Enthalpy and apparent specific heat capacity of the binary solution during the melting process: DSC modeling

Thermochimica Acta 541 (2012) 31–41

Contents lists available at SciVerse ScienceDirect

Thermochimica Acta journal homepage: www.elsevier.com/locate/tca

Enthalpy and apparent specific heat capacity of the binary solution during the melting process: DSC modeling T. Kousksou a,∗ , A. Jamil b , Y. Zeraouli a a b

Laboratoire des Sciences de l’Ingénieur Appliquées à la Mécanique et au Génie Electrique (SIAME), Université de Pau et des Pays de l’Adour – IFR – A. Jules Ferry, 64000 Pau, France École Supérieure de Technologie de Fès, Université Sidi Mohamed Ibn Abdelah Route d’Imouzzer BP 2427, Morocco

a r t i c l e

i n f o

Article history: Received 25 January 2012 Received in revised form 17 April 2012 Accepted 21 April 2012 Available online 30 April 2012 Keywords: Binary mixture Heat transfer Melting process Enthalpy Apparent heat capacity

a b s t r a c t A main purpose of using binary solutions as phase change materials is to benefit from the latent heat or enthalpy difference at melting. In the design of latent heat storage systems, the enthalpy change of the PCM has to be known with high precision. In this article, we show with the help of experimental data and numerical analysis why the use of differential scanning calorimetry measurements is troublesome for dispersed binary solutions inside an emulsion. The article shows how an enthalpy-phase diagram of salt solution during the eutectic and progressive melting can be constructed, gives chart with enthalpy values, apparent specific heat capacity and ice concentration as a function of temperature and initial salt concentration. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Latent heat storage is one of the favorable kinds of thermal energy storage methods considered for effective utilization of renewable energy sources, such as in solar and air conditioning systems. In recent years, research on latent functional thermal fluid (LFTF), a two-phase heat transfer fluid, has attracted more and more attention because of its greater apparent specific heat in its phase change temperature range compared with conventional single-phase heat transfer fluid. Phase change microcapsule slurry and phase change emulsion are two kinds of these novel two-phase heat transfer fluids composed of phase change material particles and heat transfer fluids [1,2]. Since the phase change materials (PCMs) will absorb or dissipate latent heat during the phase change process, they show much greater apparent specific heat. In addition, they may significantly enhance the heat transfer rate between the fluid and the tube wall, reduce mass flow rate and pump energy consumption [3,4]. Therefore they have many potentially important applications in the fields of heating, ventilating, air conditioning, refrigerating and heat exchangers. Many researchers made an endeavor to study the heat transfer enhancement mechanism of such two-phase heat transfer fluids [5–7]. A mixture of tetradecane and hexadecane was used to prepare an emulsion by Lorsch et al. [5]; they found that there would not be tube jam if the diameter of PCM particles was less than

∗ Corresponding author. E-mail address: [email protected] (T. Kousksou). 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2012.04.027

0.1 mm, but an evident supercooling phenomenon was observed. The determination of the heat of fusion and the melting point of some paraffin wax mixtures were described by Choi et al. [6]. The authors used the differential scanning calorimeter (DSC) method to obtain the melting point and the heat of fusion of the mixtures; they observed an increase in the specific heat and heat transfer rate. Heat transfer characteristics during crystallization and melting of the phase change material (PCM) dispersed inside an emulsion are investigated theoretically and experimentally by El Rhafiki et al. [7]. They found that the crystallization and melting processes are not symmetrical because of the supercooling phenomenon. By far the best-known PCM is water. It has been used for cold storage for more than 2000 years [8,9]. Today, cold storage with ice is state of the art and even cooling with natural ice and snow is used again. For temperatures below 0 ◦ C, usually water–salt solutions with a eutectic composition are used. Water–salt solutions consist of two components, water and salt, which means phase separation could be a problem. To prevent phase separation, and to achieve a good cycling stability, eutectic compositions are used. Eutectic compositions are mixtures of two or more constituents, which solidify simultaneously out of the liquid at a minimum freezing point [9]. Therefore, none of the phases can sink down due to a different density. Further on, eutectic compositions show a melting temperature and good storage density. The thermal conductivity of eutectic water–salt solutions is similar to that of water. Water–salt solutions are chemically very stable, but can cause corrosion to other materials like metals. Most of the salt solutions are rather safe, but should not leak in larger amounts.

