Design of an air-PCM heat exchanger unit

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Theoretical background and literature review


To accomplish the objectives set for this work, we need to fully understand the phenomenology associated with phase change and PCM systems. This understanding allows us not only to have a proper knowledge that prepares the ground for further experiments and models, but it also serves as the basis for the design of PCM systems.
In this chapter, we present in parallel, the theoretical background related to phase change materials and its thermal applications, as well as, a literature review related to experimental analysis, modeling and building applications. The first part intends to present all the necessary knowledge that even if its well known, it is vital in the understanding and development of phase change. The last part presents the approaches and solutions implemented during the last decades by different authors, which would allow us to get a better insight into our problem.

Phase Change Materials

When a material undergoes a change of phase, an endothermic or exothermic process occurs, leading the material to store or release a considerably high amount of energy in the form of heat, which generally occurs at a single temperature or within a fixed range of temperature. This type of heat is known as latent heat; the heat storage capacity per unit mass during phase change is inherent to each material.
The concept of phase change materials circumscribes those materials that undergo a solid-liquid transformation at a temperature within the operating range of a selected thermal ap-plication [44]. Their attractiveness lies in the fact that they can store a significant amount of energy in small volumes while remaining at an almost constant temperature. This attractiveness represents the major advantage of these materials as storage medium if compared with the thermal storage by sensible heat, where we need a broad temperature difference or large volumes to achieve considerable heat storage.
The PCM can be found in a wide range of temperatures and chemical compositions, whereby they can be used for numerous applications, such as [94]: building air conditioning, electronics cooling, waste heat recovery, textiles, preservation of food, solar energy storage, fabrics, and others.
Since these PCM materials can store large amounts of energy within reduced volumes, their use in building applications can potentially generate energy savings and a reduction on the greenhouse gases emissions by matching their use with the energy demands of the building. However, to select a PCM as a suitable material for LHTES applications, we have to consider if this PCM fulfill the thermal, physical, kinetic and chemical criteria to be selected as heat storage materials. Some of these criteria were gathered by Zalba et al. [121], and listed as follows:
• The melting point must be within the desired operating temperature range.
• The material must possess a high latent heat of fusion per unit mass. This way a smaller amount of material could store a given amount of energy.
• Small volume changes during phase transition.
• The material must exhibit little or no sub-cooling during freezing.
• Chemical stability, no chemical decomposition and corrosion resistance to construction materials.
• Contain non-poisonous, non-flammable and non-explosive elements/compounds.
Over the last 40 years, different classes of materials, including hydrates salts, paraffin waxes, fatty acids, eutectic of organics and inorganic compounds, and polymers have been considered as potential PCM. Abhat [3] in 1983 classified PCM into two categories: organic and inorganic materials. Later in 2009, Sharma et al. [97], extended this classification into three categories: organic, inorganic and eutectic, with subcategories in each of them, as shown in figure 1.1 [97], [106]. In this section we present a brief description of those categories:

