Techniques for the Thermal Analysis of PCM

Abstract

Thermal Energy Storage (TES) technologies based on Phase Change Materials (PCMs) with small temperature differences have effectively promoted the development of clean and renewable energy. Today, accurate thermal characterization is needed to be able to create an optimal design for latent heat storage systems. The thermo-physical properties of PCMs, namely latent heat, phase-change temperatures, enthalpy and specific heat capacity are obtained by means of differential scanning calorimetry (DSC), which is one of the most widely used techniques to study reactions related to the transformation of a material subjected to temperature constraints. This method presents some limitations due, among other things, to the fact that only a very small quantity (less than 90 mg) of material can be tested. Indeed, the small mass samples, taken out of the large testing specimen and out of testing system, is not representative of the thermal behavior of a material on a large scale. The Transient Guarded Hot Plate Technique (TGHPT) presents several advantages when compared to the commercially available thermal analysis methods (DSC, DTA) to determine PCM thermophysical properties. The most significant are large sample amount, optimized measuring time and a simple and economical built up.

1. Introduction

Phase change materials (PCMs) are thermal storage materials with a high storage density for small temperature range applications. The determination of the thermo-physical properties is a key step not just for the application itself but also for the material selection to define the suitability of a material for use in TES. The choice of the suitable thermal analysis method for experimental data acquisition depends on the device outputs, measured values accuracy, experimental setup requirements as sample size, influence of heating/cooling rate maintenance and equipment price, the implementation, etc. There are different thermal analysis techniques to characterize materials and the convenience to use them relies on the properties that want to be determined. The non-steady-state or transient technique records a measurement during the heating/cooling process. The method determines the enthalpy change of the PCM as a function of temperature with high precision by means of transient sensors. Depending on the application, the amount of PCM used can vary from a few (milli) grams (e.g., cooling of electronic equipment or clothes) up the kilograms (e.g., storage in a solar thermal power plant or in the walls of buildings in thermal management and occupant comfort). To determine the specific heat and latent heat of materials a number of thermal characterization techniques help to provide better results especially differential scanning calorimetry (DSC) are commonly used [1]. DSC is an effective method to characterize the thermal behavior of PCMs, and to determine their TES capacities, in terms of transition temperature, latent heat and specific heat capacity and its stability throughout the various melting and crystallization cycles. Using the data measured by the DSC method, it is also possible to represent the enthalpy change versus temperature and determine the amount of stored/released energy in a given temperature interval. In case of the heat capacity measurement for a sample which does not undergo phase change, the energy supplied is weak and generally not very variable. On the other hand, in the case of a fusion process, there is a rapid transient which require important heat rates from the DSC. The thermal imbalance between the two cells is then very important although the quantity of product remains low. DSC presents some problems in analyzing PCM due to their high enthalpy density per unit volume: the small sample amount (less than 90 mg), the sample size influence on its thermal behavior, the response dependence on the used heating rate, repeatability when undergoing huge number for solidification/melting cycle. For large size samples, the melting process occurs gradually through the material. The latter is then heterogeneous and the two phases may coexist over long periods of time before a complete fusion. Moreover, heat conduction in the solid and convection in the liquid occur [2]. This strongly influences the global (or apparent) behavior of the PCM. In practical application, the material volume is much more important, up the kilograms for instance, so testing using a noninvasive method for latent and specific heat determination is necessary. It was found that identification of thermophysical properties of PCMs over several cycles (solidification and fusion) requires the design of a new experimental device Transient Guarded Hot Plate Technique (TGHPT). The TGHPT being an alternative to DSC measurements allows one to determine the same thermophysical properties as DSC.

2. Differential scanning calorimetry (DSC)

DSC is nowadays the most used technique to determine the melting/solidification points and the latent heat of phase change and specific heat capacity of PCM. It is also useful to observe other phenomena such as supercooling, hysteresis and glass transition [1]. The TA Instruments DSC is a “HEAT FLUX” type system where the differential heat flux between a reference (e.g., sealed empty Aluminum pan) and a sample (encapsulated in a similar pan) is measured. The measuring device operates in the temperature range from −150 to 700°C. To attain information on the heat flows corresponding to the temperature fluctuations the differential scanning calorimeter uses an operation analogue to Ohm’s Law. In DSC analysis, the equipment has two melting crucibles, one empty and used as the reference, and the other with the substance to analyze (sample). Then it is programmed an ascendant ramp of temperature versus time. It was found that the difference between the two melting pots to obtain a signal. A schematic diagram of Heat Flux DSC is shown in Figure 1.

Figure 1.

Schematic diagram of Heat Flux DSC.

The sample and the reference are placed symmetrically in the furnace. The furnace is controlled under a temperature program and the temperature of the sample and the reference are changed. During this process, three situations can occur with respect to the sample:

• no reaction or phase transition and no peak results

• The PCM thermal properties (melting temperature, latent heat) during the endothermic peak results

• The thermal measurement data (solidification temperature, latent heat) during the exothermic phase transition process.

