2. Theory: modeling of combined thermodynamic/heat transfer

To develop the combined thermodynamic/heat mass transfer relations for the PCM/silica nanocomposite, two additional assumptions are made in the development of the relations: firstly, contact resistance between the PCM and the silica nano-materials is assumed negligible, and, secondly, three-dimensional heat transfer effects are neglected, based on the assumption that the skeleton of silica nano-materials is so closely spaced that these effects are negligible.

When the component temperature rise for a particular application exceeds the maximum operational temperature of component, the supporting material raises the equivalent thermal conductivity of the PCM by providing low thermal-resistance paths through the PCM and reduces the temperature gradient necessary to dissipate the imposed cold-plate heat load. The reduction in temperature gradient reduces the temperature excursion of the component. Consider the thermal protection system shown in Figure 1. An electrical component is thermally protected by the PCM/silica nanocomposite system. The component internally generates energy cyclically. For cyclical operation, three equations can be derived for the system based on the model.

#### 2.1. Conservation of energy

equipment in aerospace applications. Phase change materials (PCMs), which store excess heat generated from the work components and release it reversibly when needed, provide a smart approach for more efficient temperature management and thermal control utilization. Latent heat absorption phenomena associated with melting of a suitable PCM may be effectively used to delay or modify the temperature rise of the surface subjected to high heat flux. Thermal management utilizing solid-liquid PCMs is one of the most interesting passive thermal management techniques due to its simplicity and reliability. Solid-liquid PCMs including salt hydrates, paraffin waxes, certain hydrocarbons, and metal alloys are often used for thermal

Most practical applications for hypersonic vehicles require PCMs to have high density of latent heat and appropriate phase change point. In this criterion, certain hydrocarbons are very promising for temperature controlling applications for its comparative high fusion latent heats, suitable melting temperature, and chemical stability [1]. However, the applications of the kinds of solid-liquid PCMs are largely limited, as leaking of the liquid phase occurs above the phase change point. Thus, accommodation of the PCMs in appropriate host materials is necessary to prevent the leakage of the liquid phase for temperature controlling applications using the solid-liquid phase change. The leakage is usually circumvented by introducing shape stabilization support [2, 3]. Devoting to develop composites with a high PCM load and heat storage density, researchers have been recently interested in silica nanoporous ceramics with high specific area as a shape stabilization matrix or a supporting structure materials as PCMs' skeleton for avoiding leakage of solid-liquid transition [4, 5]. Silica aerogels have been used extensively in many engineering applications. They are sol-gel-derived porous inorganic mate-

thermal conductivities and high optical transparencies [9]. However, monolithic silica aerogels are very fragile and transparent to thermal radiation at high temperature, and these two defects restraint the application range of silica aerogels. Fortunately, researchers have improved both the mechanic strength property and high transparency using reinforced fibers [10] and pacifiers doped in the aerogels [11]. The composite silica aerogels are called silica nanoporous materials, and they have the similar space structure and have superior properties such as higher mechanic strength properties at high temperature [12, 13]. Thus, they have better applicability than the monolithic aerogels. The silica nanoporous materials have broad applications or application prospect in the fields which have strict limit of space or weight, for

The concept of thermal design using PCM has been well established through various studies in recent decades and is widely used in space applications [15]. To apply PCMs as alternating heat storage and discharge in space applications, the material should accommodate the special needs on the thermophysical properties that include conformance of phase change temperature to the design limits, high latent heat, and low density difference between liquid and solid phases. Structurally and thermally, the synthesis of the support materials for a PCM must be also considered. The supporting materials assure the seepage-proof for the molten PCMs and can withstand some imposed mechanical loads structurally. The supporting materials must be

) [6], high porosity (>90%) [7],

/g) [8]. These structural properties result in a few

rials recognized for their low density (as low as 0.01–0.02 g/cm<sup>3</sup>

and high specific surface area (600–1000 m<sup>2</sup>

example, in aeronautics and aerospace [14].

protection applications.

154 Advances in Some Hypersonic Vehicles Technologies

After the maximum energy that must be stored by the PCM/silica nanocomposite, EMax, is determined, the following heat balance will hold.

$$E\_{\rm Max} = \rho\_p \cdot A\_P \cdot t \cdot h\_f + \left[\rho\_S \cdot A\_S \cdot \mathbb{C}\_S + \rho\_p \cdot A\_P \cdot \mathbb{C}\_P\right] \cdot \frac{t}{2} \cdot (T\_{\rm Max} - T) \tag{1}$$

where ρP, CP, and AP are density, specific heat, and area of PCM, respectively; t is the thickness of the nanocomposite; ρS, AS, and CS are the density, specific heat, and area of silica, respectively;

Figure 1. PCM thermal control system and model of PCM/silica nanocomposite.

and TMax� T is the temperature excursion of the component. This equation treats both the energy stored through latent heat of fusion and sensible heat stored within the liquid PCM and the silica nano-materials.

