquple ~ylinder service valve •~ -
~m
glass
dr~ L~ote vatve
-~-
Thermometer well
7
I
2. 3 4. 5. 6. 7 8. 9 I0.
Test vessel
Main condenser Vapour sampling vessel Liquid sampling vessel Liquid temp. sensor Manometer Measuring jar Temp. control ter Chit let Evaporator
II
12. [3. 14. 15. 16
Expansion valve Heater Compressor Chilling unit's condenser Receiver Water pump
Fig. 1. Schematic of the experimental facility.
salt mixtures for a range of values of heat flux, pressure and salt concentrations is shown in Figs 1 to 4. The test set-up essentially consists of an insulated vessel of 150 mm dia. and 300 mm in length having the horizontal test section, a condenser, a precisely temperature-controlled water chilling unit, a single U-tube manometer for pressure measurement and instruments for measurement of temperature and heat flux. 2.1. Test vessel The test vessel essentially consists of a cylindrical vessel of about 150 mm outside dia. and 300 mm in length, as shown in Fig. 2. It is fitted with sockets and checknuts to hold the horizontal test section along its axis. Inspection windows (38 mrn dia.) were provided diametrically on opposite sides of the vessel to allow the visual observation of the boiling of the test fluid. The test vessel was connected through copper tubes to the condenser and a manometer. The vessel has a provision to withdraw a liquid sample for measurement of concentration of test fluid. A precise platinum resistance temperature (Pt-100 sensor) probe was fitted at the bottom of the test vessel in such a way that
it was well dipped in the pool of test liquid to measure the liquid bulk temperature. The vessel was properly insulated with glass wool followed by a 50-ram-thick cylindrical thermocole layer. Thermocouptes were provided at the inner and outer surfaces of the insulation to estimate the energy loss. 2.2. Test section The test section, as shown in Fig. 3, consisted of 300-mm-long concentric copper tubes of 31.6 mm outside dia. and 4 mm thickness. The effective heat transfer surface length was 200 mm. This provided a total heating surface area of about 0.0199 m 2. The test section surface was turned smooth and rubbed with emery paper of well defined grain size to clean the minute scales and to make the surface smooth. Finally the surface was burnished with a clean dry cotton resulting in mean roughness of 0.3 #m at the start of the experiments. The inner copper tube was press fitted into the outer tube. On the outer surface of the inner tube, grooves were cut axially around the circumference for the passage of the nine iron-constanton thermocouples which were fixed at equal distance and equal circumferential angle. The
433
Heat transfer coefficient for methanol-salt mixtures I 2
3
4
56
7
8
9
I0 2:)4
II
/
i 4" /
I I. 2. 3. 4. 5. 6. 7 8. 9.
Gloss wool insulation Sight glass flange Sight glass Teflon 0 ring Check nut Socket Test vessel Line to pressure relief valve and gauge Vopour outlet
//.d///
H I0. II. 12 13. 14. 15. 16. IZ 18.
///
15
/!!'/
16 17
/ /
! /
18
Line to pressure cutout and manometer Heat transfer test surface Electrical lead Fe-K thermocouple lead Viewing port Liquid return Line Liquid temp sensor port Pf-ICX) sensor Line to liquid sampling vessel
19 20. 21. 22. 23. 24.
Asbestos cement Porcelain core Heating cement Watt therrnocouple Thermocote insulation Thermecouple for radial heat loss estimation
Fig. 2. Details of test vessel.
positions of thermocouples are shown in Fig. 3. The electric heater was made of nicrome wire of 14 gauge, wound over a porcelain tube and was inserted axially into the inner tube of the concentric heating tube. Both sides of the heating element were filled with glass wool and asbestos cement to prevent any heat loss from the ends of the test section. 2.3. Condenser A water-cooled condenser was used to condense the vapour generated from the test vessel. It is kept about 1500 mm above the test vessel to enable the return of condensate easily by gravity to the test vessel. It is basically a shell and tube type condenser with water flowing inside the tubes, while vapour condenses in the shell. 2.4. Water chilling unit This unit plays a very vital function in controlling the system pressure. It consists of a vapour compression refrigeration system, water chilling tank and a precision temperature regulator. When the temperature of the water inside the chilling water tank goes below the pre-set value, the precision temperature regulator unit receives a signal from the temperature sensing device and puts the heater 'ON'.