The thermogram is a plot of heat flow against temperature profile. During thermal process reactions either liberate or absorb heat. Thus, when ∆H is positive (endothermic reaction), the sample heating device is energized and a positive signal is obtained; when ∆H is negative the reference heating device is energized and a negative signal is obtained. The peak areas in DSC are proportional to the amount of sample, the heat of reaction.

Commonly, calorimetric measurements on PCMs affect the shape, precision and accuracy of the experimental results are:

2.1 Instrumental factors

• Furnace heating rate (A fast heating rate may minimize the data acquisition time compromising salient features of the material property)

• Obtain a thermal profile with a calibration standard (e.g., sapphire, water, gallium and indium) using the same scan conditions. Provides a calibration factor that translates the measured Heat Flow units in (mW) to Heat Capacity units (J/g°C).

• Furnace atmosphere (e.g., inert, argon, nitrogen, oxygen, helium…).

• Geometry of sample holder and location of sensors (variations in baseline).

• Sensitivity of recording mechanism.

• Composition of sample container.

2.2 Sample characteristics

• Structure and amount of the sample (proper thermal contact).

• Heat of reaction.

• Sample packing.

• Nature of sample.

• Thermal conductivity.

2.3 Characterization PCM materials using DSC techniques

DSC technique allows to quantitatively determine in situ the thermodynamic changes occurring during the transformation of a solid into a liquid (heating) which directly characterizes PCM thermal properties (i.e., enthalpy, specific heat capacities and melting point).

For a TES system, it is necessary to take into account some characteristics that a phase change material must meet in order to be considered competitive and suitable for its function. These are physical, chemical, thermodynamic, kinetic and technical characteristics [3]:

• Phase change temperature suitable for the process or application.

• Phase change taking place at a unique temperature, or in a very small phase change interval.

• High phase-change enthalpy to provide a high energy storage density.

• Low price, to be competitive with other thermal storage options (heat or cold).

The correct choice of DSC measurements conditions is very important input to thermal characterize of PCM to obtain phase change temperature range and the relationship of specific heat capacity with temperature (Cp-T). Accurate determination of phase transition parameters should provide robust insights about the performance of the PCM, including energy storage capacity and phase change temperature, during several charging and discharging cycles, to meet the design requirements of thermal energy storage applications and to prevent potential failures. Based on the typical DSC thermogram, shown in Figure 2, the measured melting temperature range was usually determined manually. While some researchers recognized the temperature range between the onset temperature ($T_{0\mathit{\text{nset}}}$) and the endset temperature ($T_{\mathit{\text{endset}}}$) as the actual melting temperature range. The endset melting temperature depends on the measurement conditions (heating rate, sample mass, heat transfer).

Figure 2.

Typical characteristics of a DSC thermogram. The blue shaded area $\left(∆H\right)$ represents the enthalpy change during transition (total latent heat) of PCM, $T_1$ and $T_2$ are the temperature range at which the transition process occurs,$T_m$: Melting temperature, and $T_{0\mathit{\text{nset}}}$: Is the onset temperature.

From the sample heat–flux signal, the enthalpy $h\left(T\right)$ is determined by integration of every peak. The enthalpy-temperature curves are more useful in PCM research field and can be determined as the sum of the enthalpy intervals. Compared to the DSC thermogram, the enthalpy-sum curves perform the best representation to determine the sum of both latent and sensible heat as a function of temperature. The current way has gained increasing attention to characterize and compare the materials by one curve only.

It is of vital significance the determination of the enthalpy of PCM as a function of temperature with sufficient accuracy in enthalpy and phase change temperature range is an important data especially for the the numerical analysis of TES system.

Based on the recorded heat flow (DSC signal), changes in enthalpy (latent heat) or the specific heat capacity (sensible heat) of an examined sample are determined by recording the absorbed heat between two equilibrium states, assigned as baselines of the acquired measurement curves [4]. From the specific heat, the heat flux can be obtained as a function of temperature, and the specific enthalpy is determined easily by integration procedures from Eq. (1), as follows:

$$∆H=\underset{T_1}{\overset{T_2}{\int }}{C}_p\left(T\right).\mathit{dT}=\underset{T_1}{\overset{T_2}{\int }}\frac{\raisebox{1ex}{$\partial Q$}\!\left/ \!\raisebox{-1ex}{$\partial t$}\right.}{\raisebox{1ex}{$\mathit{dT}$}\!\left/ \!\raisebox{-1ex}{$\mathit{dt}$}\right.}.\mathit{dT}=\underset{T_1}{\overset{T_2}{\int }}\frac{\partial Q}{\partial T}.\mathit{dT}$$E1

Where $∆h$ is the enthalpy (latent heat or energy storage between the temperature increments $T_1$ and $T_2$) in units of J/g, $\mathit{Cp}$ is the specific heat capacity at constant pressure in units of J/(g.K), $T_1$ and $T_2$ represent the temperature range at which the storage operates, $\raisebox{1ex}{$\partial Q$}\!\left/ \!\raisebox{-1ex}{$\partial t$}\right.$ is the DSC heat flow signal in units of W/g, and $\raisebox{1ex}{$\mathit{dT}$}\!\left/ \!\raisebox{-1ex}{$\mathit{dt}$}\right.$ is the DSC heating rate in units of °C/sec.