#### 2.2. Conservation of mass

The mass balance shown below will hold:

$$M\_{\rm tot} = \left(\rho\_P \cdot A\_P + \rho\_S \cdot A\_S\right) \cdot t \tag{2}$$

Ktot � Atot ¼ kP � AP þ kS � AS (4)

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157

Atot ¼ AP þ AS (5)

This relation neglects three-dimensional effects and contact resistances. The total area is the

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle

Thermophysical properties are shown in Table 1. As shown in Table 1, it is concluded that neicosane's phase transition at a moderate temperature makes it a candidate phase change

Silica open-network structure supported by fibers distributed uniformly within. The reinforced silica open-network structure with high porosity and high surface area will benefit for liquid n-eicosane impregnation. The large surface area and low density of porous materials will enhance the shape stabilization capability and thus maximize the surface area per unit volume of PCM. When used in a spacecraft, the materials thermal control system must be small and light. The n-eicosane impregnates in the open network of silica nano-materials as an integrated thermal control system. Among the composite structure, the structural silica nanomaterials function not only as reinforced skeleton of the composite but also as heat-conducting materials to transfer heat from the component to the low thermal conductive PCM. The thermal design meets the requirement of total PCM service from alternate melting and freezing

According to this composite structure, the system combining PCM and silica nano-materials is suggested as a new type of thermal control device for the generated heat electronic component.

Name n-Eicosane (C20H42) Silica nanoporous material

) 856 at 308 K\*\*\* 280\*\*\*

) 247\* —

Melting point (�C) 36.7\* —

Specific heat (J/kg K) 2210 at 308 K\*\* 549\*\* Thermal conductivity (W/m K) 0.15\*\* 0.37\*\*

materials or PCM which can be used to store thermal energy and control temperature.

sum of the cross-sectional areas of the PCM and silica nano-materials.

2.5. Thermodynamic/heat transfer relations

2.5.1. Thermophysical properties

2.5.2. Structural and modeling

during the whole period of mission.

Latent heat of fusion per unit mass (J/kg � <sup>10</sup>�<sup>3</sup>

\*\*Measured by LFA 1000 Laserflash (thermal conductivity/diffusivity).

Table 1. Thermophysical properties of n-eicosane and silica nanoporous material.

Density (kg/m<sup>3</sup>

Measured by DSC.

\*\*\*Calculated by experiment.

\*

Thus,

where Mtot is the total mass of the nanocomposite.

#### 2.3. Temperature range constraints

The equation establishes a relation between the total conductivity, Ktot; the total area, Atot; the thickness, t; and the temperature excursion TMax � T

$$Q\_{pulse} = \frac{K\_{bt} \cdot A\_{tot} \cdot (T\_{Max} - T)}{t} \tag{3}$$

#### 2.4. Additive relations

For parallel conductance, the total equivalent conductance can be found from the following equation

$$K\_{\rm brt} \cdot A\_{\rm brt} = k\_P \cdot A\_P + k\_S \cdot A\_S \tag{4}$$

This relation neglects three-dimensional effects and contact resistances. The total area is the sum of the cross-sectional areas of the PCM and silica nano-materials.

Thus,

and TMax� T is the temperature excursion of the component. This equation treats both the energy stored through latent heat of fusion and sensible heat stored within the liquid PCM and

Mtot ¼ ρ<sup>P</sup> � AP þ ρ<sup>S</sup> � AS

The equation establishes a relation between the total conductivity, Ktot; the total area, Atot; the

Qpulse <sup>¼</sup> Ktot � Atot � ð Þ TMax � <sup>T</sup>

For parallel conductance, the total equivalent conductance can be found from the following

� <sup>t</sup> (2)

<sup>t</sup> (3)

the silica nano-materials.

2.2. Conservation of mass

The mass balance shown below will hold:

156 Advances in Some Hypersonic Vehicles Technologies

2.3. Temperature range constraints

2.4. Additive relations

equation

where Mtot is the total mass of the nanocomposite.