32

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

Nomenclature cp d dq/dt F,G h K LD LF M P r t TE Tem Tsol Tsol,eq X XE xi xice xsalt z

specific heat capacity (J kg−1 K−1 ) droplet diameter (m) specific heat flow (W kg−1 ) phase diagram functions mass enthalpy (J kg−1 ) heat transfer coefficient (W m−2 K−1 ) heat of dissolution of salt in the solution (J kg−1 ) latent heat of ice melting (J kg−1 ) mass (kg) mass fraction of the dispersed solution radial position (m) time (s) eutectic temperature (◦ C) temperature of the emulsifying medium (◦ C) temperature the binary mixture (◦ C) equilibrium temperature (◦ C) mass fraction of liquid solution eutectic concentration initial concentration of the salt ice mass fraction salt mass fraction space variable (m)

Greek letters ˇ heating rate (K min−1 ) S area (m2 ) ε porosity  thermal conductivity (W m−1 K−1 ) mass density (kg m−3 )  ˚ specific heat flow (W kg−1 ) Subscripts d droplet Eutectic E em emulsifying medium i initial l liquid solid s sol solution

In previous work [10], our research group has proposed a physical model for heat transfers in the case of the melting of a salt solution dispersed inside an emulsion. This model is applied to DSC in order to determine the kinetics of different transformations like the eutectic melting and the progressive melting. The proposed model is based on the energy equation with a heat source proportional to the quantity of ice which melts per time unit in each droplet. The boundary conditions take into account the heat exchange with the calorimeter plate and it is possible to calculate the corresponding heat flow versus time which constitutes the thermogram. It is interesting to note that in the process development stage of LFTF, the knowledge of thermophysical properties of PCMs is essential for design and optimization. The quantity of thermal energy possible to store depends on the enthalpy variation in the working temperature range. Also, the enthalpy function or the apparent heat capacity of the PCM has to be known in order to obtain sufficiently accurate results in numerical simulations [11,12]. This should take into account the temperature range over which the phase transition occurs under real operating conditions. The purpose of this paper is to summarize general expressions of the enthalpy and apparent heat capacity of the sample during

Fig. 1. Binary phase diagram NH4 Cl–H2 O.

eutectic and progressive melting processes of the salt solution. The influence of the thermal gradients in the salt solution on the DSC curve, the mass enthalpy and the apparent specific heat capacity is presented. The paper gives also charts with enthalpy and apparent heat capacity of the binary solution as a function of temperature and initial concentration of the salt.

2. Binary phase diagram Fig. 1 shows the equilibrium phase diagram for water–salt solution (NH4 Cl–H2 O) system. The symbols L, S and L + S denote the liquid phase, the solid phase and the solid–liquid two-phase, respectively. The lowest temperature possible for liquid salt solution is −15.7 ◦ C. At that temperature, the salt begins to crystallize out of solution, along with the ice, until the solution completely freezes. The frozen solution is a mixture of separate solute crystals and ice crystals. This mixture is called eutectic mixture. If the ice, salt and salt-water are present in the binary mixture, and their amounts are not changing over time we must be at the eutectic point (TE = −15.7 ◦ C and XE = 0.195). If the mass fraction of salt in the liquid solution xsalt,l is lower than XE the ice mass fraction xice can be calculated from the liquidus temperature of the binary mixture solution, which is a function of xsalt,l . Tsol = T (xsalt,l )

(1)

Fig. 2. Scheme of the DSC cell.

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

33

Fig. 3. Theoretical and experimental thermograms (NH4 Cl–H2 O).

Once the initial mass fraction of solute xi in the binary mixture before freezing and temperature are known, the equilibrium ice mass fraction is calculated with the following relation: xice (Tsol ) = 1 −

xi xsalt,l (Tsol )