As shown in Figure 3, the melting latent heat ($∆H$), total energy storage capacity, melting temperature ($T_m$), and specific heat capacity of the liquid and solid phases can be directly taken from the curve.

Figure 3.

The enthalpy sum as a function of temperature for (a) an ideal PCM, (b) real PCM.

The enthalpy sum as a function of temperature can be determined using Eq. (2) as follows:

$$H_{\mathit{sum}}\left(T_i\right)=\sum _{k=0}^{i-1}H\left(T_k\right)+H\left(T_i\right)$$

$$H\left(T_i\right)=\underset{T_i}{\overset{T_{i+1}}{\int }}\frac{\raisebox{1ex}{$\partial Q$}\!\left/ \!\raisebox{-1ex}{$\partial t$}\right.}{\raisebox{1ex}{$\mathit{dT}$}\!\left/ \!\raisebox{-1ex}{$\mathit{dt}$}\right.}\ast \mathit{dT}$$E2

Where $H_{\mathit{sum}}\left(T_i\right)$ is the enthalpy sum or energy storage between the reference’s initial temperature ($T_0$) and the final temperature ($T_i$), $H_{\mathit{Ti}}$ is the enthalpy at a single temperature increment between two $T_i$ and $T_{i+1}$, $\raisebox{1ex}{$\partial Q$}\!\left/ \!\raisebox{-1ex}{$\partial t$}\right.$ is the heat flow in units of W/g, and $\raisebox{1ex}{$\mathit{dT}$}\!\left/ \!\raisebox{-1ex}{$\mathit{dt}$}\right.$ is the DSC heating rate in units of °C/sec.

For accurate results, changes in enthalpy (latent heat) or the specific heat capacity (sensible heat) of an examined sample are determined by recording the absorbed heat between two equilibrium states, assigned as baselines of the acquired measurement curves. It is worth highlighting that the baseline-construction due to the DSC measurement of PCMs requires a careful procedure to achieve reliable results.

1. The heating/cooling rate effects (Trade-off between sample attaining thermal equilibrium and data acquisition times. This is done by using the real sample measurement for each temperature range and an accurate calibration using the heating rate which will be applied to the sample starting from fast rates and slowing down the heating and cooling rates of consecutive cycles by halves the previous).

2. Calibration of sensors is only one application of reference materials (e.g., sapphire, water, gallium and indium). An accurate calibration using the heating rate which will be applied to the sample is crucial with regard to all these usages thus must cover not only the temperature range, but also specifics of equipment including sample size, cost, and safety etc.

3. Measurement of the empty crucible using the determined heating and cooling rates.

4. Structure and mass of the sample (proper thermal contact) using the selection of the proper “heating rate”.

   1. Each sample test was repeated four times to ensure reproducibility of the experiments.

   2. Considering 2 different (low and high) sample masses to be tested.

5. Analysis of data

   1. Sample positioning on the DSC stage (the baseline would be a flat line of zero milliwatts).

   2. Subtract the baseline data from the sample and the calibration standard (e.g., sapphire) data, prior to analysis [Remember to change the Heat Flow (y-axis) units to mW, before subtracting the data, to ensure identical units for the sample and baseline profiles].

   3. Data evaluation; the latent heat capacity of melting and freezing of each sample was determined by numerical integration of the area under the peaks of phase change transitions.

The specific heat capacity is a key parameter for PCM, this physical property is essential to conduct sensible heat process (before and after phase transitions). From the known masses of PCM and reference, and the specific heat capacity of the standard, the specific heat capacity of the PCM is calculated based on the DSC heat-flow curve at any point of time. The conversion between time and temperature is finally done via the recorded temperature ramp.

The specific heat capacity of the PCM material can be expressed using Eq. (3):

$$C_p\left(T\right)=\left[\frac{60E}{H_r}\right]\ast \frac{∆y}{m}$$E3

$\text{Where}\mathit{Cp}\left(T\right).$ is the specific heat capacity of the PCM material at the temperature $\left(T\right)$ of interest, $E$: cell calibration coefficient at the temperature of interest (dimensionless), $H_r$: the heating rate in °C/min, and $∆y$: the deflection in the $y$ axis between the baseline curve and sample measurement curve at the temperature of interest in $\mathit{mW}$ and $m$ is the sample mass in $\mathit{mg}$

As seen in Figure 3, heat capacities and changes in heat capacity can also be determined from the enthalpy-temperature curves. While changing phase during a measurement, the sample is far away from thermal equilibrium. In contrast to materials without a phase change or with high thermal conductivity, the slope of the sensible heat part (the solid and liquid phase region) in the enthalpy-temperature curve is equal to the specific heat capacity of the tested material.

