Numerical model and simulation of a solar thermal

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 134 (2016) 429–444 www.elsevier.com/locate/solener

Numerical model and simulation of a solar thermal collector with slurry Phase Change Material (PCM) as the heat transfer fluid Gianluca Serale a, Francesco Goia b, Marco Perino a,⇑ b

a Department of Energy (DENERG), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy Department of Architectural Design, History and Technology, Faculty of Architecture and Fine Art, NTNU, Norwegian University of Science and Technology, Alfred Getz vei 3, 7491 Trondheim, Norway

Received 10 August 2015; received in revised form 8 April 2016; accepted 17 April 2016

Abstract The performance of conventional, water based, solar thermal collectors is limited by some intrinsic limitations, such as the need for high irradiation levels and the heat loss due to the relatively high temperature of the heat transfer fluid. In order to overcome these limitations and to improve the performance of solar thermal collectors, a different kind of heat transfer fluid can be proposed. This fluid is based on the exploitation of the latent heat of fusion/solidification of suspended particles, which change their state of aggregation at a micron scale, but maintain the liquid state of the fluid at a macroscopic scale. The so-called slurry phase materials, or PCS, are examples of this kind of material. In order to evaluate the effectiveness of such a concept, a numerical model of a PCS-based flat-plate solar thermal collector has been developed, presented and discussed. This model has been derived from the well-known Hottel–Whillier model, but several changes have been implemented so that a phase change of the heat transfer fluid can be handled, as well as the thermophysical properties of a nonNewtonian fluid, such as those of a PCS. The paper presents the main and auxiliary equations that have been introduced to modify the Hottel–Whillier model. A numerical analysis conducted with the newly developed model is also presented in the paper. The aim of these simulations was to test the code and obtain a preliminary evaluation of the performance of the novel concept. Different (dynamic) boundary conditions (location, orientation, PCM concentration) were adopted to evaluate the performance of the PCS-based technology and compare it with that of a conventional solar thermal collector. The outcomes of the simulations have proved model robustness and the possibility of using it for preliminary analysis. It was also shown that the adoption of the PCS as a heat transfer fluid can lead to an increase in solar energy exploitation of different magnitude according to the climate. The greatest benefit can be achieved for cold climates. The limitations of the analysis (e.g. fixed, non-optimal flow rate) are also discussed. Ó 2016 Elsevier Ltd. All rights reserved.

Keywords: Slurry PCM (PCS); Solar thermal collector; Numerical model; Collector efficiency

1. Introduction 1.1. Background

⇑ Corresponding author.

E-mail address: [email protected] (M. Perino). http://dx.doi.org/10.1016/j.solener.2016.04.030 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.

Solar thermal collectors are the most commonly used devices for the exploitation of thermal energy from the Sun. These systems have been widely investigated since

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G. Serale et al. / Solar Energy 134 (2016) 429–444

Nomenclature List of abbreviations HTF heat transfer fluid PCM Phase Change Material PCS Phase Change Slurry mPCM microencapsulated Phase Change Material mPCS microencapsulated Phase Change Slurry HDD Heating Degree Days HW Hottel Willier model for flat-plate solar thermal collectors List of symbols cp specific heat [J kg1 K1] m_ mass flow rate [kg s1] Dhlat;mPCM specific latent heat [J kg1] Dh0lat;mPCS specific fictitious latent heat [J kg1] b ratio of mass of melted mPCM to total mass of mPCM [–] ðsaÞe optical losses of the collector [–] Q_ u useful heat flux [W] T temperature [°C] A area [m2] FR collector heat removal factor [–] F0 fin effect factor [–] GT global solar irradiance [W m2] UL average thermal transmittance of the solar collector [W m2 K1] N number of pipes in the solar collector [–] l width [m] s thickness [m] L length [m] W distance between the pipes in the solar collector [m] y distance covered by the fluid inside the solar collector along the riser pipes [m] g efficiency of the solar collector [–] q density [kg m3] bmPCM;co ratio of the mPCM core mass to the mPCM shell mass [–] amPCM mPCM mass fraction in the mPCS mixture [–] agl water–glycol mass fraction in the carrier fluid [–] k thermal conductivity [W m1 K1] d diameter [m]

the ‘40 s (Hottel and Woertz, 1942) and nowadays constitute a mature technology that is applied at a large scale and is spreading significantly. At the end of 2011, the total thermal energy converted by solar thermal collectors was assessed to be about 235 GW h (Mauthner and Weiss, 2013), which corresponds to a total of approximately 335 106 m2 of collector area. A recent report by the IEA on Solar Heating and Cooling has stated that, at the end of 2013, the installed capacity rose to 374.7 GW h,

B m e j a c e n1 n2 K h / u

constant [–] constant [–] velocity gradient inside the mPCS [s1] thermal diffusivity [m2 s1] solar absorbance [–] azimuth angle [°] emissivity [–] air refraction index [–] cover refraction index [–] extinction coefficient [m1] tilt angle [°] latitude [°] volumetric concentration of the mPCM [–]

Subscripts in solar collector inlet int internal ex external pi pipe ca air cavity inside the solar collector pl solar collector plate co solar collector cover out solar collector outlet a outdoor air coll collector h higher limit of the melting range l lower limit of the melting range eff effective ins insulation bot solar collector bottom edg solar collector edge 1, 2, 3 different parts of the collector, according to the mPCS state of aggregation mPCM,co core of the mPCM mPCM,sh shell of the mPCM carrier carrier fluid in which the mPCM particles are suspended w water gl glycol opt optimal

which corresponds to a total of 535 106 m2 of collector area in operation worldwide (Mauthner et al., 2015). Among other applications, the use of solar thermal panels in buildings has become more and more common (Tian and Zhao, 2013). In this context, the thermal energy produced by solar systems can be used to: – satisfy the Domestic Hot Water (DHW) demand; – space heating.