(2)

in which xsalt,l (Tsol ) is calculated from the liquidus curve, the inverse of Eq. (1). 3. Experiments Experiments were performed using solutions of ammonium chloride NH4 Cl and water at different concentrations, smaller than the eutectic concentration XE = 0.195 (see Fig. 1). These solutions are dispersed by a high speed stirrer within an emulsifying medium made of a mixture of paraffin oil and lanolin. Emulsions were elaborated in a special tank to prevent any segregation and to obtain a homogeneous mixture. To maintain a constant temperature during experiments, and to be able to control it, the stirring tank was

placed into a thermostated vessel. It was necessary that the emulsion retain its characteristics when it came into contact with the walls of the crucible for the calorimeter. Differential scanning calorimeter is one of the most widely used analytical instruments because of the ease with which it can provide large amounts of thermodynamic data. From a single DSC test that consists in regularly cooling down and heating of a sample, it is expected to obtain qualitative and quantitative information on the phase transitions of a sample, such as transition temperature, enthalpy, heat capacity, specific heat, and latent heat. The thermal behavior of the mixtures was studied using PYRIS DIAMOND DSC of PerkinElmer. The temperature scale of the instrument was carefully calibrated by the melting point of pure ice (273.15 K or 0 ◦ C) and mercury (234.32 K or −38.82 ◦ C). The principle of the power-compensation is widely detailed in Refs. [13,14]. The DSC experiments were conducted by placing approximately 10 mg of each binary mixture in a standard aluminum DSC sample pan (see Fig. 2). The resolution of the balance is about ±0.001 mg. A sample encapsulating press was used to seal samples in these

34

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

a function of the emulsion porosity ε and of the droplet diameter d, namely: B=

6(1 − ε) d

(6)

and e P sol

ε=1−

(7)

where P is the ratio between the mass of the dispersed solution and the mass of the emulsion and e is the mass density of the emulsion. During the isothermal melting process (i.e. eutectic melting), the energy balance is quite different since Tsol = TE . (1 − ε)ice A

∂xice = −KB(Tem − TE ) ∂t

(8)

The coefficient A is given by the following expression A = LF +

Fig. 4. Effect of the initial mass fraction of the solute on the shape of the thermogram.

pans. An empty hermetic pan was used as a reference in all measurements. The DSC was calibrated for temperature and heat flow values using the melting point and enthalpy of fusion of high purity indium according to the standard procedures described in the user’s manual. The apparatus (Perkin-Elmer DSC) gives dq/dt, the difference between the heat powers maintaining the plate supporting the active cell containing the emulsion and the plate supporting the reference cell dq = dt

 dq  dt

active cell

−

 dq  dt

(3) reference cell

As indicated in Ref. [14], the power exchanged at the reference plate is practically constant and equal to (dq/dt)ref = ˇcR where ˇ is the heating rate and cR is the specific heat capacity of the reference cell. To simplify the physical model we will omit this term from the calculation of dq/dt (equivalent to the shift in the baseline).

(1 − ε)(c)sol



∂Tem ∂r

∂Tem ε(c)em = ε ∂t

(1 − ε)( c)sol

1 ∂Tem ∂2 Tem ∂2 Tem + + r ∂r ∂r 2 ∂z 2

∂Tsol = KB(Tem − Tsol ) ∂t

+ KB(Tsol − Tem )

(4)

(5)

where K is the constant heat transfer coefficient and B is the superficial droplet area per unit volume which is classically expressed as

(10)





−em

 



∂Tsol ∂x = (1 − ε)ice LF sol + KB(Tem − Tsol ) ∂t ∂t

In the above equation, the unknowns are only the temperatures Tsol since the ice mass fractions xice are themselves function of the solution temperatures according to Eq. (2) (see Ref. [14]). To take into account the air between the emulsion and the cover of the cell, we consider two different heat exchange coefficients K1 and K2 (see Fig. 2). So the boundaries conditions are:

4. Previous work



(9)

During the non-isothermal melting (i.e. progressive melting), we suppose that the heat of solute generated by dilution due to ice melting is negligible. To account for the latent heat effect in the phase change, occurring over a finite range of temperatures, the general enthalpy method of Voller and Swaminathan [15] is adopted. So, the appropriate energy equation for the binary solution is:

−em

The governing equations for heat transfer within an emulsion are obtained by considering a representative elementary volume (VER) containing emulsifying medium and salt solution droplets with volume fractions ε and (1 − ε) [10]. They consist of the binary solution and emulsifying energy equations and take into account the thermodynamic non-equilibrium between the two phases of different temperatures (Tsol , Tem ). We have modeled the active cell with a cylinder whose dimensions are 2R0 = 4.25 mm for the diameter and Z = 0.82 mm for the height of the emulsion (see Fig. 2). So the emulsifying medium and PCM temperatures depend on the two space variables r and z and also on the time t. The governing equations for the emulsifying medium and the solution temperatures are:

XE LD 1 − XE

−em

=0 r=0

∂Tem ∂r ∂Tem ∂z ∂Tem ∂z

(11)

 

r=R



z=0

= K2 (Tem − Tplt )

(12)

= K2 (Tem − Tplt )

(13)

= K1 (Tem − Tplt )

(14)

z=Z

where Tplt , the temperature of the plates is programmed to be linear function: Tplt = ˇt + Ti

(15)

At t = 0 the initial conditions are Tem (r, z, 0) = Tsol (r, z, 0) = Ti and xice (r, z, 0) = 1 − xi . Because the thermal conductivity of air is smaller than that of the metal of the cell, we consider that all the energy is transmitted to the plate by the lower boundary of the cell. So, ˚ is the sum of the thermal fluxes through the walls of the metallic cell. ˚=

 dq =− Kj (Tj − Tplt )Si dt

(16)

j

where Kj = K1 or K2 . The values of physical characteristics required in the different equations have been determined experimentally or taken in the literature [16–20], except the coefficients of heat exchange (K1 and K2 ) that have been fitted from exploratory experiments. The fitted values are K1 = 1200 W m−2 K−1 and K2 = 800 W m−2 K−1 .

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

35

Fig. 5. Influence of the heating rate on Tsol , Tem , X and xice at the center of the sample.

Using this model, it is possible to study the effect of various parameters on the melting kinetic inside an emulsion. For each initial mass fraction of the salt we have traced experimental and numerical specific heat flow  for different heating rates (see Figs. 3–5). The thermograms exhibit isothermal (eutectic melting) and non-isothermal (progressive melting) solid–liquid transition peaks. The fit between the experimental and the calculated curves is good: the rounded form of the top of the thermogram is reproduced and its width is the same. We note that when the initial mass fraction of the solute is much smaller than the eutectic concentration, the amount of the ice transformed during the eutectic melting becomes very little. The main difficulty of DSC characterization of PCM dispersed inside an emulsion lies in the heterogeneity and structure of the sample as it significantly affects the details of the heat transfer between the sample pan and PCM material. Direct utilization of the measured DSC curves could result in an inexact representation of the thermophysical properties of the sample during the phase change process. Obviously, the same sample should be

characterized by one curve only. The question is, which curve represents best the properties of the sample? Repeating the measurement with different heating rates gives results as shown in Fig. 3. Focusing on the end of the peaks a clear trend can be observed. The peak is shifted toward higher temperatures as the heating rate increases. This can be explained by an increasing thermal gradient in the sample. When a sample is heated in a DSC, heat enters from the outside of the crucible and is absorbed by the sample. During the heating process there is constantly heat supplied to the sample, and an internal gradient is created. This gradient increases with increasing heating rate (see Fig. 5). We can also note that the peak corresponding to the eutectic melting becomes larger when the heating rate increases. Increase in ˇ leads to the disappearance of the non-isothermal peak. It is clearly seen that the use of high heating rates mask the essential information concerning the progressive melting. This effect on the peak temperatures is caused by the thermal resistance between the sample and DSC plate form. To describe with accuracy the melting process in DSC cells it is desirable to use lower heating rates [21–23]. However, lower

36

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

Fig. 6. Mass enthalpy of the binary solution versus Tsol for different xi at the center of the sample.

Fig. 8. Ice mass fraction of the binary solution versus Tsol for different xi at the center of the sample.

heating rates are often associated with longer measurement times and thus higher measurements costs. Therefore, a good measurement has to find a balance of a tolerable uncertainty and reasonable costs and effort.

value is not the equilibrium value. Due the thermal gradients inside the sample, Eq. (17) is used to estimate the enthalpy values of the sample.