The heat capacity of the sample is computed by assuming that the thermal resistance of reference and sample crucible is the same. The thermal resistance is determined by a calibration using standard materials with well-known heat of fusion. The temperature sensors by the melting temperatures (onset temperatures) of these materials. In general, for a solid to liquid phase change process, the specific heat at a constant pressure is the energy stored when it experiences a temperature change of 1°C. The heat capacity can be found in the Eq. (4) as follows:

$$C_p\left(T\right)=\frac{\partial Q}{\partial T}$$E4

In the case of ideal PCM, the heat storage occurs over three distinct thermal events. When a PCM at solid state is heated and its temperature is raised uniformly from the system starting temperature until it reaches the phase change point. Over this period, heat is stored in sensible form. Further heating of the material incurs solid to liquid phase transition and heat is stored in latent form and temperature is constant during this period. Once the phase change is completed, the PCM is in liquid phase, further heating of the material increases its temperature and heat is stored again in sensible form in a rate proportional to the PCM specific heat. The reverse of the processes described above releases heat, which is also called discharge process. As can be seen, the total amount of energy stored released for a TES system involves three stages, two for sensible storage and one for latent storage, and hence the total heat storage capacity of a LHTES material can be calculated by Eq. (5) [4]:

$$Q=m\left[\underset{T_1}{\overset{T_m}{\int }}{C}_{p-\mathit{\text{solid}}}.\mathit{dT}+\underset{T_m}{\overset{T_2}{\int }}{C}_{p-\mathit{\text{liquid}}}.\mathit{dT}\right]$$E5

Where $C_{p-\mathit{\text{solid}}}$ is the average specific heat between $T_1$and $T_m$, $C_{p-\mathit{\text{liquid}}}$ is the average specific heat between $T_m$ and $T_2$, $m$: mass of PCM, $T_1$ and $T_2$ are the temperature range in which the TES process operates, $T_m$: melting temperature, and $∆h$: latent heat of solid-liquid transition.

The total energy stored “Enthalpy-sum” for PCMs can be calculated according to the upper and lower temperature limits of the TES system, as shown in Eq. (6):

$$E_{\mathit{\text{stored}}}=m_{\mathit{pcm}}\ast \left[H\left(T_2\right)-H\left(T_1\right)\right]$$E6

Where $E_{\mathit{\text{stored}}}$ is the total energy stored in the PCM TES system,$m_{\mathit{pcm}}$: the total mass of PCMs in the TES system,$H\left(T_2\right)$: the enthalpy-sum at the upper temperature limit ($T_2)$ of the TES system, and $H\left(T_1\right)$: the enthalpy-sum at the lower temperature limit ($T_1)$ of the TES system. As clearly seen in Figure 4, as considered in the enthalpy-sum curves, the heat capacity of a LHTES material depends on its specific heat of both solid and liquid and the latent heat. Therefore, a high heat capacity and a large latent heat are key for LHTES materials selection. As mentioned above, the transformation between solid and liquid states is specifically attractive due to small change in volume and has therefore been mostly investigated and utilized [5].

Figure 4.

Performance comparison of the storage mechanism for TES.

Case studies will be discussed to demonstrate many of the capabilities of this sensitive analytical instrument heat flux DSC. The PCM (RT27) as an example was studied according to the following experimental procedure [6]:

1. Cooling from 40 to −20°C at 10°C/min

2. Heats from −20 to 40°C at 10°C/min

3. Cooling from 40 to −20°C at 5°C/min

4. Heats from −20 to 50°C at 5°C/min

5. Cooling from 50 to −60°C at 0.2°C/min

6. Heats from −60 to 50°C at 0.2°C/min

Trigui et al. [6] reports a comparison of thermophysical properties of paraffin wax (RT27) obtained for two samples as summarized in Table 1. When using a DSC, the heat flux sensor is calibrated and the measurement procedure depends on the calibration mode, which is heat capacity or enthalpy calibration. With the using the enthalpy calibration, only the peak integral can be determined. That means that the sensible heat is not taken into account, and that there is no temperature resolution within the peak [7]. Using the heat capacity calibration, it is possible to determine the sum of latent and sensible heat as a function of temperature.

