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Ind. Eng. Chem. Res. 2004, 43, 5350-5357
Heat Transfer Characteristics during Melting and Solidification of Phase Change Energy Storage Process Hisham Ettouney,*,† Hisham El-Dessouky,† and Eman Al-Kandari‡ Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait, and Environment Public Authority, Kuwait
This study focuses on heat transfer characteristics of phase change material (PCM) during energy storage and release in vertical double pipe configuration. Paraffin wax with an average melting temperature of 52 °C is used as the energy storage material and water is used as the heat transfer fluid (HTF). The heat transfer fluid flows in the inner tube and the wax is stored on the shell side. Eighteen thermocouple wires are placed in the wax to provide a detailed measurement for the temperature field during energy storage and release. Measurements are made as a function of the flow direction, flow rate, and inlet temperature of the heat transfer fluid. Results indicate that natural convection dominates the melting process for upward flow of the heat transfer fluid. On the other hand, the solidification process is dominated by conduction. During melting and upward flow of the HTF, the density difference of hotter and cooler molten wax layers initiates natural convection cells. Further mixing within the melt is also caused by descent of the higher density solid wax. Introduction Endeavors of researchers to secure clean and environmentally friendly energy sources include use of energy storage systems. These systems can be used to store energy for household and industrial applications. Also, energy storage units can be combined with nonfossil and sustainable energy sources, such as solar, ocean thermal, tidal, wind, and geothermal energies. Irrespective of the attractive features of the energy storage systems its use remains to be found on a very limited scale. This is caused in part by the lower prices of fossil fuels and the huge field of experience in design, construction, and operation of fossil fuel power plants. Studies of energy storage systems were motivated in part by the rising energy costs during the second half of the twentieth century and the need for these configurations in space applications. Earlier studies focused on development of full-scale household devices, i.e., solar ovens,1 water heaters,2 etc. Results of these studies indicated the need for better understanding of various aspects of the melting and solidification through detailed modeling and experimental investigations. Examples for mathematical modeling and analysis include the studies by Sparrow et al.,3,4 Green et al.,5 Zhang et al.,6 and Chen.7 Results of these studies show a limited role of natural convection during the solidification process. On the other hand, natural convection is found to drastically enhance the melting process.8,9 Experimental investigations focused on development of the heat exchange configuration. These developments included shell and tube,10 double pipe,11 plate,12 or spherical shells.13,14 The study by Esen et al.10 was conducted for energy storage and release in shell and tube heat exchange units. Results indicate shorter energy storage * To whom correspondence should be addressed. Tel.: 965-481-1188, ext. 5619. Fax: 965-483-9498. E-mail: hisham@ kuc01.kuniv.edu.kw. † Kuwait University. ‡ Environment Public Authority.
and release times upon storing the PCM on the shell side. The study by Choi and Kim11 focused on heat transfer by use of finned tubes. The results show 4-fold enhancement upon the use of finned tubes. This is caused by the increase in the effective thermal conductivity of the phase change material due to high thermal conductivity of the metal fins. Plate heat exchangers provide higher heat transfer coefficients than regular shell and tube heat exchangers.12 This should reduce drastically the required system volume for the same thermal capacity. Also, charge and release times are reduced considerably. However, use of plate heat exchangers remains to be found on a limited scale. This is because of the lack of field experience and industrial standards. Also, the number of manufacturers and selection choices are quite limited for the shell and tube configuration. Use of spherical capsules to store the PCM is motivated by the fact that spheres provide the highest specific surface area. Spherical shells are used for ice formation in large tanks during off-peak load hours.13 Ice melting during the daytime would provide lower cost air conditioning and cooling applications. Experimental evaluation of the natural convection role inside the spherical capsules14 show a stronger role during melting than solidification. Also, the natural convection role is enhanced by the increase in the diameter of the spherical capsule. Use of paraffin wax as PCM has a major drawback of low thermal conductivity, which would increase the melting and solidification times. This problem is addressed through the use of finned tubes15 as well as metal fiber,16 metal matrix inserts,17 or metal beads and screens.18 These attempts resulted in higher effective thermal conductivity and heat transfer enhancement of 1- to 5-fold. This is achieved with replacement of less than 5% in volume of the wax with the tube fins or various forms of metal structures.16-18 The focus of this study is to evaluate natural convection effects during melting and solidification of paraffin wax in double pipe heat exchange systems. The main
10.1021/ie030495b CCC: $27.50 © 2004 American Chemical Society Published on Web 07/15/2004
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5351 Table 1. Physical Properties of PCM and HTF physical property
water (HTF)a
melting temperature, °C latent heat, kJ/kg solid density, kg/m3 liquid density, kg/m3 specific heat, kJ/kg K
N/A N/A N/A 998 4.18
thermal conductivity, W/m K
0.626
viscosity, Ns/m2
6.62 × 10-4
paraffin wax (PCM) 52 210 860 780 2.9 (s) 2.1 (L) 0.24 (s) 0.15 (L) 0.205
a Water properties are for a temperature range of 5-97 °C. N/A (not applicable).