Organic materials

Organic PCM are further described as paraffin and non-paraffins. They present congruent melting, which means that melting and solidification repeatedly occur without phase segregation and degradation of their latent heat of fusion; also they present little or no supercooling effects, and they are usually noncorrosive materials. These organic PCMs are sub-divided into the following categories:
• Paraffins. They consist of a mixture of n-chain alkanes CH3 — (CH2)— CH3. The paraffin is available in a large temperature range as shown in figure 1.2, which make them attractive for several thermal applications. They also present a reasonable cost, a predictable behavior, reliability, they are non-corrosive, and chemically inert below 500 °C. The commercial use of paraffin comes from the distillation of crude oil. Although their use as thermal storage material is attractive, they present some drawbacks such as low thermal conductivity, and in some cases, they are not compatible with plastic containers.
• Non-paraffins. In this group are included materials such as esters, fatty acids, alcohols, and glycols. They are the most numerous of the phase change materials with highly varied properties, representing the largest category of candidate’s materials for phase change storage [97]. Among their properties we have: a high heat of fusion, low thermal conductivity, varying level of toxicity, inflammability and instability at high temperature. From this group, the fatty acids are attractive for thermal energy storage due to their higher heat of fusion, compared to paraffin. These PCMs also show reproducible behaviors during melting and solidification, with no supercooling. However, their cost is about 2-2,5 times the cost of paraffin must be analyzed if the design of the system is sufficient to guarantee a good heat transfer with the conductivity of the selected material. If not, we must look for another material, increase the conductivity of the material, for instance, by adding conductive particles, or re-condition the design of the system to enhance heat transfer. In figure 1.3 it is shown the logarithm of the thermal conductivity Log(kpcm) of PCM regarding the melting temperature. Unsurprisingly, the metallic type PCM present the higher conductivities among them [106].
Furthermore, figure 1.2 results useful for PCM selection, showing the PCM ranges accord-ingly to their melting temperatures and enthalpies of fusion. In the pink area lies those materials that can be suitable for building applications, allowing us to focus on the PCM available types for these applications [28].

Encapsulation of phase change materials

Encapsulation is the process of covering the PCM with a suitable coating or shell material [94]. Since the most common PCM used as thermal energy storage material undergo a solid-liquid phase change, the PCM needs to be encapsulated; otherwise, the liquid PCM would leak out. Besides preventing liquid leakage, the encapsulation keeps the PCM isolated from the surroundings, ensuring the correct composition of the PCM, which would otherwise have changed due to the mixing with the external fluid.
The encapsulation has a direct effect on the thermal performance of the PCM. Their proper-ties directly affect the performance of heat transfer and energy storage. Encapsulation of PCM can be classified according to their size, material, and geometric properties.
(a) PCM encapsulation based on size
Based on the size of the container, the encapsulation of the PCM can be classified in:
1. macro-encapsulation (above 1,0 mm),
2. micro-encapsulation (1-1000 µm), and
3. nano-encapsulation (1-1000 nm).
For thermal storage, macro-encapsulation is the conventional way of encapsulating the PCM since it does not require a complicated process. The typical containers used for PCM are rectangular vessels, spheres, and cylindrical vessels (cylinders, tubes, annular containers). Several studies of each of these containers can be found in the literature, being the cylindrical and rectangular configurations the most found among them [7]. The macro-encapsulation of PCMs can avoid large phase separations, increase the rate of heat transfer and provide a self-supporting structure for the PCM [85].
On the other hand, micro-encapsulation presents higher rates of heat transfer; they are thermally more reliable and stable than macro-encapsulated PCM [8] [12]. Nevertheless, they present a more complicated manufacturing process. Moreover, there are also available studies on nano-encapsulated PCM, presenting even better results regarding the heat transfer rates than macro and micro-encapsulation. However, their study is still at the laboratory scale; therefore, further research is needed on this subject to be considered as commercially feasible. A complete review about nano-encapsulation in buildings can be found in [61].
(b) PCM encapsulation based on the material
The material plays an important role in heat transfer and mechanical performance of a PCM container. It has to ensure at least acceptable heat transfer rates, as well as withstand-ing the changes in pressure and temperature during the phase change. The most common materials used as PCM containers are polypropylene, polyolefin, polyamide, silica, polyurea, urea-formaldehyde, copper and aluminum [94]. Several authors have studied the performance of these materials as PCM containers, based on heat transfer performance and mechanical properties such as thermal conductivity, chemical stability with the PCM, the compressibility of the material, and deformation [20] [119] [22] and [107]. Some properties that must present the container material were listed by Salunkhe and Shembekar [94] and are presented hereunder:
1. The material should have sufficient structural and thermal strength to withstand the phase change process of PCM.
2. It should retain their thermophysical properties at the micro and nano level.
3. It should be leak proof.
4. It should not react with the PCM.
5. It should be a good water diffusion barrier.
6. It should have higher thermal conductivity.
Metallic containers are usually an attractive choice due to their thermal and mechanic characteristics. Although, they are not a viable option if the PCM is corrosive. Similarly, plastic is an attractive choice due to their weight; however, they present poor thermal conductivity, and for organic PCM it must first be analyzed if the type of plastic is compatible with the PCM because they present a similar structure than the organic PCM; this could lead to diffusion or chemical reaction.
(c) PCM encapsulation based on the geometry
As it was already stated, the most common geometries for PCM containers are spheres, cylinders, plates, and tubes. These geometries are popular due to the ease of manufacturing and handling that they entail. However, we can also find variations of these geometries as PCM containers.
The physical phenomena that are commonly associated to phase change, i.e., melting and solidification controlled by conductive and convective heat transfer mechanisms are heavily affected by the geometry and geometric disposition of the container regarding the gravity phenomenon. Therefore if these phenomena are described inadequately, it would result in an inaccurate prediction of the thermal performance [7]. Since one of the objectives of this present work is the identification of the physical phenomena occurring during phase change, more details are presented in further sections.
So far, we have presented an overview of the general concepts related to phase change, which concepts are common to all of the applications where they are generally used. Before going further in the phenomenology associated with these materials, we present a review of the use of PCM in building applications, which allows us to focus our detailed search of the phenomena, taking into account the application in which it will perform.