Properties		Values measured
		DSC calibrated on Cp	DSC calibrated on ΔH
		Sample1 $\left\{\begin{array}{l}\text{Mass},12.47\mathrm{mg}\\ \text{Scanning rate},10°\mathrm{C}/min\end{array}\right.$	Sample2 $\left\{\begin{array}{l}\text{Mass},5.11\mathrm{mg}\\ \text{Scanning rate},0.2°\mathrm{C}/min\end{array}\right.$
Heating state	solid-solid phase change temperature, $T_{\mathit{pm}}$	5.08°C	3.58°C
	Melting point, $T_m$	25.53–25.69°C^(*)	23.67–23.70°C^(*)
	Latent heat of solid-solid change, $L_{\mathit{pm}}$	23.692 J/g	23.300 J/g
	Latent heat of melting, $L_m$	155.960–140.581 J/g^(*)	134.928–158.110 J/g^(*)
Cooling state	solid-solid phase change temperature, $T_{\mathit{pc}}$	3.95°C	3.23°C
	crystallization point, $T_c$	26.2°C	24.78°C
	Latent heat of solid-solid change, $L_{\mathit{pc}}$	22.594 J/g	22.031 J/g
	Latent heat of crystallization, $L_c$	162.165–154.848 J/g^(*)	130.139–161.087 J/g^(*)
Specific heat of solid, $C_{p,s}$ (≤15°C)		3.25 ± 0.35 J/g.°C
Specific heat of liquid, $C_{p,l}$ (≥40°C)		2.23 ± 0.005 J/g.°C

Table 1.

Thermophysical properties of paraffin wax (RT27) [6].

(*)Value measured by sigmoïde.

2.4 Problems related with PCM analysis using DSC

In the selection and analyzing PCM due to their high enthalpy density per unit volume, the most problematic aspects are generally sample size, the stability to thermal cycling, phase separation, large supercooling and poor thermal conductivity. Moreover, DSC test results depend on further factors such as sample preparation, correct calibration to improve the accuracy of the PCM characterization procedure and to make measurement errors negligible [8].

• Sample size: The heating and cooling rates of DSC measurements are typically much faster than in real applications, while analysis on very small sample size of PCM (typically 20μL for the DSC analysis) is not completely representative of the thermal properties of the PCM bulk material, which might lack representativity for real size applications [9, 10, 11].

The sample size also affects the signal of the sample. If a small sample size is selected with low heating and cooling rates, the temperature shift inside the sample will be reduced. But this is not the solution. Because, both the small sample size and low heating and cooling rate lead to a weak signal and hence, decreasing the accuracy in enthalpy.

• Supercooling: Supercooling, also called undercooling, is often stronger for small sample sizes than in large sample sizes. Supercooling is the effect under which many PCM do not solidify immediately upon cooling below the melting temperature, but start crystallization only after a temperature well below the melting temperature is reached. Therefore the sample size should be large enough to obtain the real behavior of the sample. If the sample present strong supercooling in DSC analysis, it deforms the cooling DSC curve. Due to the supercooling, it becomes difficult to quantify internal gradients by comparing heating and cooling curves since the latent heat is released at a lower temperature than the intended one, and part of this heat is used to increase the temperature of the material to the melting temperature, where final crystallization occurs. Hence, as a solution to the supercooling, the large sample size should be analyzed before applying the PCM for any real TES system.

• Calibration: For calibration, materials with a known thermal effect are used. When using a DSC, the heat flux sensor has to be calibrated and the measurement procedure depends on the calibration mode, which is heat capacity or enthalpy calibration. Two common calibration modes are heat capacity (also called heat flow rate) calibration and enthalpy (also called heat) calibration. Each of the two calibration modes has advantages but also disadvantages with respect to PCM as sample. Using the heat capacity calibration, it is possible to determine the sum of latent and sensible heat as a function of temperature. Another approach to calibration is using standard materials with a well known melting enthalpy [9, 10, 11].

The thermal resistance is done by comparing measured phase change temperatures of standard materials with well-known heat of fusion and the temperature sensors by the melting temperatures (onset temperatures) of these materials.

• Thermal equilibrium: For reaching thermal equilibrium the sample should be isothermal, otherwise thus producing a shifting of the phase change temperature and also lead to non-realistic shapes of the heat capacity and/or enthalpy temperature responses h(T). If the measured temperature should be close to the real sample temperature, the heating or cooling should be slow to diminish the temperature gradient between sample and crucible. Therefore, the thermal equilibrium status in the sample is essential to improve the accuracy of the PCM characterization procedure and to make measurement errors negligible [9, 10, 11, 12, 13, 14, 15].