Figure 2. Dimensions of PCM and HTF tubes.
Figure 1. Schematic of experimental system.
feature of this study is the detailed measurement of the temperature field within the PCM. This is quiet distinguishable among literature studies, where the majority of these studies have used a small number of thermocouples and on one side only of the heat exchanger tubes. Accordingly, analysis in these studies must assume symmetry and neglect radial temperature variations. The detailed temperature fields measured in this study are quiet valuable, since they provide the literature with the actual picture for the temperature field during melting and solidification. This facilitates assessment of the heat transfer characteristics during the melting and solidification cycles, which is made in part by calculating the Nusselt and Fourier numbers for melting and solidification. Experimental System A summary of the physical properties of the PCM (paraffin wax) and HTF (water) is given in Table 1. The experimental system, Figure 1, includes constant-temperature water bath, circulation pump, the PCM and HTF tubes, thermocouples wiring, data acquisition unit,
and a PC for data analysis. The PCM tube is made of Plexiglas with an inner diameter of 69.4 mm. The HTF tube is made of copper with inner and outer diameters of 9.7 mm and 12.7 mm, respectively. The PCM is kept in the annular space between the Plexiglas and copper tubes. The HTF connections to the copper tube allow for upward and downward flow of the HTF. Thermocouple wires are used to measure the temperature field in the PCM and at the inlet/outlet of the HTF tube. The wires have a measuring range of -10 to 150 °C and an accuracy of +0.2 °C. A total of eighteen thermocouples are equally distributed in the PCM over three axial locations along the column length, Figure 2. These axial locations are 170, 510, and 850 mm, which are measured from the tube base. Each axial location contains six thermocouples, which are equally spaced over a distance of 30 mm; therefore, each two thermocouples are spaced by 5 mm. A 40-channel data logger is used to collect the temperature measurements. The logger stores the temperature measurements at an interval of 5 min. The logged data are transferred to the PC unit, where they can be processed and analyzed. A needle valve and a flow meter are used to adjust the flow rate of the HTF over a range of 0.238-0.37 kg/s. The outlet HTF stream is recycled back to the constant temperature water bath. The water bath keeps the water temperature constant at the desired value, which can be changed over a range of 5-98 °C. This allows for heating and cooling modes. Therefore, in the heating mode the HTF temperature is changed over a range of 65-85 °C and in the cooling mode the temperature is changed over a range of 1020 °C. Error Analysis. To estimate the uncertainties in the results presented in this work, the approach described by Barford19 was applied. The overall uncertainty assigned to a given measurement is defined as the rootsum-square combination of the fixed error due to the instrumentation and the random error observed during
5352 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004
measurements. The measured experimental errors are (0.2 °C for temperatures, (0.02 kg/s for water flow rate, 2.5 × 10-6 m for inner and outer diameter of the tubes, and (1 s for melting or freezing times. Accordingly, the resulting errors are (6.37% and (5.43% in the calculated Nusselt and Fourier numbers, respectively. Melting and Solidification Fourier Number. The correlations for melting and solidification Fourier number are expressed in terms of the Biot and Stefan numbers, or
Fo ) aBibStc
(1)
where a, b, and c are fitting constants, and Fo, Bi, and St are Fourier, Biot, and Stefan numbers, respectively. It should be noted that (TP) in Stefan number is set equal to the PCM melting temperature for melting, and for solidification (TP) is set equal to the PCM temperature at the start of the solidification cycle. Melting and Solidification Nusselt Number. The model equations for solidification are similar for those of melting; however, the temperature differences in eqs 3 and 4 must be reversed for solidification to take into consideration heat transfer from the PCM into the HTF. The heat transfer coefficient of the PCM during melting/ solidification is obtained from the definition of the heat transfer resistance between the PCM and the HTF, which is given by
hP ) 1 U
1 DoHln(DoH/DiH) 2kw
-
DoH
(2)
DiHhH
The overall heat transfer coefficient (U) used in eq 2 is obtained from the heat transfer rate equation for the energy storage system, which is given by
U ) MHCpH (TiH - ToH)/(AH × LMTD)
(3)
The logarithmic mean temperature difference for melting, LMTD, is defined by
LMTD )
(TiH - T1) - (ToH - T13) ln((TiH - T1)/(ToH - T13))
(4)
In eq 4 T1 and T13 are the PCM temperatures at the same level of the inlet and outlet HTF, respectively. In eq 2, the heat transfer coefficient for the HTF is calculated from the Dittus and Boelter equation.