When the temperature increases above the set temperature, the regulating unit puts the heater ' O F F ' . An electric stirrer was used to keep the temperature uniform throughout the water tank. Two water pumps were connected to the chilling water tank with a bypass arrangement. Only one pump was used at a time to circulate the water in the condenser, while the other pump was on standby. 2.5. Instrumentation Iron--constantan thermocouples (30 gauge) calibrated over a wide range of temperatures were employed to measure the copper tube (test section) temperatures at four positions. The high precision platinum resistance thermometer was used to measure the bulk liquid temperature. The e.m.f, of the abovementioned thermocouples was fed to the digital temperature indicators of accuracy _ 0.1°C, through selector switches. A single phase, 50 C s - J A.C. supply, stabilized by an automatic stabilizer, was used. Power input to the electric heater in the test section was measured with the help of a Cambridge Watt-meter. The digital ammeter and the digital voltmeter of accuracy + 0.1 A and __+0.1 V, respectively, were also used to cross check the readings measured by the Watt-meter. The
434
S. M. BIN GADH1et al. D
A
B
DE
F G
H
[
M
K
L
J
G
H
E
M
F
,//
I Sec at x-x'
A 8 C D E E
9
Thermocouple locations on the the test surface
Check nut Socket Teflon 0 ring Fe-K thermocoupte Leads Test surface outer tube 2-8 Fe-K thermocouple for walt temp measurement I end 9 for axial conduction estimation
G H I J. K L M
inner
tube of
Test surface inner tube Heating element Porcelain core Electrical. leads Glass wool Asbestos cement Thermocoupte groove
Fig. 3. Details of the heat transfer surface.
power supply to the test section heater was varied by a dimmesstat. A mercury single U-tube manometer was used to measure the system pressure. 3. EXPERIMENTAL PROCEDURE
A number of steps were taken to clean the apparatus before starting the series of experimental runs. The compressed carbon dioxide gas was admitted into the test vessel to remove all the traces of the previous fluid from it. The test surface was also cleaned with distilled water and acetone. Both the test surface and the test vessel were rinsed with the test fluid, methanol. After cleaning and rinsing, the experimental rig was tested at a pressure of about 15 bar to check against leakage in the set-up. The set-up was left at this pressure for 24 h. Similarly the set-up was tested under vacuum. It was ensured that there was no leakage in the system. Finally, electrical insulation of the test section heater was tested. 3.1. Chargin # process The system was evacuated with the help of a precision vacuum pump before charging the test fluid in
the system. First, experiments were conducted on pure methanol, in this case pure methanol was charged into the test vessel up to a certain level above the test section, making use of the atmospheric pressure to drive methanol into the evacuated test vessel. For the mixtures experiment, a mixture of an appropriate concentration (highest salt concentration 54%) was first prepared in the charging cylinder by measuring the mass of individual components on a precision balance. The mixture was then transferred to the test vessel purely by gravity and slight heating. The mixtures and lower concentration were prepared by diluting the concentrated solutions (highest concentration 54% salt) already charged into the system, by adding the requiste amount of methanol to give the required concentration. 3.2. Data recordin9 procedure The boiling heat transfer for pure methanol and methanol-salt mixture were measured by varying the pressure from a lower (270 mbar) to a higher value (530 mbar) and the heat flux from 8432 W/m 2to 17750 W/m 2. The experiment was started by switching on the test section heater and increasing the voltage
Heat transfer coefficient for methanol-salt mixtures
435
Fig. 4. Photographic view of experimental set-up for pool boiling data measurement.