The exploitation of solar energy for space heating alone can provide substantial energy savings under certain conditions, which depend on the location, and the energy demand profile, Fiorentini et al. (2015) and Marcos et al. (2011). The full profitability of this use is often limited to a great extent by the time mismatch between solar energy availability and energy demand (Raffenel et al., 2009). In winter time the limited solar irradiation that is available can barely cover the total energy demand for heating. On the other hand, the high solar radiation available in summertime far exceeds the energy demand for DHW production, and no direct or fully profitable use for this excess can be found – unless large and expensive seasonal storages are adopted (Guadalfajara et al., 2015; Pinel et al., 2011; Tao et al., 2015). Over the years, several developments have been made in order to improve the overall performance of solar thermal panels and their efficiency, and many activities are still under way. Shukla et al. (2013) have provided a complete review of solar thermal system developments that are still adopted in this technology and their limitations. In particular, solar collectors still suffer from efficiency drawbacks due to the relatively high working temperatures of the HTF. When a conventional HTF (i.e. a mixture of water and glycol) is adopted, the typical minimum temperature range necessary to provide a large enough enthalpy flux and a reasonable flow rate spans, approximately, from 50 °C to 60 °C. These high temperatures cause two different problems: – heat losses in all the system components, due to the temperature difference between the HTF and the environment. Therefore, higher efficiencies can only be reached when the environment temperature rises, a condition that is very unlikely to occur when there is an energy demand for heating; – a reduction in the periods when solar energy can be exploited efficiently and converted into heat. As a general rule, the higher the HTF temperature, the higher the minimum irradiation required to produce a useful heat gain (Harrison, 1986). An interesting concept that can be introduced to overcome the above mentioned limitations and to extend the operational time of solar thermal systems is represented by the adoption of an HTF that exploits latent heat instead of (or together with) sensible heat. By making use of the (isobaric) phase change within the HTF, which occurs at an almost constant temperature, a far greater amount of heat can be exploited in the process at lower temperature levels. High temperature-related inefficiencies can therefore be reduced. This approach, which is based on the harvesting of energy with a low-exergy content, can be particularly suitable when used in combination with low-temperature HVAC equipment, such as radiant heating systems. On the other hand, domestic hot water production probably requires a slightly higher exergy content, and therefore needs to be achieved by coupling such a solar thermal

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system with other energy conversion systems that can increase the exergy level (for example, a heat pump). 1.2. Short overview of two-phase materials and solar thermal panel systems Although the most common HTF in solar thermal panels is a mixture of water and glycol, the use of solar collectors, in combination with fluids that change their phase of aggregation, has been investigated by researchers since the ‘70 s. In these studies, heat pumps integrated with solar collectors were used to exploit the phase change of the refrigerants that were adopted as the HTF. Many types of refrigerants – such as CFC, HCFC, HFC (Charters, 1996; Fanney and Terlizzi, 1985; Soin et al., 1979), or other natural fluids, such as propane or CO2 (White et al., 2002), were successfully adopted. Although the efficiency of these solar thermal systems is higher than conventional water-based collectors, these technologies have not been adopted extensively due to the presence of substances that are harmful to the environment and because of the complexity of their installation. All these past attempts, which took advantage of the latent heat of the HTF, were based on the exploitation of liquid-to-gas transition. However, another opportunity is represented by the use of the so-called phase-change materials (PCMs) (Cabeza et al., 2011; Rastogi et al., 2015) and the exploitation of their solid-to-liquid transition. The use of PCMs has rapidly been increasing in recent years in various building applications (Nithyanandam and Pitchumani, 2014; Pomianowski et al., 2013). In general, PCMs are used to increase the thermal inertia of building components in order to reduce heating/cooling peak loads (Evola et al., 2013; Favoino et al., 2012; Goia et al., 2014) or as a storage medium for renewable energy integration, including components of solar thermal systems. Different technologies that make use of PCMs in solar thermal systems have been proposed and described in the literature. A review on this topic has recently been published by Wang et al. (2015). PCM can be integrated, for instance, in solar systems as a layer of the collector, inside a node placed in the pipes of the primary HTF loop, or in a component placed in the storage tank. Malvi et al. proposed an energy balance model and produced simulation results for a generic combined photovoltaic and solar thermal system that incorporates a layer of PCM (Malvi et al., 2011). Haillot et al. proposed a system with an additional storage unit composed of a PCM node placed inside the primary HTF solar loop (Haillot et al., 2011; Haillot et al., 2013). Recently, Huang et al. have proposed a storage tank for solar water heating with a floor that houses capillary plates and a macro-packaged PCM layer (Huang et al., 2014). Moreover, several studies can be found in literature about the introduction and heat transfer optimization of PCM modules located inside a storage tank (Cabeza et al., 2006; Canbazog˘lu et al., 2005; Khalifa et al., 2013; Kousksou et al., 2011; Li and Wu, 2015; Padovan and Manzan, 2014; Sharma et al., 2009).

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During the ‘80 s, Kasza and Chen (1985) proposed directly using the PCM in a water-based suspension, thus obtaining a fluid called slurry PCM or Phase Change Slurry (PCS). This strategy allows the temperature of the HTF to be reduced and thus the efficiency of the solar thermal system to be improved. Nevertheless, at that time, the PCM technologies did not allow PCS stability to be achieved in the loop of the system, and the result was that the PCS solidified in the pipes during its phase transition. The advancements that have been made in PCM technologies over the last few years have led to the development of materials based on micro-encapsulated Phase Change Material (mPCM) suspended in water or in a mixture of water and glycol. The resulting fluid has been called ‘‘microencapsulated Phase Change Slurry” or mPCS (Chen and Fang, 2011; Yamagishi et al., 1999). The use of mPCS offers several advantages for different thermal applications (Delgado et al., 2012; Youssef et al., 2013; Zhang et al., 2010). First, mPCS can be used both as a thermal storage material and as an HTF. The circulation of the mPCS in the pipes is always guaranteed, since the two-phase fluid has constant rheological properties and the phase-change only takes place inside the core of the microcapsules. An mPCS always remains liquid, even though it has a high viscosity, and it can be pumped regardless of the state of aggregation of the microcapsule core. Second, compared with other PCS technologies, this solution allows the heat transfer rate to be increased. Third, the heat transfer occurs at an approximately constant temperature. Moreover, since it is possible to pump the mPCS, the same medium can be used both to transport and to store energy, hence reducing irreversibility due to heat transfer in the heat exchangers. However, the use of an mPCS also introduces some challenges. For example, in order to properly exploit the latent heat, the transition temperature range must match the temperature range of the application, i.e. the mPCM must be chosen carefully taking into consideration the system. Furthermore, the viscosity of the highly concentrated mPCS suspensions can be much higher than that of water and, consequently, the pressure drops increase (Delgado et al., 2012). Finally, it should be observed that: – an mPCS can, under certain conditions, lose its physical stability, and creaming can occur, with the pipes getting clogged (Delgado et al., 2013; Serale et al., 2014b); – the thermal and mechanical loads, such as the mechanical stress generated by the circulating pump, can damage the microcapsules and cause PCM leakage from the capsules to the solvent.