• Hysteresis: There are mainly two reasons for the hysteresis phenomenon of PCM. One is the improper measurement method can lead to the observation of an “apparent hysteresis,” which in most cases, over-estimates the real hysteresis of the material. Continuous heating and cooling can also increase the apparent hysteresis. The other reason for the hysteresis phenomenon of PCM lies in its intrinsic material property. Decreasing the heating and cooling rates, sample size or temperature step can improve the measurement accuracy so that the measurement uncertainty decreases. However, the single enthalpy curve without hysteresis cannot be achieved even with infinitely slow measurement, because the existence of subcooling, incomplete crystallization or polymorphic crystal structures results in different shapes of heating and cooling curves [16, 17, 18]. In certain cases, even with the most accurate measurement method and with the smallest heating/cooling rates, the hysteresis phenomenon can still be observed.

3. Transient guarded hot plate technique (TGHPT)

The Transient Guarded Hot Plate Technique (TGHPT) provides an alternative approach to characterize some of the thermo-physical of PCMs. Most of thermal analysis techniques, such as the DSC method are designed to test small, pure and homogeneous samples. During long-term performance testing, when undergoing huge number for freezing/melting cycles, large PCM specimens often are subject to settling or stratification and are typically not perfectly homogeneous. The TGHPT being an alternative to DSC measurements allows one to determine the phase change material (PCM) thermal properties (thermal conductivity λ, sensible and latent heat thermal energy storage, $C_P$ and $L_m$ latent heat of fusion or melting enthalpy) in the solid phase, during the solid–liquid transition and in the liquid phase and its thermo-chemical stability after thermal cycling test. The TGHPT eliminates the previously mentioned limitations of DSC measurements (i.e., mass influence, low thermal conductivity and thermal diffusivity of PCMs, non-equilibrium thermal gradients in the DSC pan and heating/cooling rate) and also allows for measurement of much larger samples than DSC (about 1000 times larger) [19]. The TGHPT has some advantages over other methods: it can be used, due to large sample size, for a wide variety of PCM (inorganic and organic, being encapsulated or composite), heating and cooling rates and temperatures ranges are variable and large enough to fit PCM for different applications. Therefore, for PCM characterization large samples are preferable. The TGHPT method has also the advantages of (i) a simple experimental device as it can be built up with basic laboratory devices (ii) lowest maintenance and lowest price. To clarify the effects on the heat transfer performance, an experimental device allows to determinate changes in enthalpy (latent heat) or the specific heat capacity (sensible heat), thermo-physical properties like thermal conductivity of an examined sample by Trigui et al. [6] (Figure 5). The proposed test bench for the parallelepiped-shape of composite (4, 5 × 4, 5 × 0.6 cm³) allows the simultaneous measurements of the temperature and heat flux at the material edges. The PCM material is placed between two horizontal exchanging aluminum plates. The plates get tempered by fluid thermostats with a precision of about 0.1°C. Each side of composite is equipped with a heat flux sensors and thermocouples (type T). These heat flux sensors fixed at the sample surfaces to measure input and output heat flux have 0.2 mm of thickness, 202 μV/W/m² of sensitivity and 400 cm² surface areas. The sensors were connected to LabVIEW software to measure temperature fluctuations and heat flux exchanged during melting and solidification processes which allow the investigation of the thermal stability of the samples. The acquisition of the experimental data is recorded at regular and adjustable time steps (1–6 s). To ensure a one dimensional heat flow through the sample the lateral sides are insulated by 11 mm thickness of expanded polystyrene. The enthalpy–temperature curve of a sample is measured similar to DSC measurements by heating up and cooling two aluminum heat exchanger plates in parallel at a certain heating rate or in stepwise mode. The TGHPT was developed to test construction materials with PCM in large scale samples in different boundary conditions following:

• A steady-state temperature difference on both sides of the sample imposed by two exchanger plates to determine the thermal conductivity.

• A transient regime between two stationary regimes to measure the variation of the specific heat versus temperature and interval where the two phases coexist to measure latent heat of melting.

Figure 5.

(a) Scheme of the Transient Guarded Hot Plate Technique (TGHPT) for testing PCM materials, (b) Picture of the whole apparatus.

With the TGHPT, the thermal performance of PCM such as the thermal conductivity, its temperature in liquid and solid state for PCM, the specific heat capacity and the latent heat can be determined. Furthermore, it is possible to investigate the thermal performance of PCM material such as the thermal stability and repeatability to store and release the thermal energy.

The TGHPT optimize measurement with shorter experimental time than DSC.

3.1 Apparent thermal conductivity

The experimental sample is placed in between two aluminum heat exchanger plates, and the position of the plates is adjusted to establish a full contact with the surface of the measured sample. To determine experimentally solid and liquid thermal apparent conductivities of the composite, the apparatus establishes a steady state one-dimensional heat flux through the test sample between the two plates. The plates are set a at constant but different temperatures to establish a thermal gradient through the sample. The temperature difference between the top and bottom plates is a user defined value to perform measurements at various averaged temperatures. The apparent thermal conductivity can be calculated using Fourier’s law of heat conduction. The thermal conductivity of the test sample is given by Eq. (7) [3, 20, 21]:

$${\mathrm{\lambda }}_{s,l}=\frac{e.\sum {\varnothing }_{s,l}}{2.∆T_{s,l}}$$E7

where e is the thickness of the specimen; $\mathrm{\Sigma }{\phi }_{s,l}$ is the sum of the measured heat fluxes of the solid or liquid states.