Figure 1. PCM thermal control system and model of PCM/silica nanocomposite.

thickness, t; and the temperature excursion TMax � T

$$A\_{tot} = A\_P + A\_S \tag{5}$$

#### 2.5. Thermodynamic/heat transfer relations

#### 2.5.1. Thermophysical properties

Thermophysical properties are shown in Table 1. As shown in Table 1, it is concluded that neicosane's phase transition at a moderate temperature makes it a candidate phase change materials or PCM which can be used to store thermal energy and control temperature.

#### 2.5.2. Structural and modeling

Silica open-network structure supported by fibers distributed uniformly within. The reinforced silica open-network structure with high porosity and high surface area will benefit for liquid n-eicosane impregnation. The large surface area and low density of porous materials will enhance the shape stabilization capability and thus maximize the surface area per unit volume of PCM. When used in a spacecraft, the materials thermal control system must be small and light. The n-eicosane impregnates in the open network of silica nano-materials as an integrated thermal control system. Among the composite structure, the structural silica nanomaterials function not only as reinforced skeleton of the composite but also as heat-conducting materials to transfer heat from the component to the low thermal conductive PCM. The thermal design meets the requirement of total PCM service from alternate melting and freezing during the whole period of mission.

According to this composite structure, the system combining PCM and silica nano-materials is suggested as a new type of thermal control device for the generated heat electronic component.


\*\*\*Calculated by experiment.

Table 1. Thermophysical properties of n-eicosane and silica nanoporous material.

The PCM thermal control system and the cross section of designed structure, where the PCM is embedded in silica nano-materials, is depicted in Figure 1. The cross section of the n-eicosane/ silica nanocomposite is an area with 100 mm 100 mm. The performance of the thermal control device is investigated by numerical analysis. The main purpose of the study is to obtain the functions and relations between the mass, thicknesses, temperature excursion, and percentage area of n-eicosane through combined thermodynamic/heat transfer analysis, which raises the minimum temperature and lowers the maximum temperature. According to the thermal cycle period, composite PCMs accumulate heat and uniformly redistribute it. Thus, the phase change temperature of PCM is the target of temperature control, and it must remain within the maximum/minimum operating temperature range of the electronic component. Furthermore, it must be chemically stable for silica nano-materials, which is the material of PCM support, and there must be a small density difference between solid and liquid phases.

#### 2.5.3. Thermodynamic/heat transfer relations

It is assumed that the component heat is generated periodically according to the system. In detail, there is 3.6 102 kJ the maximum energy stored by the PCM/silica nanocomposite, Emax, is determined and then a warming up period of 100 W heating, Q-pulse, during the whole cycle. To obtain a quantitative idea of the functional relationships between the variables described above for a given application, thermodynamic/heat transfer was conducted using the given power and energy requirement, using a given area, and using the thermophysical data of the PCM and silica nano-materials, as described in Table 1. These simultaneous Eqs. (1)–(5) can be solved to yield the excursion temperature, TMax-T; the total mass, M(t); and the thickness, t, as functions of PCM area percentage, Apcm/Atot. A MATLAB program was coded to solve the five equations and yields the parametric data discussed above.

The hyperbolic function curve about the relationship between the area percentage of PCM and the excursion temperature, as shown in Figure 2, illustrates one interesting fact. The intersections of the curve with the Apcm/Atot = 0 vertical line represent the temperature excursion for only a solid silica nano-material heat sink, which means the temperature excursion for a nanocomposite without n-eicosane. The temperature excursion is highest at this condition and decreases drastically with small additions of n-eicosane until a smaller point is reached around 50% n-eicosane. Similarly, the intersections of the curve with the Apcm/Atot = 1.0 vertical line represent the temperature excursion for the whole fusion heats of PCM. At this condition, the temperature excursion reaches the smallest value, showing the inferiority of a heat sink of solid silica nano-materials compared to PCM/silica nanocomposite. But the opposite is also true (black curve as shown in Figure 2), showing the PCM better controlling ability and repeatability of temperature when intensively change.

The curves about the relationship between the area percentage of PCM and the total mass and thickness, as shown in Figure 3, illustrate a monotonic decrease in mass and thickness quantities with addition of PCM. The intersections of the curve with the Apcm/Atot = 0 vertical line represent the mass or thickness for only a solid silica nano-materials. The total mass or thickness is most for this condition, and addition of n-eicosane causes a monotonic decrease in both quantities. However, the temperature excursion is highest at this condition when compared to Figure 2. Similarly, the intersections of the curve with the Apcm/Atot = 1.0 vertical

line represent the mass or thickness for PCM. At this condition, the mass and thickness reach their minimum values, showing also the PCM better controlling the ability of temperature with

Figure 3. Relationship between the area percentage of PCM and the total mass and thickness.