stability, and two months after the preparation, no visible creaming or sedimentation was observed. 1.3. Scope of the research activity A review of the literature has revealed a lack of evidence concerning the advantages (and disadvantages) of the exploitation of solid-to-liquid transition in direct combination with solar collectors for any application, and in particular for building-related applications. Therefore, a dedicated investigation has been set up, and it is currently ongoing, with the aim of obtaining more detailed information and understanding of such a technology. The research activity has been developed along various paths, ranging from the conception and design of the novel solar system to the construction of a full-scale prototype, to be used for the experimental tests (Serale et al., 2015). In such framework, a physical mathematical model has been developed of a flat-plate solar thermal collector with an mPCS as the HTF. The present paper has the aim of presenting and discussing the algorithms and the strategies implemented to solve the heat balance and auxiliary equations. The proposed model is based on the Hottel–Willier equation, which is generally used for traditional water-filled collectors, but it has here been suitably modified in order to handle the heat exchange processes that involve latent heat. This simplified numerical model has a twofold aim: on one hand, it has been used to support the design phase of the experimental test rig; on the other hand, it has been used as a preliminary tool to analyze and test the profitability of the concept by means of comparative performance simulations against a conventional, water-based, reference collector system. The main focus of this paper has been on describing the numerical model of a solar thermal system based on sPCM. Nevertheless, the results obtained from some preliminary simulations carried out with the new code are also presented and discussed. These results offer the readers an insight into the potential of the proposed technology, as they show the annual and seasonal converted solar energy for four different European climates, for a conventional and an mPCS solar collector. It is worth mentioning that the whole mPCS-based system that has been conceived includes an mPCS-based heat storage unit coupled with solar collectors and a secondary, water-based circuit, to supply heat to the indoor environment. In this paper, focus has only been placed on the solar thermal panel, while the implications of coupling such a technology to a latent heat storage system and a lowtemperature heating system have not been dealt with here. 2. Physical–mathematical model and calculation algorithm

However, during the last few years, most of these problems have been studied and different solutions have been proposed to solve the drawbacks. For instance, Zhang and Zhao (2013) investigated an mPCS with multi-walled carbon nanotubes as additives. The material showed good

2.1. Assumptions The model of the mPCS-based solar thermal panel was developed starting from the well-known Hottler–Willier


(HW) model (Duffie and Beckman, 2013), which describes the thermo-physical behavior of a flat-plate solar panel that makes use of a single-phase HTF. Some assumptions and some simplifications were made in the HW model to make the physical–mathematical description of the components easier: – quasi steady-state of the collector components (cover, plate, back insulation casing); – forcing parameters and boundary conditions updated at each calculation time-step; – uniform boundary conditions over the whole collector; – one-dimensional heat flux (from the top cover to the back insulation); – heat loss toward the same heat sink, considered at the outdoor air temperature Ta. All these assumptions have also been adopted in the proposed new model for mPCS-based solar thermal collectors. Furthermore, other simplifications related to the HTF material properties have been taken into account. These were necessary to simplify the model and to reduce the number of input data. These main additional assumptions were: – the HTF is called mPCS and is a suspension of mPCM particles (micron scale) in a water–glycol mixture (later on indicated as ‘‘carrier fluid”); – the mPCS has constant density and thermal conductivity, regardless of its state of aggregation. This hypothesis does not introduce significant errors since the operating temperature range of the fluid, being lower than 5 °C, can be considered small (the optimal theoretical operating range of the system should be as close as possible to the phase change temperature range: Tl–Th); – the specific heat capacity depends on the state of aggregation of the material; – the phase change occurs completely in the Tl–Th range; – the contribution of the sensible heat – mostly due to the water–glycol portion of the mixture – is considered by introducing a fictitious latent heat Dh0 lat,mPCS, see Eq. (8). It is worth mentioning that the hypothesis of a quasisteady state regime, adopted in the HW model, only applies to the elements that constitute the solar collector (i.e. the energy storage in the cover, plate and casing and in the back insulation of the collector is assumed negligible). Instead, as far as the HTF is concerned, both latent and sensible heat are considered and the energy storage effects are taken into account.

2.2. Auxiliary equations used to obtain the thermophysical properties of the HFT

assessment of its thermo-physical properties therefore requires a set of suitable auxiliary equations. The properties of the mPCS are functions of the properties of the various components and of the concentration of the mPCM. In turn, the properties of the mPCM depend on the features of the microcapsule core and shell. The following equations have been adopted to calculate the properties of the mPCM (Charunyakorn et al., 1991; Chen et al., 2008; Goel et al., 1994; Gschwander et al., 2005; Mehling and Cabeza, 2008): qmPCM ¼

ð1þbmPCM;co ÞqmPCM;co qmPCM;sh qmPCM;sh þbmPCM;co qmPCM;co

ð1Þ

ðcp;mPCM;co þamPCM;co cp;mPCM;co ÞqmPCM;co qmPCM;sh ð2Þ ðamPCM;co qp;mPCM;co þqmPCM;sh ÞqmPCM 1 1 d mPCM d mPCM;co þ kmPCM ¼ ð3Þ d mPCM kmPCM;co d mPCM;co kmPCM;sh d mPCM d mPCM;co cp;mPCM ¼

The properties of the mPCS suspension have been calculated by means of the following equations: qmPCM qcarrier ð4Þ amPCM qcarrier þ ð1 amPCM Þ qmPCS amPCM cp;mPCM qmPCM;co þ ð1 amPCM Þ qcarrier cp;carrier ¼ ð5Þ qmPCS

qmPCS ¼ cp;mPCS

The thermal conductivity of the mPCS was calculated using Eq. (6) for flowing PCS. In this equation, the coefficient B and the exponent m are functions of the Peclet number. They are equal to 3 and 1.5, respectively, when the Peclet number is lower than 0.63, and are equal to 1.8 and 0.18 when the Peclet number is in the 0.63–250 range, while they are equal to 3 and 0.09 for higher Peclet numbers than 250. kmPCS ¼ 1 þ B u Pem kcarrier emPCS d 2mPCM Pe ¼ jmPCM

ð6Þ ð7Þ

The fictitious latent heat, Dh0 lat,mPCS, includes the mPCM latent heat and the sensible heat of the water–glycol solvent, in the phase change temperature range ðT h T l Þ: Dh0lat;PCS ¼ Dhlat;mPCM amPCM þ cp;carrier ðT h T l Þ ð1 amPCM Þ ð8Þ 2.3. mPCS-based flat-plate solar thermal collector model The basic equation of the HW model1 has been derived from the energy balance equation of the solar thermal collector, which relates the enthalpy flux of the HTF to several parameters that depend on the environmental conditions and thermal panel features. m_ PCS cp;HTF ðT HTF ;out T HTF ;in Þ ¼ Q_ u 1

The mPCS is a mixture of a suspended material (mPCM) and a carrier fluid (water and glycol), and the

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ð9Þ

The same nomenclature used in Duffie and Beckman (2013) is adopted throughout the paper and adjusted when necessary to describe new quantities that were not included in the original HW model.