As an example, the composites materials (LDPE/Wax) were studied for thermal energy storage with a melting point around 26°C [6]. In order to characterize the apparent thermal conductivity of the solid phase, the TGHPT has been used with temperature variation only in a single face of the sample. The state of initial balance ($T_{\mathit{\text{init}}}=15°\mathrm{C}$, lower than the melting temperature ($T_m$)) is brought back towards another state of final balance ($T_{\mathit{end}}=20°\mathrm{C}$), such that $T_{\mathit{end}}<T_m$) (fusion process)) where heat flux tightens towards a non null value corresponding to a temperature gradient generated by the two heat exchangers plates. For the liquid phase, the same experimental procedure was applied by choosing a temperature difference (40 and 50°C). Figure 6 summarizes the measured thermal conductivities and associated uncertainties of the composites with different Wax contents.

Figure 6.

Thermal conductivities of LDPE/Wax composites [6].

3.2 Sensible heat and apparent heat capacity (in solid and in liquid states)

At the beginning, the two aluminum heat exchanger plates and the composite were maintained at a constant temperature$T_{\mathit{\text{init}}}$. By modifying the temperature set point of the thermo regulated bath, the composite evolved to a steady isothermal final temperature$T_{\mathit{end}}$. Between both states, the PCM composite stored an amount of sensible heat, which represents the internal variation of the system’s energy [22]. The heat capacity of the material was determined for the solid and liquid phases by calculating the integral of the heat flux difference from the initial state $\left(t_{\mathit{\text{init}}}\right)$ and the final state $\left(t_{\mathit{end}}\right)$ using the following expression Eq. (8) [22, 23].

$$Q_{\mathit{\text{sens}}}=\frac{1}{\rho e}\underset{\mathit{\text{tinit}}}{\overset{\mathit{\text{tend}}}{\int }}∆\varnothing .\mathit{dt}=C_p.\left(T_{\mathit{end}}-T_{\mathit{\text{init}}}\right)\left[\mathit{kJ}/\mathit{kg}\right]$$E8

Where $C_P$ is the apparent specific heat capacity of the composite, $∆\varnothing$ represents the difference heat flux measured at each time step during the acquisition $\mathit{dt}$, $e$ is the composite’s width and $\rho$ is its density.

To evaluate the apparent specific heat of the PCM, Different tests were carried out:

1. The temperature was checked from $T_{\mathit{\text{init}}}=15°\mathrm{C}$ to $T_{\mathit{end}}=20°\mathrm{C}$ to determine the sensible and specific heats of the compound in the liquid state.

2. The temperature was checked from $T_{\mathit{\text{init}}}=40°\mathrm{C}$ to $T_{\mathit{end}}=50°\mathrm{C}$ to determine the sensible and specific heats of the compound in the solid state.

Figure 7 presents the evolution of the heat fluxes and temperatures on both sides of two samples during the determination of the specific heat capacities of the LDPE/Wax composite in the solid and liquid states respectively. For the liquid and solid phases, the measured temperatures on the lower ($T_1$) and the upper ($T_2$) faces of the material evolve in an asymptotic way to the set point. Also, we can note that the flow evolves very quickly at the beginning of recording and then to a steady state obtained at the end of the test. The results obtained for the specific heat capacity and the sensible heat stored for the solid and liquid states are given in Table 2.

Figure 7.

Heat flux and temperatures evolution of the solid phase (15–20°C) [6].

Samples	$Q_{\mathit{\text{sens}}}$ (kJ /kg)		Cp (kJ /kg. °C)		$Q$(kJ/kg)	$L_m$ (kJ/kg)
	solid; (15–20°C)	liquid; (40–50°C)	solid; (15–20°C)	liquid; (40–50°C)	evolution; (15–50°C)
LDPE/wax (90/10)	13.8	24.9	2.8	3.5	104.0	65.3
LDPE/wax (40/60)	20.6	32.1	4.1	3.2	159	106.2

Table 2.

Quantity of heat stored and apparent heat capacity for (LDPE/Wax) composites [6].