Physical phenomena during phase change

Whether we are studying melting or solidification, phase change results in a complex problem mainly because it involves the presence of more than one phase, creating a boundary between them, that varies in time and space. If our goal is to ease the designing and use of PCM systems, we should provide users with tools that, despite the complexities of the process, can acceptably predict the behavior and performance without going into tedious methods. To achieve this, we need a deep understanding of the phenomena so that these phenomena can be simplified without affecting their effect on phase change.
According to Regin [85], the heat transfer analysis of the phase change problem is much more complicated than single phase problems due to:
1. The non-linearity of the problem resulting from the motion of the solid-liquid interface during phase change.
2. Inadequate knowledge of the heat transfer process at the solid-liquid interface, because of the buoyancy-driven natural convection in the liquid PCM.
3. Uncertainty of the interface thermal resistance between the container and the solid PCM.
4. Volume change with the change of phase (upon shrinkage).
5. The presence of voids in the solid PCM.
Several physical phenomena are inherent to PCM during melting and solidification. Their effects in phase change and therefore, in the modeling of these processes vary according to the specific conditions of the problem, such as the shape of containers, storage material, geometry arrangement, thermal applications among others, which leads to retain or discard such phenom-ena under certain circumstances. In here we briefly mention the most important phenomena to be retained.
1. Moving solid-liquid interface. The position of the solid-liquid interface not only distin-guishes one phase from the other, but it also reflects the quantity of the PCM that has already melted or solidified at a certain instant. This measure is of great importance because it can reveal the amount of heat that has been stored or discharged from the PCM. This is probably the most important feature to determine during phase change [124], leading to the need for a prediction of this parameter as accurate as possible.
2. Density change in phase change. During the phase change, we can identify two types of density changes in the material [10]: (i) due to change of temperature in a phase, since density depends on the temperature, and (ii) due to the difference between the solid and liquid density at the melting temperature. Solid density is usually higher for most PCM, whereas the water is a notable exception [124]. When melting occurs, the PCM occupies more volume, increasing the pressure on the container; whereas for solidification, when shrinkage occurs, the PCM occupy less volume, under-pressurizing the container. This last entails void formation (bubbles or gaps from the vapor of the material and other gases) within the PCM. These voids are more likely to be formed between the PCM and the container since the weakest forces of adhesion are between them.
3. Buoyancy effects in the melt region. The temperature difference not only leads to a change in the density of the PCM, but it also induces flows in the liquid PCM due to the presence of gravity, promoting the natural convection. These flow interactions with the remaining solid, create 2-D melting patterns. These patterns are linked to the amount of PCM remaining on the process by a certain instant; therefore, it should be addressed when studying phase change. The role of natural convection in solidification is much less important and in many cases may be discarded [124].
4. Phase change over a wide temperature range. Pure substances offer a sharply, well-defined phase change temperature, which is desirable for most of the thermal applications since the temperature of operation can be well predicted. However, these materials present a high cost, making them impractical solutions as a storage material. Nevertheless, there are commercial PCM that present attractive phase change temperature ranges. In either way, this parameter must be taken into account during the design and modeling of PCM systems.
5. Enthalpy hysteresis. Some PCM can present subcooling or superheating effects during phase change, where phase change does not occur at the expected temperature. For instance, for building applications, this is a phenomenon which should be avoided in the PCM.
Melting and solidification for several shapes of containers and PCM have been widely studied. The first to acknowledge the moving boundary problem of phase change was Jožef Stefan, and since then, this problem has been called the « Stefan Problem. »
Usually, if we want to understand a physical problem, we resort to experimental and analytical approaches to accomplish this task. The problem with the analytical solutions for the Stefan problem is that they are mostly available for one-dimensional cases, and for simple boundary conditions. They have been addressed in the literature, especially in heat transfer textbooks as the theoretical solution of phase change problems [21], [10], [77]. Therefore, for air-PCM applications, the phase change comprehension relies mostly on experimental and numerical approaches. These approaches usually express the performance in terms of melting fraction, temperature profiles, operation time and melting rate or power [7]. Besides, these approaches are often associated with a group of dimensionless numbers used in the study of PCM. Before explaining these approaches, we define these dimensionless numbers in the following section.