5. Enthalpy of the sample

hsample = Phtot + (1 − P)htot em sol

(17)

where The integral of the curves and the onset of the peaks are found to have little dependence on the heating rate. Therefore, for binary solutions, the onset of the peak is commonly used to mark the eutectic melting temperature, and the integral of the peak denotes the melting enthalpy. However, in the context of binary mixture, this is not a useful approach, as the information needed is the slope of the enthalpy function h(T) and not just the two punctiform values TE and h. It is interesting to note that during dynamic measurements, the sample is not in thermal equilibrium, and therefore the measured

= htot sol

N 

hsol,j (Tsol,j )

(18)

j=1

and htot em =

N 

hem,j (Tem,j )

(19)

j=1

where N is the number of the representative elementary volume (VER) in the sample. In our case the reference state for enthalpy calculations is chosen to be the solid phase for both ice and salt. The pressure is supposed to stay constant, equal to 1 atm. The enthalpy of pure ice, salt and emulsifying medium in each VER can be evaluated by simple relations (20)–(22):



Tem

hem (Tem ) =

cem (Tem ) dTem Ti



(20)

Tsol

hice (Tsol ) = −LF +

(21)

cice (Tsol ) dTsol Ti



Tsol

hsalt,s (Tsol ) = −LD +

csalt,s (Tsol ) dTsol

(22)

Ti

During the eutectic melting, the mass enthalpy of the binary solution is the sum of the mass enthalpies of ice, salt and liquid solution at the eutectic temperature hsol (TE ) = xice (TE )hice (TE ) + xsalt,s (TE )hsalt,s (TE ) + (1 − xsalt,s (TE ) − xice (TE ))hl (TE , xsalt,l (TE ))

(23)

where Fig. 7. Apparent specific heat capacity the binary solution versus Tsol for different xi at the center of the sample.

XE =

xi − xsalt,s 1 − xsalt,s − xice

(24a)

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

37

Fig. 9. Mass enthalpy of the sample versus Tplt for different xi .

and X = 1 − xsalt,s − xice

(24b)

where X is the mass fraction of the liquid solution in the sample. It is interesting to note that there is discontinuity of the enthalpy function when the temperature approaches that of eutectic temperature and the expression of the apparent heat capacity discontinuity at TE h =

lim h −

Tsol →T − E

lim h = hsol (TE+ ) − hsol (TE− ) = / 0

Tsol →T + E

(25)

where

From a mathematical point of view, Eq. (23) is non differentiable at TE and the heat capacity of the binary solution becomes infinite during the eutectic melting. During the progressive melting, the mass enthalpy of the binary solution is the sum of the mass enthalpies of ice and liquid mixture at the same temperature [24,25]: hsol (Tsol ) = xice (Tsol )hice (Tsol ) + (1 − xice (Tsol ))hl (Tsol , xsalt,l )

If the temperature–concentration phase diagram of the binary solution is known as functions Tsol = F(xsalt,l ) or xsalt,l = G(Tsol ) it is possible to write xice (Tsol ) = 1 −

hsol (TE+ ) = xice (TE+ )hice (TE+ ) + (TE+ )) + (1 − xi − xice (TE+ ))hl (TE+ , xsalt,l

(26)

(27)

xi G(Tsol )

(29a)

and X = 1 − xice

hsol (TE− ) = xice (TE− )hice (TE− ) + xsalt,s (TE− )hsalt,s (TE− , xsalt,s (TE− ))

(28)

(29b)

Starting from Eq. (28) and considering the salt mass fraction of the whole mixture xi as parameter, it is possible to express the

38

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

Fig. 10. Apparent specific capacity of the sample versus Tplt for different xi .

enthalpy of the slurry as a function of the binary solution temperature only: hsol (Tsol ) =



1−

xi G(Tsol )



xi h (T , G(Tsol )) G(Tsol ) l sol

hice (Tsol ) +

(30)

An interesting property of Eq. (30) is that the enthalpy varies continuously with temperature; Eq. (30) implies that there is no discontinuity in the enthalpy of the binary solution when the temperature approaches that of thermodynamic equilibrium: lim h =

− Tsol →Teq

lim h = hsol (Teq )

(31)

+ Tsol →Teq

Starting from Eq. (30), it is possible to derive a general expression for the apparent heat capacity of the binary solution defined by: cp,app (Tsol , xi ) =



 dh(T , x )  sol i dTsol +

dxice dTsol



= p

∂h(Tsol , xi ) ∂Tsol

∂h(Tsol , xi ) ∂xice





xice ,p

(32) Tsol ,p

which becomes:

cp,app (Tsol , xi ) = xice cp,ice (Tsol ) + (1 − xice )cp,l (T, xsalt,l )



+

dxice dTsol

 hice − hl + (1 − xice )

∂hl (Tsol , xi ) ∂xice





(33) Tsol ,p

with



∂hl (Tsol , xsalt,l ) ∂xice



 = Tsol ,p



∂xsalt,l

 =

∂hl (Tsol , xsalt,l )