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Fig. 1. Schematic of the heat fluxes involved in a flat-plate solar thermal collector. 1: Solar radiation incident on the panel; 2: Optical loss; 3: Convective and radiative heat loss through the glass cover; 4: Convective heat loss through the edge; 5: Convective heat loss through the bottom.

The various heat transfer fluxes involved in this thermal balance are highlighted in the scheme shown in Fig. 1. The right-hand side of Eq. (9) is the so-called useful heat flux, Q_ u , which can be written as: Q_ u ¼ Acoll F R ½GT ðsaÞe U L ðT HTF ;in T a Þ

ð10Þ

Eq. (10) establishes a balance between the incident solar radiation GT, the optical losses (accounted for by means of the (sa)e product) and the heat flux lost toward the outdoor environment UL(THTF,in–Ta), while FR is the collector heat removal factor. This latter term takes into account the different temperatures along the panel surface. Such a temperature distribution is due to the so-called ‘‘fin effect” (evaluated with parameter F0 ) and the ‘‘heat-exchanger effect”. The calculation of F0 and UL is not affected by the nature of the heat exchange (sensible or latent) that takes place in the HTF, but their values are functions of the temperature levels at which the fluid operates. Therefore, in the proposed model, they have been assessed using the same equations as those used in the conventional HW model. On the contrary, changes were implemented in order to correctly take into consideration any phase changes that occur in the HFT during the path of the fluid along the solar collector. In fact, these phase changes can determine a considerable modification of the temperature distribution over the plate, and can consequently influence the value of the FR factor (which not only depends on the inlet and outlet fluid temperatures, but also on other parameters). The proposed model is still based on Eqs. (9) and (10) to allow a simple comparison to be made with the traditional one. In a mPCS-based collector, the ‘‘temperature increase per unit of length” of the HTF flowing along the panel pipes varies, according to whether only sensible heat or both sensible and latent heat are exploited. In general, the temperature gradient is much smaller when latent heat is used, in spite of the sensible heat. If the mPCS temperature is lower than the lowest temperature of the transition phase, Tl, or higher than the

highest temperature of the transition phase, Th, only sensible heat exploitation takes place. On the other hand, when the mPCS temperature is in the Tl–Th range, a combination of latent/sensible heat is involved (the effect of this blend is evaluated by means of the fictitious latent heat, Dh0 lat,mPCS, as described by Eq. (8)). For these reasons, the temperature distribution in an mPCS-based solar thermal panel is very different from that of a traditional water-based collector. As already mentioned, FR is a function of the temperature distribution along the panel. Since only sensible heat is considered in the HW model, just one value is calculated for the overall panel surface. On the contrary, in an mPCS based solar collector, the value of FR varies over the panel surface, according to the state of aggregation of the mPCS. In the general case, the mPCS enters the collector at a lower temperature (TmPCS,in) than Tl. Therefore, the temperature of the fluid increases along the first part of its path inside the panel as it collects solar energy. After reaching the temperature level at which the phase change starts, Tl, the mPCS starts exploiting its latent heat of fusion. When the phase change has been completed (TmPCS > Th), the mPCS again starts to only exploit the sensible heat. The HTF leaves the collector at a higher temperature than Th, when and if the mPCM is in a complete liquid state. The solar thermal collector can thus be divided into three virtual segments along the flow path (y-axis): – Dy1: is the panel segment between the collector inlet and the point at which the HTF reaches a temperature equal to Tl; – Dy2: is the segment where the PCM inside the microcapsules undergoes the phase change and the mPCS temperature rises from Tl to Th (transition range); – Dy3: is the segment where the temperature of the mPCS increases further, sensible heat is once again exploited, and the TPCS,out temperature is reached. The lengths of the three virtual2 segments along the y-axis can be obtained by solving the energy balance equations. The length of each segment at each time step is calculated using appropriate boundary conditions. The length of Dy1 can be obtained by solving the differential equation of the heat exchanger (Duffie and Beckman, 2013), assuming Tout1 = Tl as a boundary condition; that is: " # G ðsaÞ T in;mPCS T a T U L e m_ cp;mPCS ln Dy 1 ¼ ð11Þ G ðsaÞ N W F 0 UL Tl Ta T e UL

Similarly, Dy2 can be calculated assuming that the mPCS temperature at the end of this segment is Tout2 = Th and that the whole mass of the mPCM has melted. In this section, the mPCS mainly exploits the phase change and its energy content can be assessed by means of the fictitious latent heat Dh0 lat,mPCS (see Eq. (8) for the Dh0 lat,mPCS 2

The word ‘‘virtual” has been used here because there are conditions in which some of these segments may have a length equal to zero or to a negative value, as will be shown in Section 2.4.


formulation). By introducing the mass ratio of the melted mPCM over the total mass of mPCM, b, it is possible to formulate Eq. (12) for the Dy2 segment in which the phase change occurs. It therefore results that: m_ Dh0lat;mPCS db ¼ W F 0 U L ðT y;mPCS T Þ dy N

ð12Þ

In order to simplify the model, a constant mPCS temperature has been considered in segment Dy2, which is assumed to be equal to the mean value of the melting range (the smaller the melting range, the better the approximation). Furthermore, in Eq. (10) the boundary condition b = 1 is imposed, which means that the mPCS has melted completely at the end of the Dy2 segment. Under these hypotheses, Eq. (12) becomes: m_ Dh0lat;mPCS h i Dy 2 ¼ G ðsaÞ l N W F 0 U L T h þT TU L e T a 2

ð13Þ

The length of the third segment, Dy3, is obtained from the difference between the sum of the two previous segments and the total length of the panel: Dy 3 ¼ Lcoll Dy 1 Dy 2

ð14Þ

After calculating the length of the three effective virtual segments, their related areas can be calculated as: Dy 1;eff Lcoll Dy 2;eff ¼ Acoll Lcoll Dy 3;eff ¼ Acoll Lcoll