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Dimensionless numbers associated with phase change

The dimensionless numbers are algebraic expressions, generally in the form of fractions, where the numerator and denominator are powers of physical quantities with the total physical dimension equal to unity [90]. These numbers are obtained by dimensional analysis and by a scaling of the governing equation of a specific phenomenon.
Their use is well extended in the fields of chemistry, transport of momentum, heat, and mass, since they simplify the description of phenomena and the governing equations to a reduced number of variables. Besides, they provide a clear physical interpretation of the phenomenon under study.
In an LHTES system where a single container is in contact with an external fluid, from which it will be transferred the necessary heat to the phase change to happen, the heat and mass transport can be explained by the Reynolds, Prandtl, and Nusselt numbers.
The Reynolds number Re determines whether a flow is laminar or turbulent. It can be defined as :
Re = Dhyd •vmax convection (1.1)
νf luid viscosity
where Dhyd is the hydraulic diameter, vmax is the maximum velocity of impact between the fluid and the container, and νf luid , the dynamic viscosity of the fluid.
The Prandtl number Pr approximates the ratio of momentum diffusivity to thermal diffusiv-ity. Low Pr means effective heat conduction with dominant thermal diffusivity. High Pr means effective heat convection with dominant momentum diffusivity. The Prandtl number is given by:
Pr = ν momentum diffusion (1.2)
heat diffusion
The Nusselt number determines the ratio of actual heat transferred by a moving fluid to the heat transfer that would occur by conduction and it is defined by:
Nu = hair •Dhyd conductive thermal resistance (1.3)
kair convective thermal resistance
where hair is the overall convective heat transfer coefficient, and kair is the air conductivity.
The Biot number, Bi , defines the ratio of the heat transfer resistances inside of and at the surface of a body. This can determine whether or not the temperatures inside a body will vary significantly in space, from a thermal gradient applied to its surface. With this number, we can define if the heat transfer across the tube wall can be considered as unidimensional conduction, and it can be defined as:
Bi = Lc •hair conductive thermal resistance . (1.4)
kwall convective thermal resistance
Regarding the phenomena occurring within the PCM container, we first consider here the Stefan number Ste which is associated with the phase change, it expresses the ratio between the sensible heat and latent heat available from the PCM. This Stefan number is a dimensionless form of the temperature difference between the outer surface of the tube and the PCM melting 26 1. Theoretical background and literature review
temperature given by:
cppcm • Twall −Tpcm sensible heat
Ste = . (1.5)
L latent heat
We also consider the Fourier number, Fo , as a dimensionless measure of time. It expresses the ratio between the amount of heat transmitted to the body and the sensible storage capacity of the body, and it is defined by:
Fo = αpcm •t unsteadiness (1.6)
2 mass diffusion
where αpcm is the thermal diffusivity of the PCM, and Lcpcm is the characteristic length of the PCM, which corresponds to the length through which conduction occurs.
Both the Fourier number together with the Stefan number, are sufficient to describe the heat transfer when the phase change is only considered by conduction [17]. Finally, if we want to account the presence of natural convection during phase change, Rayleigh number Ra, which defines the ratio of buoyancy forced and thermal momentum diffusivity, and it is related to the effects of natural convection in the liquid PCM. Rayleigh number is defined as:
Ra = g •ρ2 •c β • T −T •L3 buoyancy force . (1.7)
p owpcm c
µ •k viscous force