gradually to the maximum value. The liquid in the test vesssel was kept in the boiling condition for several hours at the saturation condition. The liquid and wall thermocouple readings were recorded only when the steady state was achieved. These steps were repeated several times to attain the stability of the test section. Only after obtaining good reproducibility of observation for certain conditions of heat flux and pressure, was the test section used for actual runs, assuming that the test section surface was stabilized. During a particular experimental run the required system pressure was first obtained by circulating water from a water chilling unit in the condenser. The system pressure was maintained by controlling the water temperature with the help of an automatic temperature regulator and with the refrigeration unit. After attaining the required pressure the test section heater was switched on and the voltage was gradually increased to the required value with the help of an auto-transformer. At steady state conditions, the readings of the ammeter, volt-meter and watt-meter, the liquid and the heating surface temperatures and the system pressure were recorded. The system pressure was varied to the next highest value by increasing the temperature of the condenser
water, while the heat flux was kept the same. It took nearly 2-3 h to attain the next steady state condition. The uniformity of concentration was maintained constant as far as practicable during the period of experimentation. At the steady state condition, a liquid sample was drawn from the test vessel into the sampling unit, and its saturation pressure was tested by measuring the vapour and pressure data. At each steady state condition, it was confirmed through liquid sampling test that the concentration was maintained in the test vessel, within + 1%.
3.3. Reproducibility and consistency of experimental
data The experimental data were checked for their reproducibility by conducting the experiments at different times under the same operating conditions. Further, the reproducibility was ascertained by conducting the experiments on pure methanol, and comparing the data obtained with the available data of Cryder et aL [14], Borishanskii [15] and Sharma et al. [16] (Fig. 5). It was found that the data were within the moderate experimental error limits. The range of operating parameters used in this investigation is given in Table 1.
436
S. M. BIN GADHI et al. 3
Table 2. Experimental data for boiling heat transfer from a horizontal tube to the pool of pure methanol Run no.
• J2"/'0mbarJSharma,Gul:¢~~ Var~ney(~ b × f~
! ,o 8 I
P (mbar)
I
6
I
I I
[
IO
2
7 8 9
I
3
Heot fLUXq X10-3 , W/m2 Fig. 5. Comparison of heat transfer coefficient during pool boiling methanol by different investigators. zO I
"J
Pr~sure,mb x 525
~q~
x
ATw(°C) ~ ( W m -2 K)
1 2 3 4
280 328 450 525
q = 9175W/m 2 35.0 10.08 36.9 9.01 43.8 9.24 47.5 10.19
910 1018 993 900
5 6 7 8
270 350 447 525
q = l1481W/m 2 35.0 11.82 37.7 11.51 43.8 10.49 47.9 10.07
971 987 1094 1140
9 10 II 12
260 336 448 525
q = 14026W/m ~ 35.0 12.49 38.1 12.0I 44.6 12.36 48.6 12.30
1123 1167 1135 1t40
13 14 15 16
283 315 480 525
q = 16847W/m ~ 35.0 14.55 38.2 14.20 44.3 1[.75 47.3 10.04
1158 1186 1434 1678
17 18 19 20
265 328 456 525
q = 18656W/m: 35.0 12.07 38.1 11.80 44.5 11.90 47.6 10.65
1546 1581 1568 1752
6
5
TL(°C)
9
z
5 5
I
I
I
6
7
8
1
I
I
9 IO" ZO Heat ftux q x I0 3,W/rn z
3O
while Tables 2-5 tabulate the experimental data o f the present work. The average heat transfer coefficient, was calculated from the values o f heat flux, q and the average values o f wall superheat, AT~ by using the following expression
Fig. 6. Heat transfer to boiling pure methanol at different pressures.