Figure 2. Relationship between the area percentage of PCM and the excursion of temperature.

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle

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159

less mass or volume quantities.

Porous Ceramic Matrix Phase Change Composites for Thermal Control Purposes of Hypersonic Vehicle http://dx.doi.org/10.5772/intechopen.70863 159

Figure 2. Relationship between the area percentage of PCM and the excursion of temperature.

The PCM thermal control system and the cross section of designed structure, where the PCM is embedded in silica nano-materials, is depicted in Figure 1. The cross section of the n-eicosane/ silica nanocomposite is an area with 100 mm 100 mm. The performance of the thermal control device is investigated by numerical analysis. The main purpose of the study is to obtain the functions and relations between the mass, thicknesses, temperature excursion, and percentage area of n-eicosane through combined thermodynamic/heat transfer analysis, which raises the minimum temperature and lowers the maximum temperature. According to the thermal cycle period, composite PCMs accumulate heat and uniformly redistribute it. Thus, the phase change temperature of PCM is the target of temperature control, and it must remain within the maximum/minimum operating temperature range of the electronic component. Furthermore, it must be chemically stable for silica nano-materials, which is the material of PCM support, and there must be a small density difference between solid and liquid phases.

It is assumed that the component heat is generated periodically according to the system. In detail, there is 3.6 102 kJ the maximum energy stored by the PCM/silica nanocomposite, Emax, is determined and then a warming up period of 100 W heating, Q-pulse, during the whole cycle. To obtain a quantitative idea of the functional relationships between the variables described above for a given application, thermodynamic/heat transfer was conducted using the given power and energy requirement, using a given area, and using the thermophysical data of the PCM and silica nano-materials, as described in Table 1. These simultaneous Eqs. (1)–(5) can be solved to yield the excursion temperature, TMax-T; the total mass, M(t); and the thickness, t, as functions of PCM area percentage, Apcm/Atot. A MATLAB program was

The hyperbolic function curve about the relationship between the area percentage of PCM and the excursion temperature, as shown in Figure 2, illustrates one interesting fact. The intersections of the curve with the Apcm/Atot = 0 vertical line represent the temperature excursion for only a solid silica nano-material heat sink, which means the temperature excursion for a nanocomposite without n-eicosane. The temperature excursion is highest at this condition and decreases drastically with small additions of n-eicosane until a smaller point is reached around 50% n-eicosane. Similarly, the intersections of the curve with the Apcm/Atot = 1.0 vertical line represent the temperature excursion for the whole fusion heats of PCM. At this condition, the temperature excursion reaches the smallest value, showing the inferiority of a heat sink of solid silica nano-materials compared to PCM/silica nanocomposite. But the opposite is also true (black curve as shown in Figure 2), showing the PCM better controlling ability and

The curves about the relationship between the area percentage of PCM and the total mass and thickness, as shown in Figure 3, illustrate a monotonic decrease in mass and thickness quantities with addition of PCM. The intersections of the curve with the Apcm/Atot = 0 vertical line represent the mass or thickness for only a solid silica nano-materials. The total mass or thickness is most for this condition, and addition of n-eicosane causes a monotonic decrease in both quantities. However, the temperature excursion is highest at this condition when compared to Figure 2. Similarly, the intersections of the curve with the Apcm/Atot = 1.0 vertical

coded to solve the five equations and yields the parametric data discussed above.

2.5.3. Thermodynamic/heat transfer relations

158 Advances in Some Hypersonic Vehicles Technologies

repeatability of temperature when intensively change.

Figure 3. Relationship between the area percentage of PCM and the total mass and thickness.

line represent the mass or thickness for PCM. At this condition, the mass and thickness reach their minimum values, showing also the PCM better controlling the ability of temperature with less mass or volume quantities.

## 2.6. Enlightening

We performed combined thermodynamic/heat transfer analysis to obtain the total mass, thickness, and temperature excursion as functions of percentage area of PCM under given maximum energy and thermal flux based on the composite structural model and the measured thermophysical data. The relationship between the area percentage of PCM and the excursion temperature is the hyperbolic function, showing the nanocomposite better temperature control management. The relationship between the area percentage of PCM and total mass and thickness shows the nanocomposite better temperature control without much mass or volume quantities. These results are attributed to the strong interaction between the n-eicosane and the silica skeleton, which exhibits novel temperature management and energy utilization.