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The mPCS instead shows a rather moderate temperature rise over the Acoll,2 area. Therefore, in the proposed model, due to this fairly small variation, its value has been assumed to be constant and equal to the average value of the melting range. Adopting such an approximation, the FR,2 parameter becomes equal to F 0 . Moreover, since complete melting of the mPCM occurs, Q_ u;2 can be simply calculated according to: Q_ u;2 ¼ m_ Dh0lat;mPCS

ð22Þ

Finally, the total useful heat flux delivered by the whole solar thermal panel, Q_ u is obtained as the sum of the contributions from each area of the collector: ð23Þ Q_ u ¼ Q_ u;1 þ Q_ u;2 þ Q_ u;3 Once the useful heat flux is known, the efficiency g of the solar thermal collector is calculated from the ratio of the useful heat flux delivered by the collector and the solar irradiation on the collector cover: R Q_ u dt R g¼ ð24Þ Acoll GT dt The previously presented equations represent the most general behavior of a solar thermal panel capable of exploiting the latent heat of an mPCS. Fig. 2 shows the expected temperature profiles along the rising pipes of the collector.

Acoll;1 ¼ Acoll

ð15Þ

2.4. Particular cases of the model

Acoll;2

ð16Þ

It is worth mentioning that Eqs. (11), (13) and (14) refer to the general behavior of the system (Fig. 2), but five other particular cases are also possible:

Acoll;3

ð17Þ

Each of these areas has a different collector heat removal factor, FR, since the heat exchange occurs in temperature fields that have different temperature distributions. It is therefore necessary to calculate the useful heat flux delivered by each area of the collector separately. The process in AC,1 and AC,3 only involves a sensible heat exchange, and the temperature of the mPCS increases as in a normal, water-based collector. The equations are therefore similar to those of the HW model: Acoll;1 F 0 U L m_ cp;mPCS mc _ p;mPCS F R;1 ¼ 1e ð18Þ Acoll;1 U L Acoll;3 F 0 U L m_ cp;mPCS _ p;mPCS 1 e mc ð19Þ F R;3 ¼ Acoll;3 U L Substituting these values on the right hand side of Eq. (2), one obtains: Q_ u;1 ¼ Acoll;1 F R;1 ½GT ðsaÞe U L ðT HTF ;in T a Þ Q_ u;3 ¼ Acoll;3 F R;3 ½GT ðsaÞe U L ðT HTF ;in T a Þ

ð20Þ ð21Þ

Fig. 2. Schematic of the temperature profile along the rising pipes of the collector in the ideal functioning of an mPCS-based flat-plate solar thermal collector.

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– Case a: The mPCS enters the panel at a lower temperature than the minimum value of the melting range: Tin < Tl, and the absorbed heat is not enough to reach the melting range. Therefore, no phase change occurs along the path inside the collector (Fig. 3a). In this case, the mPCM is always solid and the panel only exploits sensible heat and works as a traditional collector. – Case b: The mPCS enters the panel at a higher temperature than the maximum value of the melting range: Tin P Th (Fig. 3b). In this case, the mPCM is always in a liquid state and the panel only exploits sensible heat and works as a traditional collector. – Case c: The mPCS enters the panel at a lower temperature than the minimum value of the melting range: Tin < Tl. The material then starts to melt, but the absorbed heat is not enough to complete the phase change or to fully exploit the latent heat (Fig. 3c). In this case, the mPCS is only partially melted (b < 1) at the panel outlet. – Case d: The mPCS enters the panel at a temperature that falls within the melting range Tl < Tin < Th. For this reason, the mPCM is partially melted at the collector inlet (b > 0), the phase change occurs completely and the sensible heat is exploited in segment Dy3 (Fig. 3d). – Case e: The mPCS enters the panel at a temperature that falls within the melting range Tl < Tin < Th. For this reason, the material is partially melted at the collector inlet (b > 0). Moreover, the absorbed useful heat is not enough to complete the phase change or to fully exploit the latent heat (Fig. 3e). The mPCS at the panel outlet is therefore only partially melted (b < 1). The heat exchange in the collector occurs completely in the phase-change range.

In order to take these particular cases into due account, some additional equations need to be implemented in the model. Where Case a occurs, the mPCS does not reach the lowest limit of the phase change, Tl, before leaving the collector. In these circumstances, the real length of the solar thermal collector along the y-axis, Lcoll, is shorter than the virtual segment Dy1. Therefore, the effective length of Dy1,eff needs to be introduced to consider this situation: Dy 1 Dy 1;eff ¼ min ð25Þ Lcoll In Case c, even though Tl is reached, the mPCS leaves the solar collector at a lower temperature than Th. In this situation, a fraction of the mPCM remains in a solid state and the phase change does not involve the entire mass of the mPCM. For this condition, Dy1 can be assessed by means of Eq. (11), Dy3 is zero, and a suitable value, Dy2,eff has to be introduced in relation to the second segment: ( Dy 2 Dy 2;eff ¼ min ð26Þ Lcoll Dy 1;eff In this case, it is worth noting that the Q_ u;2 calculation also needs to be modified, since the latent heat of the mPCM is not completely exploited. Firstly, the fraction of the mPCM that has melted, b, is assessed as follows: bout ¼

Dy 2;eff Dy 2

ð27Þ

The exploited useful heat of the Dy2,eff segment can then be evaluated as:

Fig. 3. Schematic of the temperature profile along the rising pipes of the collector: possible cases considering different boundary conditions.


Q_ u;2 ¼ bout m_ Dh0lat;mPCS

ð28Þ

In the condition of Case e, the lengths of the first and third segments are equal to zero: Dy1 = Dy3 = 0. The length of the second segment is equal to the total collector length: Dy2 = Lcoll. However, the model needs a further input parameter: the mass fraction of the melted mPCM at the inlet of the panel. This value can be determined as follows: bin ¼

T h T in Th Tl

ð29Þ

In this case, Eq. (28) becomes: Q_ u;2 ¼ ðbout bin Þ m_ Dh0lat;mPCS

ð30Þ

Case b and Case d can be solved by suitably combining the above equations.

2.5. Implementation of the physical–mathematical model in a calculation environment: the MatLab-Simulink algorithm The physical–mathematical model of the mPCS-based solar thermal collector has been implemented in the Matlab-Simulink environment. A brief description of the Simulink model structure is provided hereafter for the sake of completeness. Fig. 4 shows the general scheme of the Matlab-Simulink blocks in which the sub-systems and the data flow have been highlighted. Diverse elements of the code are represented by different colours.