q a =
_ - :. AT~
(1)
4. RESULTS AND DISCUSSION
4.1. Effect of heat flux on boilin 9 heat transfer
Table 1 gives the range o f operating p a r a m e t e r s o f pure m e t h a n o l and m e t h a n o l - L i B r . ZnBr2 mixtures,
Figures 6 to 9 show the effect o f heat flux, q, on average heat transfer coefficient, c~, on a log-log plot
coefficient
Table 1. Values of operating parameters Boiling fluid
Heat flux (W m 2)
Pressure (mbar)
Pure methanol
9175, 11481, 14026, 16847, 18656
270, 330,460, 525
Methanol-LiBr. ZnBr2
7700, 9850, 12389, 14637,
270, 330, 460, 525
16754
Salt concentration (Wt%)
40, 48, 54
437
Heat transfer coefficient for methanol-salt mixtures Table 3. Experimental data for boiling heat transfer from a horizontal tube to the pool ofmethanol-LiBr. ZnBr2 mixture at 40% salt concentration
Runno.
P(mbar)
TL(°C) AT~(°C) a(Wm-2K)
Table 4. Experimental data for boiling heat transfer from a horizontal tube to the pool ofmethanol-LiBr. ZnBr2 mixture at 48% salt concentration Runno.
P(mbar)
TL(°C) AT.(°C) a ( W m - 2 K )
1 2 3 4
272 337 446 525
q = 8042W/m 2 44.6 24.09 48.0 20.45 55.0 19.70 61.0 16,95
334 393 408 474
1 2 3 4
265 325 464 538
q = 7626W/m 2 51.0 24.73 54.1 22.55 61.0 22.13 64.2 18.27
308 338 345 417
5 6 7 8
280 336 443 540
q = lO182W/m 2 44.7 23.30 49.2 23.68 55.0 21.55 60.5 21.25
437 432 472 479
5 6 7 8
265 325 479 535
q = 9847W/m 2 50.9 24.98 54.0 23.08 61.2 22.75 64.0 22.15
394 427 433 445
9 10 11 12
275 332 444 525
q = 12606W]m 2 44.5 26.35 48.8 30.05 55.9 30.57 60.0 21.86
479 420 412 577
9 10 11 12
265 333 462 525
q = 12192W/m 2 51.0 25.71 54.2 24.21 61.0 23.16 63.8 22.68
474 504 526 538
13 14 15 16
246 332 444 522
q = 14505W/m 2 44.7 30.61 47.7 28.25 57.0 34.88 60.0 22.83
474 513 415 635
13 14 15 16
266 325 476 536
q = 14830W/m 2 51.0 26.43 54.0 24.81 61.3 24.66 64.0 24.66
561 598 601 601
17 18 19 20
279 356 451 531
q = 16967W/m 2 45.2 26.41 50.3 25.54 56.1 24.01 59.2 22.08
642 664 707 768
17 18 19 20
260 335 462 520
q = 16567W/m 2 50.8 26.72 54.8 25.49 60.7 24.44 63.7 23.29
620 650 678 711
with pressure as a parameter. F r o m the figures, the following features can be seen : (a) The values of heat transfer coefficient changes with the heat flux linearly at a fixed value of pressure. (b) The value o f the heat transfer coefficient increases with the rise in pressure. On both cases it can be reasoned out as the flux and or the pressure increases, the number of bubbles per unit area of heating surface increases, thereby the turbulence due to bubble dynamics also increases. This is in fact, responsible for increasing the value of the heat transfer coefficient with heat flux and pressure. It may be added that the heat transfer coefficient is also affected by the heating surface characteristics. 4.2. Heat transfer for the methanol-salt mixture As anticipated, the heat transfer from the heating surface to the boiling methanol-salt mixtures would depend upon the parameters, namely, nature o f the salt, its concentration, heat flux, pressure and heating surface characteristics. 4.2.1. The effect of salts and their concentration on the boiling heat transfer coefficient. The m e t h a n o l salt mixtures exhibit boiling point increases depending
upon the nature of the salts, their concentration and pressure. This in fact results in an increased boiling point of the mixtures over the boiling point of pure methanol at a given pressure. This in turn, is likely to make the heat transfer coefficient of the mixture lower than that of pure methanol on a given heating surface for a given heat flux and pressure. Keeping the above in view, Figs 7-9 were drawn for ~ vs heat flux, q at different pressures for the boiling of m e t h a n o l - L i B r . ZnBr2 mixtures (salt concentration 40, 48 and 54%). The following characteristic features emerge from the plots : (a) F o r the boiling of the mixtures investigated, the value o f ~ decreases with the increase in salt concentration for a given pressure. (b) F o r a given concentration, with the fall in pressure on the mixture, the values o f ~ decrease. (c) F o r a given concentration and pressure the values of ~ increase with the increase in heat flux, q. 5. EMPIRICAL CORRELATIONS
Empirical correlations have been developed for heat transfer coefficients in terms of significant parameters,
438
S. M. BIN GADH1 et aL I0
Table 5. Experimental data for boiling heat transfer from a horizontal tube to the pool of m e t h a n o l - L i B r . ZnBL, mixture at 54% salt concentrations R u n no.