3.3 Storage and release of latent heat

LHTES is the most promising method in this field due to excellent phase change behavior and high heat storage capacity. The amount of total energy storage/release can be calculated by a temperature variation from 15 to 50°C. Between these two positions, the composite stores and releases a sensible $\left(Q_{\mathit{\text{sens}}}\right)$ heats and latent ($L_m$) heats. The Latent heat is calculated by subtracting the sensible heat from the total amount of heat. This quantity can also be expressed by Eq. (9) [24, 25]:

$$Q=Q_{\mathit{\text{sens}}}+L_m=\left(C_{\mathit{ps}}.∆T_s+C_{\mathit{pl}}.∆T_l\right)+L_m\left[\mathit{kJ}/\mathit{kg}\right]$$E9

where $C_{\mathit{ps}}$ and $C_{\mathit{pl}}$ are the heat capacities of composite at solid and liquid state, respectively, $∆T_s$ and $∆T_l$ are the temperature variations in solid and in liquid state and $L_m$ is the latent heat par unit mass of melting.

The selected temperatures (15–50°C) are sufficiently far from the melting point to consider the material as being strictly in one state or the other. Figures 8 and 9 show that the heat stored is much more important than sensible heat transfer influenced by the paraffin wax addition. Hence, the addition of PCM significantly improves the thermal performance of composite in terms of saving energy.

Figure 8.

Heat flux and temperatures evolution from solid to liquid (15–50°C) [6].

Figure 9.

Latent heat of LDPE/Wax composites [6].

Figure 10 shows present the evolution of the heat fluxes and temperatures on both sides of the composite during the solidification process where the temperature evolves from 15–50°C. Initially, it can be observed a normal evolution of measured heat flux corresponding to the cooling of the liquid phase. At the end of this phase (t = 33 min), when the temperatures of surfaces are in the vicinity of 28°C, it can be seen the release of latent heat, and the appearance of a distinct inflection point in the heat flux curves. From this critical moment, the cooling of the sample continues, the material is solidified slowly and cools until it reaches the prescribed 15°C: after more than 1 h30 min, the sample reaches an equilibrium state. Notably, heat restitution was a very long process since at the start of the solidification. At the beginning of solidification, a layer solid Hexadecane was formed at the upper surface of the material which was in contact with the heat exchanger plate. This slight layer “insulates” the liquid PCM from the cooling source and reduce the effect of the convection mode. Then, the solidification continued slowly because of the low thermal conductivities of the solids SS-PCMs until the sample temperature reached 15°C at the end of the test. Furthermore, it can be noted that the period for solidification was much longer than the melting process.

Figure 10.

Heat flux and temperatures evolutions (50–15°C) [6].

4. Conclusion

Phase change materials (PCMs) with its capacity of storing thermal energy as latent heat is a viable approach of the utilization of solar heat, a green source of energy, and the optimization of energy consumption in buildings. An accurate material characterization of thermal energy storage materials including energy storage capacity and phase change temperature, during several charging and discharging cycles is significant to develop an efficient thermal storage device or application. Conventionally, thermal characterization of materials is performed using thermal analysis techniques especially Differential Scanning Calorimetry (DSC). However, all these methods involve very small samples that can be significantly influenced by local heterogeneities, the response dependence on the used heating rate, etc. For investigation of PCMs in real conditions, it is essential to design an experimental device to provide robust insights on the steady-state parameters, the dynamic thermal responses, the heat storage capacity of PCM at large scale, to meet the design requirements of thermal energy storage applications and to prevent potential failures. This chapter reports on successful use of a specific experimental method to measure the temperatures and the heat fluxes in order to characterize the phase change effects. The Transient Guarded Hot Plate Technique (TGHPT) provides reliable information about thermal conductivity, fusion enthalpy, specific heat and thermal stability for large phase change materials samples. Heat flux measurements make it possible to highlight very specific behaviors of these products and are thus a very interesting experimental source of data which comes to complete the traditional measurement methods like calorimetric device (differential scanning calorimetry). The Transient Guarded Hot Plate Technique (TGHPT) allows large samples analysis and entails less maintenance, equipments price and time evaluation than the DSC. Thus, it is the most suitable method for PCM characterization.

Nomenclature

$T$

Temperature (°C)

$C_P$

Specific heat capacity ($\mathrm{J}/\mathrm{g}.°\mathrm{C})$

λ

Thermal conductivity (kJ/kg)

$T_{0\mathit{\text{nset}}}$

melting onset temperature (°C)

$T_{\mathit{\text{endset}}}$

melting endset temperature (°C)

$T_m$

melting temperature (°C)

$∆H_m$

latent heat of fusion or melting enthalpy ($\mathrm{kJ}/\mathrm{kg}$)

$T_{\mathit{\text{range}}}$

temperature range of phase transformation (°C)

Subscripts and abbreviation

TES

Thermal Energy Storage

LHTES

Latent Heat Thermal Energy Storage

PCMs

Phase Change Materials

SS-PCMs

Shape-Stabilized PCMs

TGHPT

Transient Guarded Hot Plate Technique

DSC

Differential Scanning Calorimetry

DTA

Differential Thermal Analysis

init

initial thermal steady state

end

final thermal steady state

sens

sensible

s

solid state

l

liquid state

m

melting