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– Green: input variables of the model. They can be computed using a Matlab script, adopting scalars or vectors for parameters that change in time (assuming a mean hourly value). These inputs are fluid properties, solar thermal panel characteristics, climatic conditions and locations; – Yellow: these are the different subsystems that implement the model equations. In particular: S1: defines the direct incident radiation normal to the collector surface; S2: calculates the (sa)e product that represents the optical energy losses of the panel; S3: determines the heat-transfer coefficients that can be used to calculate the energy loss the panel, and its outputs are the thermal resistances and the corresponding UL; S4: describes the heat exchange between the panel and the HTF; S5: is the ‘‘core” of the model. It allows the following to be determined: the FR,1, FR,2 and FR,3 parameters, the various lengths Dy1,eff, Dy2,eff, Dy3,eff that identify the various zones of the solar collector (see, for example, Sections 2.3 and 2.4) and the temperature of the HTF at the outlet of the panel; S6: gives the cover temperature through an iterative calculation. Its output depends on the outputs of sub-systems S3 and S5; S7: provides the main outputs of the model, that is: the useful heat flux (Q_ u ) and the collector efficiency, g. – Orange: outputs of the model. The most important ones are: the useful heat flux and the instantaneous efficiency of the collector. Moreover, it is also possible to evaluate

Fig. 4. Matlab-Simulink model for the PCS-based solar thermal system.

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some additional information that may be useful for analysis of the system, such as: the mean HTF temperature and the temperature at the outlet of the panel, the critical radiation and the stagnation temperature of the collector.

3. Model verification 3.1. Procedure The reliability of the model was evaluated comparing the numerical results of the simulations with experimental data monitored in a real solar thermal panel used as a reference. The facility used for this purpose was the solar thermal system described in Serale et al. (2015), which consists of a South oriented flat-plate solar collector coupled with a 200 l storage tank. A secondary loop, connected to a heat exchanger, allows the energy stored in the tank to be removed for different time profiles, thus simulating the heating demand. The whole experimental setup is monitored by sensors to measure the temperatures, solar radiation, flow rates and the energy use of the auxiliaries. This installation has been specifically designed and built with the aim of creating and testing a full-scale prototype of an mPCS solar system for building applications. Owing to the necessity of debugging and tuning the experimental set up and of optimizing the control strategies, the first set of measurements were carried out using a traditional water–glycol solution (the use of the mPCS in a non-perfectly tuned and optimized systems would have been problematic and could have led to clogging phenomena caused by the creaming process). For this reason, in this first phase of the research, the model was just verified for a water based HTF

(this configuration being the only one for which experimental data were available). In the near future, as soon as mPCS measured data are available, the model will be rechecked. Therefore, the following input data were assumed in the Simulink model (that is, the same values adopted in the experimental investigations): – mPCM concentration equal to 0% (this is the same concentration that was used as a reference in the simulations shown in Section 4 for a water–glycol based collector). – aHTF flow rate equal to 60 l h1 in the time interval between 8 am and 19 pm. The tests were started on 23rd of June 2015 and were continued for 7 days, which were characterized by a prevalence of sunny weather conditions. The sampling time was set equal to 1 min. The monitored environmental conditions and the boundary conditions measured on the flatplate collector prototype were used as additional input parameters in the Matlab-Simulink model. The demand side simulator extracted a sufficiently high constant heat flux to keep the temperature of the HFT in the storage tank at a constant level for the entire duration of the experiment. Therefore, the temperature at the inlet of the panel also remained constant. The main features of the panel are summarized in Table 1, while a simple scheme of the experimental set-up is shown in Fig. 5. 3.2. Comparison between experimental and simulated data The simulated and measured time profiles of the useful heat power (hourly average) per square meter of panel are shown in Fig 6a. The daily useful heat energy for each square meter of panel is instead presented in Fig. 6b.

Table 1 Details of the solar thermal collector. Specification

Symbol

Value

M.u.

Solar collector length Solar collector width Solar collector thickness Number of heat exchanger pipes Distance between heat exchanger pipes External diameter of pipes Inner diameter of pipes Plate thickness Plate absorbing coefficient Plate emissivity Plate conductivity Bond width Cavity thickness Cover thickness Cover extinction coefficient Air refraction index Cover refraction index Cover emissivity Thickness of the bottom insulation Thickness of the edge insulation Insulation conductivity

Lcoll lcoll scoll N W dex,pi dint,pi spl acoll epl kpl sbond sca sco kco n1 n2 eco sins,bo sins,edg kins

2.1 1.1 0.20 8 0.13 0.008 0.0076 0.0002 0.95 0.05 385 0.0002 0.025 0.004 16.10 1 1.526 0.8 0.05 0.02 0.04

m m m – m m m m – – W m1 K1 m m m m1 – – – m m W m1 K1


439

Fig. 6. a: Comparison between the hourly values of irradiance on the panel and the simulated and monitored useful heat produced. b: Comparison between the simulated and monitored useful heat produced daily by each square meter of panel.

Fig. 5. a: The solar thermal system used for reference purposes. b: Schematic of the experimental set-up for model validation.

These figures allow an easy comparison to be made between the numerical prediction and experimental data, and a rather good performance of the Simulink model is highlighted. It is worth noting how the accuracy of the simulation is excellent during the first part of the day (rising side of the curves), when the measured and predicted profiles are almost coincident. On the contrary, the model tends to fail in the prediction of the peak values of the useful heat; this is the condition for which the greatest difference with the measured data has been shown. This is probably due to the heat exchange coefficients, which are considered

constant in the model, but can show significant changes in reality, when the temperature of the system rises considerably. The model also seems to systematically overestimate the flat-plate collector heat production during the second half of the day (decreasing side of the curves). The numerical model tends to slightly overestimate the overall heat converted by the panel (Fig. 6b), as highlighted by the RSME and PRMSE values (Goia et al., 2012), which were assessed for the entire week and resulted to be equal to 39.3 W h m2 and 18%, respectively. This result can be explained considering two phenomena. The first is the fouling of the cover glass during the monitoring period. Although the cover glass was carefully cleaned before the start of the experimental campaign, it became more and more soiled during the week (some showers also occurred during the monitoring period). This phenomenon is only partially considered in the numerical model by means of an ‘‘artificial” and overall increase of sa (as suggested by the original HW model, switching from sa to sae). The second cause of overestimation could be due to some small shadows on the plate which were not considered in the model. These shadow areas are caused by the metal guides and the rolling shutter case (which is used as a solar shading device when the system is switched off, to prevent the collector from overheating and to limit the

