An experimental investigation of solidification in a rectangular enclosure under constant heat rate condition

Int. Comr~ Heat Mass Transfer, Vol.26, No. 7, pp. 925-934, 1999

Copyright © 1999 Elsevier ScienceLtd Printed in the USA. All rights reserved 0735-1933/99/S-see front matter

Pergamon

PII S0735-1933(99)00082-2

AN EXPERIMENTAL INVESTIGATION OF SOLIDIFICATION IN A RECTANGULAR ENCLOSURE UNDER CONSTANT HEAT RATE CONDITION

F.L. Tan and K.C. Leong School of Mechanical and Production Engineering Nanyange Technological University Nanyang Avenue, Singapore 639798 Republic of Singapore

(Communicated by J.P. Hartnett and W.J. M i n k o w y c z )

ABSTRACT The solidification of pure n-hexadecane inside a rectangular cavity enclosure under constant heat rate condition is investigated in this paper. The experiments are carried out in two rectangular test rigs of aspect ratios 1 and 1.5. Solidification of the n-hexadecane occurs on a vertical copper wall held under constant heat rate condition while the remaining walls are adiabatic. The rate of heat extraction from the vertical wall is controlled using a thermoelectric cooler. The solidification experiments are conducted for three different heat rates at 10 W, 15 W, and 20 W with an initial liquid superheat of 9 ° C . A rather fiat solidification phase front parallel to the cold wall is observed for all heat rates, thus indicating that the natural convection in the liquid is negligible under constant heat rate condition. The solidification rate is larger at higher heat rate and at lower aspect ratio. © 1999 Elsevier Science Ltd

Introduction

Solidification in an enclosure is intrinsically characterized by thermal gradients in the liquid and natural convection that can greatly affect the progression of the solidification process. Natural convection arises as a result of density changes within the liquid due to the changes of temperature. During the solidification process, natural convection decreases the growth of the solid phase and also affects the profile of the soldification phase front. Phase change heat transfer relating to melting and solidification involving natural convection within an enclosure has received a fairly great degree of attention. Yao and Prusa [1] gave a pretty good review of melting and freezing researches carried out up to the 1980s. The review covered both experimental and numerical experiments on melting and freezing. Viskanta [2] provided a good summary on melting and solidification problems involving natural convection. 925

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Szekely and Chhabra [3] were among the first to demonstrate, experimentally and analytically, the effect of natural convection on the shape of a stationary and a transient solid-liquid interface in a rectangular test cell with a heat source and sink on the two vertical side walls. Many experiments were performed using relatively high Prandtl number liquid such as n-paraffin waxes and water as phase change materials. Natural convection has been shown either to enhance the melting rate or to retard the solidification rate (Hale and Viskanta [4]). Cole and Boiling [5] determined that the role of natural convection in the melt during solidification of metals has the influence on the solid structure. In the manufacturing of semiconductors and castings, experiments have shown that the structure and distribution of inclusions in the solid is significantly affected by the buoyancy-induced flow in the melt during solidification reported by Morizne et al. [6]. Cole and Wingard [7] had shown that the amount of thermal convection during a horizontal and undirectional solidification is a function of the temperature gradient in the liquid, the rate of solidification, the height of the solid- liquid interface, the angle deviation of the interface from the vertical plane, and the fluid parameters of the liquid metal. Many experiments have been reported for solidification inside an enclosure in the recent years, for example, Webb and Viskanta [8], Christenson and Incropera [9], Wolff and Viskanta [10], Ketkar et al. [11], and Leong and Tan [12]. A lot of research work were carried out for solidification involving natural convection under isothermal wall condition inside an enclosure.

However, no

attention has been focused on the experimental study of solidification under constant heat rate or heat flux condition.

This may be due to the reason that solidification under constant heat

rate or heat flux is difficult to achieve and maintain in practical applications. This paper presents the results of an extensive investigation on the solidification of n-hexadecane inside a rectangular enclosure under three constant heat rates at 10 W, 15 W, and 20 W, respectively with an initial liquid superheat of 9°C, and at two aspect ratios of 1 and 1.5.