Experimental Approaches

Early experimental studies were carried out by Sparrow et al. [104], for pure and impure substances used as PCM. Besides, Farid et al. [42], Zalba et al. [121], and Stritih et al. [105] conducted studies in systems with PCM to determine the phenomena involved in phase change. Their results show different heat transfer mechanisms governing melting and solidification.
Zalba et al. [121], observed that the thickness of the encapsulation, the inlet air temperature, and the airflow have a significant influence on the solidification process, whereas for melting, the inlet air temperature showed more significant than the encapsulation thickness. They also showed that solidification is mainly dominated by conduction while melting by convection.
Similar results were found by Stritih [105], who performed experimental studies on melting and solidification on rectangular containers. During their studies, they found heat transfer correlations, relating the Nusselt number as a function of the Rayleigh number. From these correlations made for melting and solidification, it can be observed that the natural convection during melting is almost ten times higher than natural convection during solidification.
Ettouney et al. [34], found that, for a vertical double pipe configuration, the natural convection was dominant during melting for upward flow of the heat transfer fluid, whereas, for downward flow, it was negligible. Thus these experimental studies relate conduction as the main heat transfer mechanism during the solidification process, while convection to melting process.
The heat transfer rates during melting and solidification are greatly affected by the geometric configuration and orientation of the container regarding the gravity, as well as the thermal boundary conditions between the fluid and the container. They play a significant role in the evolution of the shape of the remaining solid, the movement of the currents of liquid PCM and the liquid-solid interface, and the thermal characteristics of the PCM during phase change. In general, the heat transfer rate is higher in the upper portion of all containers where natural convection dominates [27].
In general, we can classify heat transfer problems during phase change as [7]:
• conduction controlled phase change,
• convection controlled phase change, and
• conduction and convection controlled phase change.
In the next section, we cover further details about the phase change phenomena dividing the process according to the container shape. We decided to evaluate the phenomena according to this parameter, since, as we have already stated, the container geometry affects heat transfer, and therefore the thermal performance.
Melting in rectangular vessels
Rectangular shape for PCM containers has been widely studied. Their use as PCM containers has been widely spread since they are easy to obtain and manufacture. Their thermal behavior can be categorized, according to their thermal boundary, into two types of phase change [27]:
1. constant heat flux, and
2. constant temperature.
Jany and Bejan [56] in 1987 presented a scaling theory of melting with natural convection in an enclosure heated from the side, which can be well applied to rectangular vessels. They show that the phenomenon consists of a sequence of four regimes:
1. the pure conduction regime,
2. the mixed regime, where the upper portion of the liquid gap is controlled by convection and the lower portion by conduction,
3. the convection regime, and
4. the last or « shrinking solid » regime.
An early study performed by Zhang et al. [123] presents experimental results of the melting process within a rectangular vessel filled with n-octadecane (C18H38). Discrete sources heated one wall of this container at a constant rate. Their main findings include the observation of the significant role of natural convection and the Stefan number during melting, making the liquid-solid interface more pronounced when this number increases.
Later, Faraji and El Qarnia studied numerically the phenomenon of melting of n-eicosane within a rectangular vessel heated with three protruding heat sources with a constant volumetric heat generation from one side. The other sides were thermally insulated. They described three stages during melting. At the early stage, conduction was predominant at the bottom part of the PCM. They describe a second stage where natural convection was involved. During this stage, the liquid streamlines became relatively packed next to the active wall and the melting front, which leads to a relatively fast-moving flow next to those boundaries. During the third stage, the location of the intersection of the melting front and non-active vertical wall moved downward.
Yanxia et al. performed an experimental study on the thermal characteristics of the melting process of ethanolamine–water binary mixture used as PCM. This PCM was contained in a rectangular vessel heated from a vertical side. Their experiments indicated a heat transfer enhancement due to natural convection, compared with only conduction-dominated phase change. They described that the mechanism of pure conduction only occurred during the initial stage of melting and a conduction–convection coupled model was necessary for predicting melting process accurately at later stages.
Melting in spherical capsules
Melting in spherical capsules can be classified into two groups [27]:
1. constrained melting, and
2. unconstrained melting.
The first type occurs in experimental studies where a thermocouple is placed inside the capsule; the positioning of the thermocouple prevent the PCM from sinking or raising to the bottom or top of the sphere due to gravity. The second group of melting occurs where there is no anchor inside the capsule. In this case, the PCM will sink or rise and experience thermal contact with the wall.