hH ) 0.023 Re0.8PrakH/DiH
(5)
where a ) 0.3 (for cooling) and a ) 0.4 (for heating). Re and Pr are the Reynolds and Prandtl numbers. The heat transfer coefficient for the PCM given by eq 2 is used to obtain the Nusselt number correlation. For solidification the Nusselt number is found to have negligible dependence on natural convection. Therefore, the correlation for Nuseelt number during solidification is defined in terms of the Stefan (St) and Fourier numbers, where
Nu ) aStbFoc
(6)
Equation 6 is valid for both cases of upward or downward flow of the HTF. Also, it is valid during melting
Figure 3. Transient temperature profiles in PCM, surrounding air, and HTF for downward HTF flow, TiH (hot) ) 85 °C, TiH (cold) ) 15 °C, MH ) 0.303 kg/s.
for downward flow of the HTF. In presence of natural convection, or upward flow of the HTF, the Nusselt number correlation is expressed in terms of Rayleigh (Ra), Stefan (St), and Fourier (Fo) numbers
Nu ) aRabStcFod
(7)
Results and Discussion The experimental system is operated for the following set of conditions: (a) flow rates of HTF are 0.238-0.37 kg/s; (b) inlet temperatures of heating HTF are 65-85 °C; and (c) inlet temperatures of cooling HTF are 1020 °C. In addition, the system is operated at the following modes: (a) melting (energy storage) and solidification (energy release); and (b) upward and downward HTF flow. The following points should be mentioned regarding the discussion and the developed correlations. The correlations developed in the following sections are valid for the above experimental ranges as well as the type of PCM and HTF used in the measurements and the geometry of the energy storage unit. A limited number of illustrations is given in the following sections. However, the discussion covers all experimental conditions considered in the measurements. Transients of Axial and Radial Temperature Profiles. The measured data for the axial temperature profiles at the outer surface of the HTF tube are shown in Figure 3. The data set includes the melting and solidification modes. Also, the temperature profiles for the inlet and outlet HTF and the surrounding air are shown in the figure. Analysis of the measured axial temperature profiles shows the following: (a) The temperature difference of the inlet and outlet HTF for cooling or heating vary over a range of 0.5-2 °C. (b) Downward flow of the HTF results in a higher temperature for the PCM located at the top of the tube than the PCM located at the bottom of the tube. This behavior remains unaltered throughout the experiment even after melting of the PCM. This is because the molten wax has lower density than the solid wax. Also, the melt density decreases with temperature increase. This implies that for downward HTF flow the system will be stable with no natural convection effects. (c) Upward flow of the HTF results in higher temperature for the PCM located at the bottom of the tube. This behavior is altered as the PCM starts to melt. This is because the hotter melt with lower density moves to the top part of the tube. Consequently, unmelted solid wax and cooler molten wax would descend to lower part of the
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5353
Figure 4. Transient variations in the PCM radial temperature profiles at three axial locations for melting, downward HTF flow, TiH ) 65 °C, and MH ) 0.238 kg/s.