Experimental Setup and Procedures Rectangular test cells were used in the soldification experiments. Two test cells of aspect ratios (ratio of height to width) 1 and 1.5 were constructed using 10 mm thick plexiglas. The rectangular test cell having aspect ratio 1 has an inside dimension of 60 mm height by 60 mm width and a depth of 100 mm, while cell of aspect ratio 1.5 has an inside dimension of 90 mm by 60 mm and a depth of 100 mm. Plexiglas was used for ease of visualisation of the solidification phase front due to its good optical properties which allows 92% light transmission. Plexiglas also has low thermal conductivity

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of 0.15

W/mK

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to reduce heat gain through the walls. Each test cell was made from five plexiglas

walls machined to the required dimensions. The walls were joined together using chloroform as a bonding agent to prevent any leakage of liquid n-hexadecane during the experiment. Holes were drilled at the top and bottom of the test cells to facilitate the filling and removal of the liquid n-hexadecane. There were six thermocouple rakes, with a total of forty eight Type-K thermocouples, installed inside each test cell to measure the horizontal and vertical temperature distribution of the solidifying n-hexadecane. The thermocouple rake was made of plexiglas tube having an outer diameter of 7 mm and inner diameter of 5 mm. Eight Type-K thermocouples were carefully embedded into each thermocouple rake with eight tiny holes of 1 mm diameter drilled along the rake. The distance between thermocouples were spaced at an increasing interval from the tip of the rake at 3, 6, 10, 14, 18, 24, 30 and 40 mm, respectively. High thermal conductivity epoxy compound was used to hold the thermocouples in position. The test cell was mounted on a vertical 10 mm thick copper plate. Copper was chosen as the vertical wall for the test cell to ensure uniform temperature due to its excellent thermal conductivity. The other side of the vertical plate was mounted onto an aluminium plate heat exchanger with a thermoelectric cooler (Melcor CP2.8-32-06L) sandwiched between the copper plate and the aluminium plate. The temperatures of the copper plate (cold side temperature) and the aluminium plate (hot side temperature) were measured using thermocouples. The thermoelectric cooler pumped the heat extracted from the P C M in the test cell to the heat exchanger. Channels were milled on the aluminium plate to circulate refrigerated fluid through the plate. The inlet and outlet of the exchanger were connected to a low temperature refrigerated circulator. The design of the channels was to ensure uniform temperature distribution on the hot side of the thermoelectric cooler. A material with both relatively good machinability and thermal conductivity like aluminium was chosen for the fabrication of the heat exchanger. Thermal grease was applied on both sides of the thermoelectric cooler to improve heat conduction at the contact surfaces.

The thermal grease has a temperature range o f - 4 0 ° C to +200°C, which was within

the range of the experiments. The maximum heat that can be absorbed on the cold side of the thermoelectric cooler is 30 W. The maximum current allowable for the thermoelectric cooler is 23 A. A general purpose DC power supply (Philips PE-1642) supplied constant voltage and constant current to the thermoelectric cooler. The DC power supply can supply constant voltage up to a maximum of 20 V or a constant current up to a maximum of 20 A. The vertical plate and heat exchanger assembly with the thermoelectric cooler was calibrated with a known heat from a heater attached to the copper plate. During calibration, the heater was set to a constant power, say 10 W. The current to the thermoelectric was set to say 1 A. The temperature difference between the cold side and hot side of the thermoelectric cooler was recorded once it had stabilised. The current to the thermoelectric cooler was then increased by 1 A, and the temperature difference was monitored as before. The thermoelectric current can be increased up

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to a maximum of 18 A without damaging the thermoelectric cooler. The experimental setup was insulated with 50 mm thick styrofoam all round to reduce heat gain from the surroundings. A small window opening was provided in the insulation for photographic and visual observations of the phase front during solidification. A removable piece of styrofoam was plugged into the window opening throughout the experiment. DC P o w ~ Supply