Melting in cylindrical vessels

Regarding the airflow direction, the cylindrical containers are usually arranged horizontally or vertically. The effects of gravity, diameter size, and heat exchanges are different for these two configurations; therefore, different melting patterns and performances are obtained.
Bareiss and Beer [15] performed experiments to test melting inside a cylindrical container. They found that as long as conduction is the controlling mechanism heat transfer can be expressed by correlating the Nusselt number to the Rayleigh number. When convection is controlling phase change, then, the Nusselt number is a function of the Stefan, Fourier, and Rayleigh numbers, as well as the height-to-diameter aspect ratio, H/D. They observed that for longer tubes, the melting layer found in the top of the tube does not increase significantly.
During the early studies performed by Sparrow et al. [104], [33], these authors carried out a melting cycle for a vertical cylinder, analyzing the natural convection effects. Besides, they focused on finding the shape of the remaining solid during melting. This process was done by interrupting the melting process at various stages and then observing the solid taken outside the tube. They suggested a strong relationship between the melting fraction and the dimensionless numbers of Fourier, Stefan, and Grashof. From these results they stated that melting in vertical cylinders includes three effects that can be observed:
1. Natural convection in the melt phase (liquid PCM).
2. The downward melting at the upper section of the tube.
3. The change of density of the PCM as it melts.
Furthermore, these authors observed a conical pattern in the remaining solid, which became more visible as the amount of liquid increased in the cylinder. Menon et al. [91] also observed this conical pattern for a similar study using commercial paraffin wax in slender tubes of small diameters between 1,91 cm and 3,18 cm; and heights between 30,5 cm and 61 cm. They reported that the melting fraction is also a function of the height-to-diameter aspect ratio, H/D.
Wu and Lacroix [62] performed a numerical study of natural convection controlling melting of a PCM, with isothermal boundaries. They found that heat transfer is dominated by conduction when the container is heated from the top. They also find that the melting patterns of those containers heated from different sides are far more complicated by those single side heated containers.