PCM tube. The upper motion of the hotter molten and the downward motion of the cooler molten wax would forms natural convection cells. This would enhance mixing within the PCM melt. (d) The PCM approaches the HTF temperature more rapidly as the HTF temperature is increased. This is because of the increase in the driving force for heating. Increasing the HTF flow rate gives a similar but less pronounced effect. This is because of the increase in the system thermal load. The transients of the radial temperature profiles during melting and solidification are shown in Figures 4 and 5, respectively. Examining the data shown in these figures confirms the findings for the transient data for the axial temperature profiles along the outer surface of the HTF tube. However, the transients of the radial temperature profile at three axial locations give a more detailed picture for the melting and solidification processes, where: (a) the radial temperature profiles indicate higher temperature near the HTF tube during the melting process and lower temperature during solidification, (b) at the outer surface of the PCM tube, the temperature profile has zero gradient because of the effect of the insulation layer,. (c) melting and solidification rates are high at small times. However, these rates diminish at larger times. The high rates are caused by
Figure 5. Transient variations in PCM radial temperature profiles at three axial locations for solidification, downward HTF flow, TiH ) 15 °C, and MH ) 0.238 kg/s.
the large temperature differences between the PCM and the HTF at small times. However, for large times the PCM temperature approaches the HTF temperature. Transient Temperature Contours. Transient temperature contours are shown in Figures 6 and 7. Figure 6 corresponds to large operating times, where the entire PCM has changed to the molten phase. As is shown in Figure 6, the melt is formed of several horizontal layers of hotter melt on top of colder melt. The lowest temperature is found in the lower outer perimeter of the PCM tube. The temperature contours during solidification show radial progression from the outer surface of the HTF tube. As is shown in Figure 7 the coldest zone is found near the HTF tube and hottest zone is found near the outer surface of the PCM tube. The solidification isotherms are almost vertical and the solid layers have a shape similar to that of the HTF tube. Natural convection effects during solidification are negligible because of the continuous decrease in the melt volume
5354 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004
Figure 6. Temperature field in PCM for melting, downward HTF flow, TiH ) 65 °C, MH ) 0.238 kg/s.
Figure 7. Temperature field in PCM for solidification, downward HTF flow, TiH ) 15 °C, and MH ) 0.238 kg/s.
Figure 8. Variation in PCM Nusselt number during melting, upward HTF flow, and as a function of the HTF temperature.
and the small temperature gradient found within the melt in the vertical direction. Variations in the PCM Nusselt Number. Variations in the PCM Nusselt number for melting are shown in Figures 8-11. Results are shown for upward HTF flow. The data for the downward HTF flow are not displayed because of similarities in their dependence on the system parameters. However, the Nusselt number is higher for the upward HTF flow because of natural convection effects. Analysis of the Nusselt number for both types of flow shows the following behavior. (a) Nusselt number increases with the increase in the system temperature or the HTF temperature, Figure 8. This is because at higher temperatures the viscosity of the melt decreases and results in the increase of natural convection within the melt. (b) Nusselt number decreases with the increase in Fourier number, Figure 9. This is because Fourier number is proportional to the melting time. Therefore, increase in the melting time
Figure 9. Variation in PCM Nusselt number during melting, upward HTF flow, and as a function of Fourier number.
Figure 10. Variation in PCM Nusselt number during melting, upward HTF flow, and as a function of Stefan number.
Figure 11. Variation in PCM Nusselt number during melting, upward HTF flow, and as a function of Rayleigh number.
implies lower HTF temperature. (c) Nusselt number increases with the increase in the Stefan number, Figure 10. This is because Stefan number is proportional to the temperature difference of the HTF and the melting point of the PCM. Therefore, higher Stefan number implies higher HTF temperature. (d) For upward HTF flow, the decrease of Nusselt number with the increase in Rayleigh number is caused by the assumptions used to calculate Rayleigh number. The only parameters that vary in Rayleigh number upon the increase of the HTF temperature are (∆TH) and (βP). Rayleigh number is proportional to ∆TH, which is defined as TH - Tm. Also, it is proportional to the thermal expansion coefficient of the PCM, which is defined by βP ) 1/FP ∆FP/∆TP. In this definition, ∆Tp is the temperature difference between the bottom and top of the PCM melt. This implies that Rayleigh is proportional to the ratio (∆TH/∆TP). This ratio is found to
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5355
Figure 12. Variation in PCM Nusselt number during solidification, downward HTF flow, and as a function of the HTF temperature.