∂hl (Tsol , xsalt,l ) ∂xsalt,l



Tsol ,p

dxsalt,l dxice xi

Tsalt ,p (1 − xice )

2

During the progressive melting, the apparent heat capacity of the binary solution never reaches infinite values. Eq. (34) allows the calculation of the limits of the apparent heat capacity when the binary solution temperature tends toward the solid–liquid

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

39

Fig. 11. Mass enthalpy of the sample versus Tsol for different xi .

equilibrium temperature of the binary solution in the absence of ice (with xsalt,l = xi ): lim cp,app = cp,l (Tsol , xi ) +

− Tsol →Teq

dxice dTsol



hice − hl + xi

∂hl (Tsol , xi ) ∂xsalt,l



(34)

with (dxice /dTsol )(Teq ) = xi ((dG(Teq )/dT)/(G(Teq ))2 ) = / 0. From Eq. (33) the expression of the apparent heat capacity discontinuity at Teq cp,app =

lim cp,app −

− Tsol →Teq

= xi

dG/dT G2



lim cp,app

+ Tsol →Teq

hice − hl + xi

dhl (Teq , xi ) dxsalt,l

 (35)

To sum the progressive melting of the binary solution is characterized by the continuity of the enthalpy and a discontinuity of the apparent heat capacity at the equilibrium temperature. By comparison, the phase changes of eutectic solution or pure water result in a discontinuity of the enthalpy, whereas the heat capacity becomes infinite. This fact is illustrated by Figs. 6–8 which show the evolutions of the enthalpy, the apparent heat capacity and the ice concentration versus the binary solution temperature for different

initial concentrations xi . It can be seen that discontinuities in the curves or in the slope of the curves occur at the eutectic temperature TE and the solid–liquid equilibrium temperature Teq (xi ). Figs. 9 and 10 present the mass enthalpy and the specific heat capacity of the sample versus the plate temperature for different heating rates. We note that it is difficult to describe with accuracy the melting process (eutectic and progressive melting) inside the sample by increasing ˇ. The main reason for this difficulty is due to the temperature gradients inside the sample. Additionally, the large gradient is formed at temperatures close to the phase change temperature, where a high precision in the shape of the enthalpy function is desired. Unfortunately, users of the DSC technique often represent thermophysical properties like enthalpy and apparent specific heat capacity as function of the plate temperature without taking into account the effect of the thermal gradients inside the sample. This representation can cause significant errors in determining the thermophysical properties of the studied materials using DSC technique. To remedy this problem, we felt that it was more appropriate to represent the specific enthalpy and the apparent specific heat capacity function versus the sample temperature (for example at the center of the sample) as seen in Figs. 11 and 12. Using this representation, we can describe and predict with accuracy the evolution of the enthalpy and the apparent

40

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41

Fig. 12. Apparent specific capacity of the sample versus Tsol for different xi .

specific heat capacity of the binary mixture during the eutectic and progressive melting. Unfortunately, the sample temperature is inaccessible from DSC technique. 6. Conclusion The general expression of the enthalpy and apparent heat capacity of the binary solution show that the non-isothermal melting process is characterized by the continuity of the enthalpy and a discontinuity of the apparent heat capacity at the equilibrium temperature Teq . By comparison, the eutectic melting results in a discontinuity of the enthalpy, whereas the heat capacity becomes infinite at TE . During dynamic measurements, the sample is not in thermal equilibrium, and therefore the enthalpy value is not the equilibrium value. To characterize with precision the sample the effect of the heating rate needs to be considered [21–23]. References [1] S. Gschwander, P. Schossing, H.M. Henning, Micro-encapsulated paraffin in phase change slurries, Sol. Energy Mater. Sol. Cells 89 (2005) 307–315. [2] R. Yang, H. Xu, Y. Zhang, Preparation, physical property and thermal physical property of phase change microcapsule slurry and phase change emulsion, Sol. Energy Mater. Sol. Cells 80 (2003) 405–416.