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stagnation temperature) and these have the effect of virtually reducing the surface of the absorber plate. In light of such considerations, the model can be considered verified, though only for a water based HFT, and can be used reliably to perform sensitivity analyses with the aim of assessing the behavior of a collector under different operating conditions.

optimal tilt angle for systems with different boundary conditions (e.g. Lewis (1987) and Shariah (2002)). Different ‘‘rules of thumb” are also suggested to design the tilt of the panels but, in general, two values for the optimal tilt angle, one for the summer and one for the winter, are correlated to the latitude. Among others, Lewis suggested adopting the following rule (Lewis, 1987):

4. Simulation of an mPCS solar thermal collector

#opt ¼ / 8

Once the numerical model had been verified, it was used to simulate the behavior of an mPCS-based solar collector. The results of these simulations give an indication of the potential of such a technology and provide a first estimate of its performance in comparison to more traditional water-based installations.

where ‘‘+” stands for winter, and ‘‘” for summer. In this paper, an optimal tilt angle of #opt = / was considered when the overall year productivity was prioritized. However, considering that the innovative solar thermal system was mainly conceived to supply, among others, thermal energy for space heating, simulations adopting the tilt angle optimized for the winter season were also carried out. The resulting best tilts for the chosen locations are summarized in Table 2.

4.1. Climate condition and orientation of the collector The performance of the mPCS-based thermal panel has been assessed for four different climates in order to understand the impact of different combinations of outdoor air temperature and solar irradiation on the energy output of the system. The four selected locations are representative of different climates and cover a large mid-latitude region. They are: Palermo (South Italy), Turin (North Italy), Frankfurt (Germany) and Oslo (Norway). Data on the location and climate classifications can be found in Table 2. While the panel azimuth (c) was kept constant (e.g. South) for all the climates, the tilt (#) angle was changed in order to obtain the optimal performance for each latitude (the energy output of the solar thermal panel is affected to a great extent by the tilt angle). Several investigations can be found in literature on the estimation of the

ð31Þ

4.2. Features of the HTF As previously explained, mPCS is a fluid made up of two components: a carrier fluid and a suspended material. The carrier fluid is a mixture of water and glycol. Generally, the mass percentage of glycol is related to the climate conditions of the location where the collector is installed. In this work, a 40% concentration of glycol was adopted in the glycol–water solution for all the simulations. This is the typical mean value adopted for traditional panels installed in Europe (2500–3000 HDD). Table 3 shows the main data of the HTF used for the numerical simulations. The suspended material in the slurry is the mPCM. The two main concerns when it comes to the choice of this

Table 2 Climate characteristics and optimal tilt angle for different locations. Location

Latitude

Palermo Turin Frankfurt Oslo

38° 45° 50° 59°

070 040 070 570

N N N N

Climate description

Ko¨ppen climate classification

Annual global solar horizontal radiation [kW h m2]

Heating degree day [°C]

Optimal tilt (for heating demand) [°]

Hot-summer mediterranean Humid subtropical Oceanic Humid continental

Csa Cfa Cfb Dfb

1673 1294 1035 879

585 2617 3269 4714

46 53 58 68

Table 3 Details of the water and glycol mixture: carrier fluid. Specification

Symbol

Value

M.u.

Water density Glycol density Mass percentage of glycol Carrier fluid (water + glycol) density Carrier fluid (water + glycol) specific heat Carrier fluid (water + glycol) conductivity

qw qgl agl qcarrier cp,carrier kcarrier

1000 1110 40.0 1044 3600 0.369

kg m3 kg m3 % kg m3 J kg1 K1 W m1 K1


component are: the melting temperature and the latent heat of fusion. In general, if exergy issues are not considered, the lower the HTF temperature, the higher the energy amount that can be extracted by the system, and therefore its efficiency (Koca et al., 2008). Nevertheless, in order to allow heat exchange with the other loops of the heating system (e.g. the pipes that connect the heating terminal units), the mPCS in the storage tank should always remain at a slightly higher temperature level than the one required for the final application. For example, in low temperature radiant panel systems, which usually adopt flow and return temperatures of 35 °C and 30 °C, respectively, the minimum temperature level in the thermal storage should be in the 35–40 °C range. A micro-encapsulated n-eicosane was chosen to satisfy these requirements. The temperature range of the phase-change process for n-eicosane is 36–38 ° C. Data on this material are available in literature and other data have been provided by the manufacturer (Alkan et al., 2011; Genovese et al., 2006; Microtek Laboratories, 2015). Wherever different values of the same property were found in literature, their mean value was adopted. Table 4 summarizes the main thermo-physical properties of the n-eicosane adopted in the simulations. Apart from the orientation and tilt of the panel, two other parameters needed to be set: the concentration of the mPCM and the flow rate of the HTF in the panel. These two variables were chosen so that a compromise between the heat transfer characteristics and the pressure drops of the fluid could be reached. This is not a trivial trade-off, since the improvement of one feature could lead to the deterioration of the other one (Serale et al., 2014a). As far as the concentration of mPCM is concerned, a parametrical analysis was performed and the performance of the system was obtained at different concentration values (0%, 15%, 30%, 45% and 60%). The optimal flow-rate is influenced to a great extent by the concentration, since both the thermo-physical and rheological properties of the mPCS depend on the concentration of the mPCM. In a previous work (Serale et al., 2014a), it was found that the optimal flow rate is the one which allows the outlet temperature of the HFT to be kept at a constant value equal to the highest temperature of the melting range

441

(i.e. 38 °C). In this way, the whole mass of the material changes the phase completely and melts during its flow path inside the collector. Such a condition, on one hand, allows the latent heat to be fully exploited, and, on the other, keeps the HTF temperature as low as possible, thus reducing the heat losses. Sensitivity analyses have demonstrated that the temperature reached by the mPCS at the outlet of the panel depends to a great extent on the solar irradiance. For this work, a constant flow rate of 5.70 106 m3 s1 (approximately 20 l h1) was assumed, which corresponds to the optimal flow rate for a solar irradiation equal to 800 W m2 (Serale et al., 2014a). 4.3. Results and discussion The performance of the panel has been evaluated with reference to two different time periods: – throughout the entire year; – during the heating season. A conventional six-month heating season, from mid-October to mid-April, was considered for all the locations. The useful specific heat converted by the panel throughout the whole year is presented in Fig. 7a, for different locations and various mPCM concentrations (tilt angle of # = /). Similarly, Fig. 7b shows the same quantity with reference to the heating season alone. In this case, the numerical analysis was carried out using #opt = / + 8°. A comparison between the performance of the mPCS solar collector and that of the traditional water-based one is shown in Fig. 8. The productivity increase is obtained from the ratio of the heat converted by the mPCS panel to the heat converted by the water collector. In general, it can be observed that the higher the concentration of mPCM, the higher the productivity increase of the panel (as expected). However, it should be considered that these results do not take into account the increased pressure drop due to the less favorable rheology proprieties of the mPCS when higher concentrations are adopted or the associated increase in the energy demand for fluid circulation.