Figure 13. Variation in PCM Nusselt number during solidification, downward HTF flow, and as a function of Fourier number.
Figure 15. Variation in PCM Fourier number during melting, upward HTF flow, and as a function of the HTF temperature.
ture driving force in the system. Therefore, decrease in the cold water temperature increases in the temperature driving force and the values of the Nusselt and Stefan numbers. Correlation for the PCM Nusselt Number. The heat transfer coefficient data, for all inlet HTF temperatures and flow rates, are used to develop the Nusselt number correlations for melting and solidification. As discussed before, the heat transfer process for melting with upward HTF flow involves natural convection cells. This phenomenon is taken into consideration for the development of the Nusselt number. On the other hand, the heat transfer process for the other three sets of data is dominated by conduction. These include downward HTF flow for solidification or melting and upward HTF flow for solidification. The Nusselt number correlations include the following: (a) melting with downward HTF flow
Nu ) 1.2565 St-10.0318 Fo-8.0612
(8)
with a coefficient of determination equal to 0.88; (b) melting with upward HTF flow
Nu ) 8.5692 × 1020 St-1.5541 Fo-1.2317 Ra-3.0311
(9)
with a coefficient of determination equal to 0.91; (c) solidification with downward HTF flow
Nu ) 105.0247 St1.3552 Fo-0.8718
(10)
Figure 14. Variation in PCM Nusselt number during solidification, downward HTF flow, and as a function of Stefan number.
with a coefficient of determination equal to 0.93; and (d) solidification with upward HTF flow
decrease at higher HTF temperatures, which results in lower Rayleigh number at higher HTF temperatures. Variations in the Nusselt number for solidification are shown in Figures 12-14. Results are shown for downward HTF flow. The data for the upward HTF flow are not shown because of similarities. Features of the solidification Nusselt number include the following. (a) The Nusselt number decreases with the increase in the HTF temperature, Figure 12. This is because increase in the cold water temperature reduces the driving force for heat transfer and in turn reduces the heat transfer coefficient. (b) The Nusselt number has relatively small dependence on Fourier number, Figure 13. This implies limited variations of Nusselt number during solidification. (c) The Nusselt number increases with the increase in the Stefan number, Figure 14. This is because Stefan and Nusselt numbers are proportional to the tempera-
Nu ) 121.6519 St1.3019 Fo-0.6351
(11)
with a coefficient of determination equal to 0.93. Variations in Fourier Number. Variations in Fourier number for melting and solidification as a function of temperature are shown in Figures 15 and 16, respectively. As is shown in Figure 15 the melting Fourier number varies over a range of 6 to 1. Also, Fourier number for melting decreases with temperature increase. This is because at higher HTF temperatures the driving force for heat transfer increases and as a result, the melting time decreases. The solidification Fourier number varies over a lower range of 0.6-0.4. This is because the solidification time is 1 order of magnitude lower than the melting time. As shown in Figure 16 the increase in the solidification Fourier number with the increase in the temperature
5356 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004
couples is 5 min. Therefore, exceeding the melting temperature might occur within the same cycle or it might occur over two cycles. If reaching the melting temperature takes two measuring cycles then some of the molten wax would have acquired a larger amount of sensible heat. This would increase the solidification time. Conclusions
Figure 16. Variation in PCM Fourier number during solidification, upward HTF flow, and as a function of the HTF temperature.