Low per~re culator plate

FIG. 1 Schematic of the experimental setup A schematic diagram of the experimental setup is shown in Figure 1. The thermoelectric cooler was connected to the DC power supply. All fifty Type-K thermocouples were labelled and plugged into the PC-based data acquisition system. The emf output of the thermocouple, normally in terms of m V , were converted by the data acquisition board based on a built-in standard conversion table for Type-K thermocouple. The data acquisition system was calibrated using Thermacal Calibration Cool/Heat Source Model 18B which can provides accurate temperature source for both high and low temperatures. All the sixty-four terminals of the data acquisition system were fitted with Type-K thermocouples that were then inserted into the wells of the T h e r m a c a l . A few temperature settings, ranging from -15°C to +80°C, were used to plot curves comparing with the actual readings. The sixty four thermcouples were divided into four groups, each group having sixteen thermocouples in the calibration. Each group of the thermocouples can be represented the equation of y = m x + C and compared with the actual temperature data.

The gradient (m) and the constant (C) were

recorded and keyed into the offset feature of the d a t a acquisition software to correct the difference with the actual plot. The data acquisition system was calibrated to achieve an average accuracy of less than I°C. Liquid n-hexadecane was selected for the solidification experiments due to the closeness of the melting temperature to the ambient temperature and it gave a sharper soldification phase front based on previous experiences of the authors. The properties of n-hexadecane are listed in Table 1:

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TABLE 1 Thermophysical Properties of n-Hexadecane Melting Temperature Density Latent Heat Thermal Conductivity Kinematic Viscosity Specific Heat Capacity Thermal Coefficient of Expansion

18.2 °C 780 kg/m 3 228.9 kJ/kg 0.1505 kW/mK 3.68 ×10 -6 m2/s 2310 J/kgK 0.9 ×10 -3 K -1

The solidification experiments were performed with two test cells of aspect ratios 1.0 and 1.5, respectively for three different constant heat extraction rates at the verticle wall of 10 W, 15 W and 20 W, respectively. The low temperature refrigerated circulator (Neslab LT-50) was set to a temperature at IO°C. The n-hexadecane was maintained at a superheat temperature of 9°C:l=I°C. The liquid n-hexadecane was then poured into the test cell through a filler tube at the top of the test cell. A digital camera (Sony Digital Mavica MVC-FD7) was placed in front of the small window opening to capture the solidification phase front. The valve on the refrigerated circulator was open to circulate the refrigerated ethyl alcohol through the aluminium plate heat exchanger. The data acquisition software was started to record the temperature data inside the test cell. An appropriate direct current was applied to the thermoelectric cooler to maintain a constant heat rate condition at the copper plate through monitoring the A T with the calibrated chart. The solidification phase front was captured at an interval of 5 to 10 minutes. The solidification experiment was stopped when the DC current to the thermoelectric cooler reached 18 A.

R e s u l t s and D i s c u s s i o n A series of photographs in Figure 2 shows the solidification phase front of n-hexadecane progressing from right to left in the rectangular test cell of 1 aspect ratio at 10 W at various instants of time. It was observed that the solidification phase front was rather planar and parallel to the vertical cold wall throughout the solidification process. The solid at the top and bottom of the test cell are thicker and cornered at the intersection of the phase front and the plexiglas wall. Similar observation was observed for the test cell of 1.5 aspect ratio. The solidification phase front are rather flat and parallel to the cold wall. It can be inferred that the natural convection in the liquid is rather weak under the constant heat rate condition to cause any significant slope on the phase front. The mode of heat transfer inside the test cell is predominantly through heat conduction in the solid and liquid. A sloped phase front was observed for solidification process under isothermal wall condition [13]. Similar observation on the solidification phase front was seen at larger constant heat rate at the cold wall. The phase front was flat and parallel to the cold wall. It is a clear indication that even at larger heat rate at the cold wall, the natural convection in the liquid is not sufficiently

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strong to cause a sloping phase front. The solidification rate was larger for the test cell of lower aspect ratio and for higher heat rate at the wall. The n-hexadecane PCM gave a rather sharp and clear solid-liquid interface at the initial stage of solidification.