P (mbar)
TI
(:C)
9
, x 5~
!
2u46o
|
/ / J 3 4
ATw ('C) ~(W m 2 K)
bo 1 2 3 4
290 342 450 527
q = 7434 W/rn: 61.2 21.86 65.0 20.10 72.0 20.90 73.8 19.06
5 6 7 8
290 340 450 536
q = 9523W/m 2 61.2 22,3 65.0 19.8 72.0 17.1 74.0 17.2
9 10 11 12
283 342 450 525
q = 12368W/m: 60.8 22.80 65.0 24.83 72.0 24.30 74.7 24.71
13 14 15 16
286 342 453 526
17 18 19 20
288 336 453 526
x
340 370 356 390 427 481 497 495
a/
{o I 2
q
q
=
=
542 498 509 501
14576W/m ~ 61.1 27.0 65.0 26.18 72.0 26.30 75.0 26.16
540 557 554 557
16727W/m 2 61.0 27.34 64.8 24.39 72.0 24.66 75.0 25.73
612 686 678 650
I
525
x
/
/
/
6
7'
8
9 I0
20
50
Fig. 8. Heat transfer to boiling methanol LiBr. ZnBr, mixture at 48% salt concentration and different pressures.
Y
I0
Pressure, mb
,~ 6 -
-
|
~,-/
-
I
I
.
/
2= ~ 3 • 25
~9
5
Hoot flux q x 10-3,W/m 2
Pressure, mb I0
:¢
/
z
/
5
6
7
8
9
10
20
30
Heot ftux q x l O -3 , W / m 2 x 6
Fig. 9. Heat transfer to boiling m e t h a n o l - L i B r . ZnBr2 mixture at 54% salt concentration and different pressures.
7
4
I 2
5
I
I
I
I
6
5'
8
9 I0
I
I 20
30
T h e v a l u e s o f c o n s t a n t C a n d e x p o n e n t s n, a n d n2 are given in T a b l e 6, f o r p u r e m e t h a n o l a n d methanol--salt m i x t u r e s . Similarly, t h e h e a t t r a n s f e r coefficients, cL f o r m e t h a n o l - L i B r . Z n B r 2 m i x t u r e s are c o r r e l a t e d by t h e f o l l o w i n g e m p i r i c a l c o r r e l a t i o n in t e r m s o f salt c o n c e n t r a t i o n , X a n d h e a t flux q.
He(:R flux q x l O - 3 , W / m z
Fig. 7. Heat transfer to boiling methanol LiBr. ZnBr2 mixture at 40% salt concentration and different pressures.
viz p r e s s u r e a n d h e a t flux f o r p u r e M e t h a n o l as well as m e t h a n o l - s a l t m i x t u r e s . = Cp",q"~.
(2)
(3)
~2 = C ~ X " ~ q "4.