of the cooling HTF is caused by the decrease in the driving force for heat transfer. As a result the solidification time increases with the increase in the HTF temperature. Scatter of the data at constant HTF is caused by variations in the initial PCM temperature, where higher Fourier numbers correspond to higher initial PCM temperatures. Also, part of the scatter is caused by variations in the HTF flow rate. Correlation of Fourier Number. The Fourier number gives a measure of the melting or solidification times. Fourier number is proportional to the Biot and Stefan numbers in the PCM. The Biot number is the ratio of the heat transfer rate by convection to conduction, while the Stefan number gives the ratio of the sensible heat to the latent heat. In the Stefan number, ∆T depends on the phase change process, i.e., melting or solidification. For melting, ∆T is equal to the difference between the hot HTF and the PCM melting temperature. For solidification, ∆T is equal to the temperature difference of the PCM at the start of the cooling cycle and the cold HTF temperature. The Fourier number correlations include the following: (a) melting with downward HTF flow
Fo ) 0.5848 St-1.3196 Bi -0.0457
(12)
with a coefficient of determination equal to 0.99; (b) melting with upward HTF flow
Fo ) 0.8118 St-1.2928 Bi -0.0957
(13)
with a coefficient of determination equal to 0.98; (c) solidification with downward HTF flow
Fo ) 50.956 St1.3199 Bi -0.8737
(14)
with a coefficient of determination equal to 0.89; and (d) solidification with upward HTF flow
Fo ) 262.285 St1.7196 Bi -1.1884
(15)
with a coefficient of determination equal to 0.89. The above results show higher coefficient of determination for the melting process. This is because time measurements for all experiments cover the same temperature range, i.e., room temperature to melting temperature. On the other hand, measuring the solidification time is not as accurate. This is because switching between the hot and cold HTF is made as all thermocouple readings exceed the melting point. As mentioned before, the measuring cycle for all thermo-
Experimental measurements are performed for phase change energy storage in paraffin wax. The system is formed of a vertically aligned double pipe configuration. In this system, the heat transfer fluid is routed in the inner tube. On the other hand, the PCM is kept in annulus of the two pipes. The experiments included measurements of melting and solidification times as well as the temperature field within the PCM. These data were used to calculate the system thermal load, the heat transfer coefficients within the PCM and HTF. The results of the experimental measurements were then used to calculate a number of dimensionless groups that include Nusselt number, Fourier number, Biot number, Stefan number, and Rayleigh number. The dimensionless groups were then correlated to develop empirical relations for the Nusselt and Fourier numbers. The measured temperature field during melting and solidification is a new addition to the literature of phase change energy storage systems. Measured data and analysis show the presence of natural convection during melting for the case of upward HTF flow. On the other hand, natural convection effects are negligible during melting for the case of downward HTF flow. Similarly, solidification is dominated by condition and has negligible dependence on the HTF flow direction. Acknowledgment This research was supported by the Research Administration of Kuwait University, projectELC-012. Nomenclature A ) Heat transfer area, m2 Bi ) Biot number, Bi ) hH req/kP Cp ) Specific heat at constant pressure, kJ/kg K D ) Tube diameter, m Fo ) Fourier Number, dimensionless, Fo ) (RPt)/(req)2 g ) Gravitational acceleration, m/s2 h ) Heat transfer coefficient, kW/m2 °C k ) Thermal conductivity, kW/m K LMTD ) Logarithmic mean temperature difference, °C M ) Mass flow rate, kg/s Nu ) Nusselt Number, dimensionless, Nu ) hP req/kP Pr ) Prandtl number, dimensionless, Pr ) CpH µH/kH req ) Equivalent tube radius, req ) (DoH - DoP)/2, m Ra ) Rayleigh number, dimensionless, Ra ) gβP CpP F2P req3∆TH/µPkP Re ) Reynolds number, dimensionless, Re ) 4MH/πDiHµH St ) Stefan number, dimensionless, St ) CpP ∆TH/λP t ) Time, s T ) Temperature, °C ∆TH ) Temperature scale in Rayleigh and Stefan numbers, ∆TH ) TiH - Tm, °C ∆TP ) Temperature difference between bottom and top of molten PCM, °C U ) Overall heat transfer coefficient, kW/m2 °C
Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5357 Greek Symbols βP ) Thermal expansion coefficient of PCM, βP ) 1/FP ∆FP/ ∆TP, 1/K RP ) Thermal diffusivity of PCM, RP ) kP/(FP CpP), m2/s µ ) Dynamic viscosity, kg/m s F ) Density, kg/m3 ∆FP ) Density difference of the PCM over a temperature range of ∆TP, kg/m3 λP ) Latent heat of melting/solidification of PCM, kJ/kg Subscripts 1 to 18 ) Location of thermocouple in PCM, at HTF wall and the PCM tube H ) Heat transfer fluid i ) Inlet HTF stream or inner HTF tube m ) Melting point o ) Outlet HTF stream or outer HTF tube P ) Phase change material w ) Wall
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Received for review June 13, 2003 Revised manuscript received March 24, 2004 Accepted May 26, 2004 IE030495B