However, after about an hour of

solidification, corner solidification started to appear at the intersection of solid-liquid interface and the walls.

.... a

(a) 40 rains

(b) 50 mins

(c) 60 mins

(d) 70mins

(e) 80mins

(f) 90 mins

FIG. 2 Progression of phase front at 10 W for aspect ratio of 1 Tan and Leong [18] and Ketkar et al. [11] conducted similar experiments for pure PCM (nhexadecane and caprillic acid, respectively) under isothermal wall condition.

The solidification

phase fronts under isothermal wall condition were significantly different compared to the solidification phase front under constant heat rate. The isothermal case had significant sloping phase front as a result of stronger natural convection in the liquid. The "corner" solidification occurring at the intersection of the phase front and the wall was explained by Tan and Leong [18] using temperature distributions in the plexiglas wall and n-paraffin wax. The melting temperature of n-hexadecane is 18.2°C with a thermal conductivity of 0.150

W/mK which is quite close to that of the plexiglas at 0.153 W/mK. The plexiglas wall was initially at ambient temperature of 27°C and cooled by the vertical plate to subzero temperatures. The

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plexiglas wall was cooled down faster t h a n the liquid n-hexadecane. The t e m p e r a t u r e distribution along the plexiglas wall would go below the melting t e m p e r a t u r e of the P C M near the solid-liquid interface after a specific time. This was supported by the observation where corner solidification occured at the test cell side walls after a b o u t 60 minutes. The solidified mass fraction is the ratio of the mass of the solid to t h e total mass of solution in the test cell. The solidified mass fraction curves of both aspect ratios 1 and 1.5 are shown in Figure 3 for a c o n s t a n t heat extraction at 10 W. T h e test cell of aspect ratio 1, having a steeper gradient, has a higher solidification rate compared to the aspect ratio 1.5. This agrees with the observation in the comparison of phase front with aspect ratio. T h e curves for the solidified mass fraction fit a 3rd order polynomial equation [19] of the form, y -- at -t- bt 2 + ct 3, where a, b, and c are constants. 04

/o

035 03 z

~

0~

~ o2 ~0.15 //

÷

01 0.06

l'hme Is)

FIG. 3 Effect of aspect ratio on solidified mass fraction at 10 W It can be clearly seen from the slopes of the curves t h a t the solidification rate is slow for b o t h aspect ratios at the initial stage. The solidification rate increases to a r a t h e r steady rate under c o n s t a n t heat rate. Figure 4 shows the plot for solidification under different heat rate setting for aspect ratio 1.5. All the three curves obey the 3rd order polynomial characteristic. It was observed t h a t the solidification rate increases with an increase in the heat extraction rate at the vertical cold

wall.

O2 I 0.15 p=

~Y 1ooo

.

2ooo

3OO0

400O nine

5QO0

6OOO

~000

8OOO

Isl

FIG. 4 Effect of heat extraction on solidified mass fraction for aspect ratio at 1.5

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Figure 5 shows the heat extraction rate and the wall t e m p e r a t u r e curves for test cell of aspect ratio 1.5. The heat extraction rate was maintained fairly constant at 10 W through the fine current control of the thermoelectric cooler. Thus, the solidification experiments were carried out under an approximately good constant heat rate condition. The wall t e m p e r a t u r e was decreasing almost linearly to a low of about -12°C after 2 hours. 40

, ....... -

30

ov

q Wall Temperature Heat Extraction

20

1 10 g

211 "'.

Q

E i

i

20

40

6 0'

' "" "'gg

i

i

100

120

o !