T h e v a l u e s o f c o n s t a n t C, a n d e x p o n e n t s n3 a n d n 4 are given below : C , = 0.4976,
n3 = - 0 . 0 3 8 3 9 ,
n4 = 0.7337.
T h e R M S e r r o r is a b o u t 8 % . A n e r r o r a n a l y s i s h a s also b e e n c a r r i e d o u t for all
439
Heat transfer coefficient for methanol-salt mixtures Table 6. Values of constants for finding out heat transfer coefficient in eqn 2 Solution salt concentration, Wt%
C
nt
n2
RMS error %
Pure methanol 40 48 54
0.488 0.250 0.0646 0.510
0.192 0.277 0.195 -0.00113
0.700 0.632 0.830 0.735
8.6 13.0 3.8 5.7
the experimental data and it has been observed that the order o f magnitude o f error is about _ 6%. The detailed error analysis calculation is given in Appendix A.2. 6. CONCLUSIONS Based on the results obtained from this investigation the following conclusions may be drawn : 1. The data for the heat transfer coefficient for pure methanol obtained from a horizontal tube are in agreement with the data obtained by different authors. This indicates reliability in the data obtained from the present work. 2. The addition of LiBr. ZnBr2 salt into methanol causes a considerable loss in boiling heat transfer capability of methanol. The magnitude of this loss depends upon the salt concentration. 3. The boiling heat transfer coefficient for the metha n o l - L i B r . Z n B r 2 mixture increases with the increase o f heat flux and with the increase in pressure at a fixed level o f salt concentration. 4. The heat transfer coefficient for the boiling of m e t h a n o l - L i B r . Z n B r 2 mixture can also be obtained by using the empirical correlation (~ = ClXtl3qn4
8. I. E. Smith, lnt. Advanced Course on Heat Pump Fundamentals, NATO Advanced Study Institute Programme. Espinho, Portugal (1980). 9. M. A. Olama, Evaluation of some methanol-salt solutions for absorption refrigeration, Ph.D. thesis, King's College, London (1980). 10. F. Stiemle and M. Renz, Absorptions-W/irmepumppenTheorie und Praxis. VDI Berichte 427, 37 (1981). 11. E.R. Grosman, Methanol as a working medium in sorption type thermal converters. LLR. Congress of Refrigeration, Paris 9, 359 (1983). 12. V. N. Filarkin, Boiling heat transfer to water-ammonia mixtures. Problems of Heat Transfer and Hydraulics of two-Phase Media (a symposium edited in Russian and translated by O. M. Blunn). Pergamon Press (1969). 13. F. P. Minchenko and E. V. Firsova, Heat transfer to water and water-lithium salt solutions in nucleate pool boiling. Problems of Heat Transfer and Hydraulics of Two-Phase Media (a symposium edited in Russian by S. S. Kutatetedze and translated by O. M. Blunn). Pergamon Press (1969). 14. D. S. Cryder and A. C. Finalborgo, Heat transmission from metal surface to boiling liquids: Effect of temperature of the liquid on the liquid film coefficient. Trans. Am. Inst. Chem. Engrs 33, 346 (1937). 15. V. M. Borishanskii, Problems of Heat Transfer and Hydraulics of Two-Phase Media, S. S. Kutateladze, Ed. Pergamon Press, Oxford (1969). 16. P. R. Sharma, P. Kumar, S. C. Gupta and B. S. Varshney, Nucleate pool boiling of liquids on horizontal cylinders at subatmospheric pressure. 4th National Heat and Mass Transfer Conference (1981).
which gives ~ at a given salt concentration, x and heat flux, q, with an R M S error of 8%. Acknowledgements--The authors gratefully acknowledge the help and cooperation of Mr S. Dorairaj during the experimental observations and fruitful discussions.