Table of contents :

Current Problematic: Global outlook
Phase change materials for cooling and heating applications
PCM systems for building applications developed by I2M of Bordeaux
Box shape tube bundle: Napevomo house
Slabs PCM system: Sumbiosi house
Further Research
Departure point for the present work
Problem statement
Thesis Objectives
Thesis Structure and Methodology
1 Theoretical background and literature review 
1.1 Scope
1.2 Phase Change Materials
1.2.1 Organic materials
1.2.2 Inorganic materials
1.2.3 Eutectic materials
1.3 Encapsulation of phase change materials
1.4 Physical phenomena during phase change
1.4.1 Dimensionless numbers associated with phase change
1.4.2 Experimental Approaches
Melting in rectangular vessels
Melting in spherical capsules
Melting in cylindrical vessels
1.4.3 Numerical Approaches
1.4.4 Empirical correlations for conduction and convection during phase change
1.4.5 Visual tracking of the melting front
1.5 Basic concepts in Image Processing
1.6 Concluding Remarks
2 Air-PCM heat transfer unit definition
2.1 Scope
2.2 Design of an air-PCM heat exchanger unit
2.2.1 Methodology for the design of an air-PCM unit
2.2.2 System Overview
2.2.3 Physical phenomena involved in phase change applications for cooling and heating
Global Phenomena
Local Phenomena
2.2.4 General Analysis
Operational Architecture (Structural Analysis)
2.2.5 Functional Analysis
2.2.6 Keywords search and analysis
Matrix Description
Matrix Analysis
Selection of the line of evolution
2.3 Concluding remarks and perspectives
3 Experimental Approaches 
3.1 Scope
3.2 Experimental setup and procedures
3.2.1 Design of the experiment
3.2.2 Experimental setup
Experimental Apparatus
Air-PCM heat exchanger
PCM selection
Metrology of the experimental setup
3.2.3 Experimental Procedure
Airflow rate measurements
Temperature measurements
Testing protocol
3.3 Experimental results and discussion
3.3.1 Melting cycle results
Temperature measurements:
Image Analysis
3.3.2 Solidification cycle results:
Temperature measurements
Image Analysis
3.4 Thermal performance of the unit
3.4.1 Data processing for thermal performance evaluation
Global Domain
Local Domain
3.4.2 Results and Analysis of the thermal performance evaluation
Global Domain
Local Domain
3.5 Physical phenomena identification
3.5.1 Physical phenomena related to phase change
3.5.2 Dimensionless numbers associated with an air-PCM heat exchanger
3.5.3 Results from the phenomena identification by dimensionless numbers
3.6 Concluding remarks
4 Modeling of a tube bundle type air-PCM unit 
4.1 Scope
4.2 Experimental Correlations
4.2.1 Previous analysis before obtaining the correlations
4.2.2 Statistical tests to validate the multiple linear regression
4.2.3 Results from the correlations for the melting fraction
4.3 Thermal resistance model
4.3.1 Problem statement for the model
4.3.2 Resolution methodology
4.3.3 Assumptions
4.3.4 Mathematical formulation
Air sub-domain:
Wall sub-domain:
PCM sub-domain:
4.3.5 Initial and boundary conditions
4.3.6 Numerical Resolution
4.3.7 Validation of the model
Validations from the First tube
Results from the eighth tube
Global validation of the heat exchanger
4.4 Non-isothermal phase change with natural convection model
4.4.1 Main assumptions for the model
4.4.2 Energy conservation in the air
4.4.3 Energy conservation in the wall and PCM
4.4.4 Supplementary assumptions
4.5 Concluding remarks
5 Building Applications 
5.1 Scope
5.2 Mobile air-PCM unit
5.2.1 PCM containers
Filling of the tubes with RT21
Filling the tubes with SP25E
5.2.2 Unit Structure
5.2.3 Experimental setup and Procedure
5.2.4 Results under controlled conditions : Office room at I2M laboratory
Results and analysis
5.2.5 Results under real conditions : Sumbiosi PEH
Platform overview
Metrology of the platform
Results and analysis
5.3 Concluding Remarks
General Conclusions 
Limitation of the Research
Regarding the design
Regarding the experimental approaches
Regarding the modeling approaches
Regarding the building application
Perspectives and future research
Regarding the design
Regarding the experimental approaches
Regarding the modeling approaches
Regarding the building application


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