Table 4 Thermo-physical properties of the chosen mPCM: n-eicosane. Specification

Symbol

Value

M.u.

Mass percentage of the core Core density (solid/liquid) Shell density Average particle diameter Conductivity (solid/liquid) Specific heat (solid/liquid) Latent heat Nominal phase change temperature Phase change range

acore qcore qshell DmPCM kmPCM cp_mPCM rmPCM Tn_mPCM Tinf_mPCM-Tsup_mPCM

87.5 815/780 1190 17–20 106 0.23/0.15 1.92/2.46 103 1.95 105 37 36–38

% kg m3 kg m3 m W m1 K1 kJ kg1 K1 kJ kg1 °C °C

442


The productivity increase for Turin and Palermo is very similar, even though the two cities have different climates. This is partially due to the fact that the used flow rate is the optimal one for an irradiation of 800 W m2, which is more similar to the winter time irradiation of Palermo than that of Turin. As mentioned before, all the simulations have been conducted assuming the same HFT flow rate. Nevertheless, an optimization of the mPCS technology should involve a careful evaluation of the most suitable HFT flow rate to be adopted for each instantaneous – working condition. A future research development will be aimed at addressing such an issue for both the numerical model and the control strategies of the full-scale prototype. 5. Conclusion and future works

Fig. 7. a: Thermal energy produced throughout the entire year for each square meter of panel tilted at # = / and with different mPCM concentrations. b: Thermal energy produced during the heating season (from mid-October to mid-April) for each square meter of panel tilted at #opt = / + 8° and with different mPCM concentrations.

Fig. 8. Productivity increase for the mPCS filled solar panel for different MPCM concentrations.

It is worth mentioning that the productivity increase is higher for colder climates, because the panel efficiency depends on the temperature difference between the HTF and the outdoor environment. The exploitation of the latent heat allows this temperature difference to be lowered and thus the heat loss to be reduced (and this phenomenon is more pronounced in cold climates than in warmer ones).

The physical–mathematical model of an mPCS-based solar thermal collector has been developed and presented in this paper. It is based on mass and energy conservation equations and shares the fundamental features of the traditional approach suggested by Hottel and Wilier for a flatplate solar collector with single-phase HTF. The model has been suitably adapted in order to handle the phase transition of the HTF (an mPCS). The general and auxiliary equations of the model are presented and described in the paper, together with the strategy adopted for their numerical solution. In order to verify the proposed model, a comparison has been made between the simulated and measured performances of a water–glycol based system. The model has been verified using a water glycol flat-plate solar collector, since measured data were only available for this kind of system. After the validation phase, the numerical model was then used to perform several simulations of an mPCSbased solar thermal system. The numerical results have shown that both the instantaneous efficiency and the overall solar energy conversion of the collector increase when an mPCS is used as the HTF in place of a common water–glycol mixture. The increase in performance is higher in colder climates, where this new technology allows low irradiance levels to be exploited more effectively. Moreover, heat losses toward the colder outdoor environment are reduced, thanks to the lower temperatures of the HTF. As can be expected, the increase in performance is greater when higher mPCM concentrations are introduced. The numerical analysis has shown that, when realistic mPCM concentrations are considered (from 30% to 40%), the increase in energy conversion is in the 4–6% range. The results from this preliminary performance evaluation are related to some conventional choices, as far as some boundary conditions are concerned, such as the flow rate (which might not be optimal for the location where the system is installed).


Simulations were in fact carried out assuming a fixed and constant flow rate for all the locations and over time (e.g. for different working conditions). The adoption of a variable and optimized flow rate should result in a greater improvement in the performance of the innovative mPCS based technology than the traditional one. In the future, more parametric simulations will be carried out in order to: Optimize the working parameters of the solar thermal system, for example by using dynamic flow rate values. Optimize the design of the single flat-plate components for mPCS-based solar thermal systems (e.g. solar collector, storage tank). Finally, the developed model of the solar collector will be coupled with other numerical models that will be able to simulate both the behavior of the mPCS in the heat storage tank and the heating demand of the building. In this way, it will be possible to analyze the overall performance of the solar heating system (and not only the panel) when it is coupled to other components of the HVAC plant under realistic operating conditions. Acknowledgments Part of this work was carried out within the ‘‘SolHE-PCM” research project (2010–2013) funded by the Piedmont Region (Italy) on ERDF funds in a competitive grant programme, aimed at developing a demonstrator of this solar system. The research activity is also supported by ENEA (PAR 2013 and 2014) and is part of the IEA – EBC Annex 59 research programme. Special thanks are also due to the industrial partner and co-founder TeknoEnergy for its continuous support in the prototype development and to Sara Baronetto and Mathilda Grille for their precious collaboration in the development of the Matlab-Simulink model and in monitoring the system. References Alkan, C., Sarı, A., Karaipekli, A., 2011. Preparation, thermal properties and thermal reliability of microencapsulated n-eicosane as novel phase change material for thermal energy storage. Energy Convers. Manage. 52, 687–692. http://dx.doi.org/10.1016/j.enconman.2010.07.047. Cabeza, L.F., Castell, A., Barreneche, C., de Gracia, A., Fernańdez, A.I., 2011. Materials used as PCM in thermal energy storage in buildings: a review. Renew. Sustain. Energy Rev. 15, 1675–1695. http://dx.doi.org/ 10.1016/j.rser.2010.11.018. Cabeza, L.F., Ibań˜ez, M., Sole´, C., Roca, J., Nogue´s, M., 2006. Experimentation with a water tank including a PCM module. Sol. Energy Mater. Sol. Cells 90, 1273–1282. http://dx.doi.org/10.1016/ j.solmat.2005.08.002. ´ .G., Akarsu, Canbazog˘lu, S., S ß ahinaslan, A., Ekmekyapar, A., Aksoy, Y F., 2005. Enhancement of solar thermal energy storage performance using sodium thiosulfate pentahydrate of a conventional solar water-

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