REFERENCES
1. W. Will, Z. ges. Kiilteind. 47, 65 (1940). 2. W. R. Hainsworth, Refrigng Engng 48, 97, 201 (1944). 3. J. E. Aker, R. G. Squires and L. F. Albright, A S H R A E Trans. 71, 14 (1965). 4. T. Uemura and S. Hasaba, Rie-to 43, 784 (1968). 5. T. Uemura and S. Hasaba, Rie-to 44, 502 (1969). 6. T. Uemura, Rie-to 51, 590, 1027 (1976). 7. R. Best, Proc. 1st Int. Conf. on Solar Building Technique 2, 54, 436. R.I.B.A., London (1977).
APPENDIX A.1. SAMPLE CALCULATIONS FOR COMPUTATION OF HEAT TRANSFER COEFFICIENT The heat transfer coefficient was calculated as the quotient of heat flux to the temperature difference between the outer surface temperature of the test section and the bulk liquid temperature. General data used for heat transfer coefficient calculation : Outside dia. of heating surface, do = 0.03165 m. Inside dia. of heating surface, ~ = 0.02505 m. Length of heating surface, L = 0.200 m. W Thermal conductivity of heating surface, 2 = 383 m-I(" (copper material)
440
S. M. BIN GADH! et al.
A. 1.1. Heating surface area.
corrected surface temperature of the heating test section tube.
Area of heating surface, A = nd,,L = 3.14 × 0.03165 × 0.20 = 0.01989428 m ~'. From Table 2 for boiling of pure methanol input data is selected here to demonstrate the calculation procedure. Data corresponding to run number 1 l are reproduced below :
AT,,, = Tw~- ire = 56.85--44.6 = 12.2Y~C; AT\,, = T ~ - T ~ . = 59.65-44.6 = 15.0YC: AT,,~ = T,,~
Voltage, V = 191V
AT,~ = T , . - T ~ = 5 2 . 5 5 - 4 4 . 6 = 7.95'C.
Current, l = 1.62A
_
Heatflux, q
T~ = 57.0 T2 = 59.8 T 3 = 58.9 T4 = 52.7 T~ = 44.6.
d,
6T~=--ln-, 22w c/~
-
(A. 1.2)
A.I.5. Heat loss to surroundings. There is always some heat loss from the test vessel to the surroundings. The heat loss can be classified into two types. (i) Radial heat loss through wall insulation. (ii) Axial heat loss, Radial Heat: The radial heat loss can be calculated by using the following expression [16]: QR = H L R = 2n2iL
d~ = 0.02505 m. Substituting the values of q, du, 2w and d~ in eqn (A. 1.1), the 6T~ can be obtained 15553.4 x 0.03165 0.03165 2x383 ln0~02~0~ = 0.15'C.
Therefore, the corrected surface temperatures of the test section are calculated using the following equation
rw~--6T~
where subscript r denotes the recorded surface temperature. Hence
T~,, = T~,,-~T~ = 57.0-0.15 = 56.85'C; T,~ = T,r~-bTw = 59.8-0.15 = 59.6Y'C;
where, 2~ represents the thermal conductivity of the test vessel's insulation 2i = 0.029 W/mK. L represents the test vessel's insulation length = 0.500 m; Do represents the test vessel's insulation outer diameter: Do = 0.33 m ; D~ represents the test vessel's inner diameter : D~ = 0.18 m ; T, represents the test vessel's inner surface temperature: T~ = 48. I'~C : To represents the vessel's insulation outer surface temperature : To = 24.1°C. Substituting the values of 2~, L, Do, D~, T, and 7',, from (A.1.5) in eqn 3, we get QR=HLR=
2 x 3.14 x 0 029 x 0 500 " " × (48.1-24.1)=3.6l W. 1 /0.33~
Axial heat loss : The axial heat loss can be calculated using the following expression [16]: }'c7~
2
2
A.1.4. Calculation of average wall superheat. The values of local wall superheat at the circumferential position of the heating surface are calculated by subtracting the values of liquid bulk temperature from the corresponding values of
'
'
QA = HLA = ~ (do -d~ ) [(Tw: T~,)/I, + (Tw~-- 7w~)//2l
T,,~ = T~3--fTw = 58.9~0.15 = 58.75:C;
T~, = T,,.,.--fTw = 52.7-0.15 = 52.55 C.