-10 Time (minutes)

-10

-20

FIG. 5 Cold wall and heat extraction versus time Figure 6 shows the isotherms inside the test cell of 1.5 aspect ratio at 10 W at a time of 120 minutes. The isotherms were rather flat and parallel to the cold wall at the constant heat rate, which was in agreement with the observed phase front. The isotherms curved outwards at the top and bottom of the test cell, which gave rise to corner solidification at the walls. The isotherms clearly indicated t h a t the dominant mode of heat transfer was conduction through the solid and liquid. The natural convection in the liquid is insignificant to cause a sloping phase front under constant heat rate condition. 70 60 50

40 >30 20 10

111

t

i

211

30

40

X (mm)

FIG. 6 Isotherms inside the test cell at 10 W for aspect ratio of 1.5

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Conclusion The soldification phase front is rather sharp and clear at the initial stage of solidification. However, at a later stage of solidification, "corner" solidification starts to appear at the intersection of solidification phase front and the side walls. The natural convection in the liquid has negligible contribution to the solidification process where conduction is the predominant mode of heat transfer. The solidification phase front is rather fiat and parallel to the cold wall. The phase front under isothermal condition at the cold wall has been observed to have significant sloping phase front. This is not observed under the constant heat rate condition at the cold wall. Thus, it can be inferred that the the natural convection in the liquid is sufficiently weak to cause a sloping phase front under constant heat rate condition. The enclosure with lower aspect ratio has a larger solidification rate compared to the enclosure with higher aspect ratio. The solidification rate is larger for a higher heat rate condition at the cold wall.

Acknowledgement This work was carried out as part of a research project funded by the Nanyang Technological University under grant number AcRF RG 67/96.

References 1. L.S. Yao and J. Prusa, Melting and Freezing, in J.P. Hartnett and T.F. lrvine, Jr. (eds.), Advances in Heat Transfer 19, Academic Press, New York (1989). 2. R. Viskanta, Natural Convection in Melting and Solidification, in S. Kakac, W. Aung, and R. Viskanta (eds.), Natural Convection: Fundamentals and Applications, Hemisphere, Washington D.C. (1985). 3. J. Szekely and P. S. Chhabra, Metallurgical Trans. B 1, 1195 (1970). 4. N. W. Hale, Jr. and R. Viskanta, Int. J. Heat Mass Transfer 23, 283 (1980). 5. G. S. Cole and G. F. Boiling, Trans. TMS-AIMS233, 1568 (1965). 6. K. Morizne, A. F. Witt and H. C. Gatos, J. Electrachem. Soc. 114, 738 (1976). 7. G. S. Cole and W. C. Winegard, J. Inst. Metals 93, 153 (1964). 8. B. W. Webb and R. Viskanta, Proc. 8th Int. Heat Transfer Conf., San Francisco, USA, pp. 1739-1744 (1986). 9. M. S. Christenson and F. P. Incropera, Int. J. Heat Mass Transfer 32, 47 (1989). 10. F. Wolff and R. Viskanta, Int. J. Heat Mass Transfer 31, 1735 (1988).

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11. S. P. Ketkar, M. Parang and R. V. Arimilli, J. Thermophysics Heat Transfer 5, 40 (1991). 12. V. R. Voller, M. Cross and N. C. Markatos, Int. J. Numerical Methods in Engineering 24,

271 (1987). 13. K.C. Leong and F.L. Tan, J. Materials Processing Technology 70, 129 (1997). 14. F. Alavyoon, Int. J. Heat Mass Transfer36, 2479 (1993). 15. C.H. Charach and P.B. Kahn, Int. J. Heat Mass Transfer30, 233 (1987). 16. R.V. Seeniraj and T.K. Bose, Warme und Stoffubertragung 16, 105 (1982). 17. J.S. Good]ingand M.S. Khader, J. Heat Transfer97, 307 (1975). 18. F.L. Tan and K. C. Leong, Int. Comms. Heat Mass Transfer 21,641 (1994). 19. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford University Press, London (1959). Received June 8, 1999