[3] T. El Rhafiki, T. Kousksou, Y. Zeraouli, Thermal performance of microencapsulated phase change material slurry: laminar flow in circular tube, J. Thermophys. Heat Transfer 24 (2010) 480–489. [4] T. Kousksou, T. El Rhafiki, K. El Omari, Y. Zeraouli, Y. Le Guer, Forced convective heat transfer in supercooled phase-change material suspensions with stochastic crystallization, Int. J. Refrig. 33 (2010) 1569–1582. [5] H.G. Lorsch, K. Murali, Y.I. Cho, Improving thermal and flow properties of chilled water. Part 1. Material selection and instrument calibration, ASHRAE Trans. 103 (1997) 188–197. [6] E. Choi, Y.I. Cho, H.G. Lorsch, Thermal analysis of the mixture laboratory and commercial grades hexadecane and tetradecane, Int. Comm. Heat Mass Transfer 19 (1992) 1–15. [7] T. El Rhafiki, T. Kousksou, A. Jamil, S. Jegadheeswaran, S.D. Pohekar, Y. Zeraouli, Crystallization of PCMs inside an emulsion: supercooling phenomenon, Sol. Energy Mater. Sol. Cells 95 (2011) 2588–2597. [8] I. Dincer, M.A. Rosen, Thermal Energy Storage Systems and Applications, John Wiley & Sons, London, 2002. [9] B. Zabla, J.M. Marin, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications, Appl. Therm. Eng. 23 (2003) 251–283. [10] T. Kousksou, A. Jamil, S. Gibout, Y. Zeraouli, Thermal analysis of phase change emulsion, J. Therm. Anal. Calorim. 96 (2009) 841–852. [11] E. Palomo del Barrio, J.L. Dauvergne, A non-parametric method for estimating enthalpy temperature functions of shape-stabilized phase materials, Int. J. Heat Mass Transfer 54 (2011) 1268–1277. [12] T. Kousksou, A. Jamil, K. El Omari, Y. Zeraouli, Y. Le Guer, Effect of heating rate and sample geometry on the apparent specific capacity: DSC applications, Thermochim. Acta 519 (2011) 59–64. [13] T. Kousksou, A. Jamil, Y. Zeraouli, J.P. Dumas, DSC study and computer modeling of the melting process in ice slurry, Thermochim. Acta 448 (2006) 123–129.

T. Kousksou et al. / Thermochimica Acta 541 (2012) 31–41 [14] T. Kousksou, A. Jamil, Y. Zeraouli, J.P. Dumas, Equilibrium liquidus temperatures of binary mixtures from differential scanning calorimetry, Chem. Eng. Sci. 62 (2007) 6516–6523. [15] V.R. Voller, C.R. Swaminathan, General source-based method for solidification phase change, Numer. Heat Transfer B 19 (1991) 175–189. [16] J. Timmermans, The Physico-Chemical Constants of Binary Systems in Concentrated Solutions, Vol. 4, Inderscience Publishers, New York, 1960. [17] G. Beggerow, Heats of mixing and solution, in: Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology—New Series, Group 4: Physical Chemistry, Band 2, Springer, Berlin, 1976. [18] D.R. Lide, Handbook of Organic Solvents, CRC Press, Boca Raton, 1995. [19] D.R. Lide, CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 84th edn, CRC Press, Boca Raton, 2004. [20] V.M.M. Lobo, Handbook of Electrolyte Solutions, Elsevier, Amsterdam, 1989.

41

[21] B. He, V. Martin, F. Setterwall, Phase transition temperatures ranges and storage density of paraffin wax phase change materials, Energy 29 (2004) 1785–1804. [22] A. Lazaro, E. Güther, S. Hiebler, H. Mehling, S. Hiebler, J.M. Marin, B. Zalba, Verification of a T-history installation to measure enthalpy vs. temperature curves of phase change materials, Meas. Sci. Technol. 17 (2006) 2168–2174. [23] E. Güther, S. Hiebler, H. Mehling, Determination of the heat storage capacity of PCM and PCM-objects as a function of temperature, in: Ecostock 2006, Thermal Energy Storage Conference, 2006. [24] O. Lottin, V. Ayel, H. Peerhossaini, Ice slurries phase transition thermodynamics: relations for determining concentration–temperature domains of application, Int. J. Refrig. 27 (2004) 520–528. [25] A. Melinder, Accurate thermophysical property values of water solutions are important for ice slurry modeling and calculations, in: Proceedings of the Third Workshop on Ice Slurries of the International Institute of Refrigeration, Horw/Lucerne, Switzerland, May 16–18, 2001, pp. 11–18.