(A.I.3)
Di
(A.I.I)
where, d~ represents the outer diameter of the inner copper tube
=
4
= 12.35 'C.
QM _ 309.42 _ 15553.4W/m2 A 0.01989428
T,,
-
12.25+ 12.05+ 14.15+7.95
A.I.3. Calculation of corrected surface temperature, Tw. The corrected temperatures of the heating surface were calculated by subtracting the temperatures drop across the thickness of the heating tube surface from the recorded values of surface temperatures. The temperature drop across the wall thickness of heating surface is obtained by using the following equation [161:
fir~ =
~
=
191 x 1.62 = 309.42W.
qdo
-
4
A.1.2. Calculation of heat flux, q. Power input to heating surface : QM - V x l =
ATw,+ATw,+AT,,+ATw,
AT,,.=
= 310W
Temperature, C :
44.6 = 14.15 (':
The values of local wall superheat are averaged linearly by means of the following equation to get the value of the average wall superheat :
Pressure, P = 448 mb
Watt, W
T~ = 58.75
(A.l.4) where )~¢ represents the copper tube thermal conductivity : ).~ = 383 W / m K where do and di are defined in eqn A. 1.1. T,~,, T,,:, T~ and T~., are the temperatures recorded by the
441
Heat transfer coefficient for methanol-salt mixtures thermocouples, nos. 1, 2, 3, and 4, respectively as shown in Fig. 3. lj represents the distance between the thermocouples 1 and 2; l~ = 0.098 m. 12 represents the distance between the thermocouples 8 and 9; 12 = 0.09 m. Substituting the values of 2c, do, a~, Two, T,~, Tw¢ Twv l~ and 12 in eqn (A. 1.4), we get HLA
heater, wall and liquid temperatures. In fact the instruments used for measuring these quantities each had their respective accuracies. Consequently, an error results in the calculation of the heat transfer coefficient. In order to find out the size of the error, an error analysis for the experimental data of this investigation was carded out. A typical calculation of error analysis is given below. The experimental error is the absolute value of the maximum expected deviation from the reported experimental results and is given by :
383 x 3.14 [(0 03165) 2 - (0.02505) 2] 4 x
F. /a~
(A.2.1)
[(57 - 4 8 . I)/0.098 + (52.7-48.1)/0.09] = 25.86 W.
A. 1.6. Computation of net heat supplied to the test fluid. The net heat load QN supplied to the test fluid is computed by subtracting the axial heat loss and radial heat loss from the power heat input to the test section. Hence, QN = QM - - (HER + HLA) = QM - (QR + QA) QN = [309.42- (3.61 + 25.86)] = 279.95 W.
(A.I.S)
A. 1.7. Calculation of the average heat transfer coefficient, ~. The value of the average heat transfer coefficient is calculated by :
QNIA = ~
k~7 °~
e~ = L,~/~.e=,j j
279.95 12.385 x 0.01989428
1138.2W/m2K. (A. 1.6)
A.2. ERROR ANALYSIS
The present investigation involved the measurement of quantities like heating surface area, electric power to the
where E~ represents the error in the measurement of the heat transfer coefficient and z~ represents any of the n variables affecting this coefficient, since QN 07 = A(Tw -- Tr)"
(A.2.2)
Thus the overall uncertainty in the average heat transfer coefficient can be obtained by partial differentiation of eqn A.2.2 which becomes the following :
Pl
EQs ~2 f
+(
Qs" EA
e,.-,, y
A~)#
(
'~2
+ k ~ }
ylO,
1 " (A.2.3)
A typical calculation of error analysis of run number 11 in Table 2 was carded out using the above method with the help of a computer. An average error of the order of 6% was found for the set of parameters taken in this paper.