Heat transfer of phase change materials (PCMs) in porous materials

Abstract

In this paper, the feasibility of using metal foams to enhance the heat transfer capability of phase change materials (PCMs) in low- and high-temperature thermal energy storage systems was assessed. Heat transfer in solid/liquid phase change of porous materials (metal foams and expanded graphite) at low and high temperatures was investigated. Organic commercial paraffin wax and inorganic calcium chloride hydrate were employed as the low-temperature materials, whereas sodium nitrate was used as the high-temperature material in the experiment. Heat transfer characteristics of these PCMs embedded with open-cell metal foams were studied. Composites of paraffin and expanded graphite with a graphite mass ratio of 3%, 6%, and 9% were developed. The heat transfer performances of these composites were tested and compared with metal foams. The results indicate that metal foams have better heat transfer performance due to their continuous inter-connected structures than expanded graphite. However, porous materials can suppress the effects of natural convection in liquid zone, particularly for PCMs with low viscosities, thereby leading to different heat transfer performances at different regimes (solid, solid/liquid, and liquid regions). This implies that porous materials do not always enhance heat transfer in every regime.

Keywords

heat transfer / thermal energy storage / phase change materials / natural convection / porous media

Introduction

Latent heat storage systems using phase change materials (PCMs) as heat storage media have become an attractive technology in many engineering applications. These types of storage systems have high heat storage density and the capability to store heat as latent heat of fusion with a small PCM volume at a moderate temperature variation [1]. In low-temperature latent heat storage systems, paraffin and hydrated salts are often used as heat storage media; most of these media suffer from the common problem of low thermal conductivity of approximately 0.2 and 0.5, respectively, which prolongs the charging and discharging period. Bugaje [2] reported that phase change time is the most important design parameter in latent heat storage systems. Suitable thermal conductivity parameters are used to provide a high thermal conductivity to the designed heat transfer rates. Bugaje [2] found that adding aluminum additives into paraffin wax can significantly reduce the phase change time in heating and cooling processes. Koh and Stevens [3] observed that the effectiveness of regenerative devices is increased by filling the flow passage with steel particles. Chow et al. [4] concluded that the effective thermal conductivity of PCMs can be increased using smaller encapsulated PCMs enclosed in a container filled with a liquid metal. However, the use of metal fillers results in significant weight increase and high cost of the storage system. Other researchers used low-density additives, such as porous silica catalyst [5] or activated carbon [6], to enhance effective thermal conductivity. These studies demonstrated the critical role of mean pore size (neither too big nor too small), especially for activated carbons. Nonetheless, those two porous media do not improve effective thermal conductivity [7]. Fukai et al. [8,9] inserted carbon-fiber brushes into the shell side of a heat exchanger to enhance the conductive heat transfer rates in PCMs. They discovered that the brushes essentially improve heat exchange rate during the charge and discharge processes even when the volume fraction of the fibers is ~1%, and proposed a numerical model describing anisotropic heat flow in the composite. Elgafy and Lafdi used carbon nanofibers to enhance the thermal performance of a PCM [10]. They reported that increasing the mass ratio of carbon nanofibers can significantly increase the cooling rate during the solidification process of the new nanocomposites.

The use of a porous matrix due to its light weight and high surface area has gained increasing importance. In 1992, Hoogendoom and Bart [11] reported that the low thermal conductivity of PCMs can be enhanced by embedding a metal matrix structure in them. Mauran et al. [12] used a solid matrix made of graphite as a support for reactive salts; meanwhile, Tong et al.[13] inserted a high-porosity metal matrix into the PCM to increase heat transfer. Py et al. [7] developed a supported PCM made of paraffin impregnated by capillary forces into a graphite matrix, which they found to have high stability and high thermal conductivity. Pincemin et al. [14] tested the thermal performances of different composites made of graphite and PCMs, including organic and inorganic PCMs, and discussed their manufacturing methods. Lafdi et al. [15] developed surface-treated paraffin wax/carbon foam composites, and proposed that the increase of surface energy of carbon foams can improve the overall thermal performance of wax/carbon foam composites.

For high-temperature storage systems, Pincemin et al. [16] tested several conductive thermal storage composites at both laboratory and industrial scales within high temperature ranges. They found that the tested composites have isotropic properties and thermal conductivity intensification in the medium range [a factor of 10% (wt) for 7% (wt) in graphite] and cold compressed composites have highly anisotropic properties and strong intensification in thermal conductivity [a factor of 31 at 200°C for 20% (wt) in graphite]. Siahpush et al. [17] evaluated how copper porous foam (CPF) enhances heat transfer performance in a cylindrical solid/liquid phase change thermal energy storage (TES) system. (The CPF had 95% porosity and the PCM was 99% pure eicosane.) Their experimental results revealed that the CPF can increase effective thermal conductivity from 0.423 to 3.060 W/(m·K).

Thermal transport processes in metal foams, such as forced convection, thermal radiation, and boiling heat transfer, have been extensively studied [18-25]. Although extensive investigations have been conducted on the positive effect of porous materials in low-temperature thermal energy storage applications, few papers have reported the results of PCM/Metal foam and PCM/expanded graphite composites applied to low and high temperature thermal storage. In this paper, the heat transfer characteristics of PCMs embedded in porous materials (metal foams and expanded graphite) at low and high temperatures are investigated to examine the feasibility of using metal foams in enhancing the heat transfer capability of PCMs in both low- and high-temperature thermal energy storage systems.

Experimental test

Materials

In this experiment, three kinds of PCMs were used, i.e., commercial paraffin wax RT 27 and calcium chloride hexahydrate salts for low-temperature storages, and sodium nitrate for high-temperature storages. Their physical characteristics are presented in Table 1. The PCMs were embedded in highly conductive porous materials, i.e., metal foams and expanded graphite. Open-cell metal foams composed of inter-connected dodecahedral-like cells with 12-14 pentagonal or hexagonal faces were made by sintering technique. The cells were randomly oriented and mostly homogeneous in size and shape. Porosity (ϵ) and pore density in pores per inch (ppi) were used to describe the porous medium. Three different kinds of metal foams (MF1, MF2, and MF3) were used: MF1 only for low-temperature thermal storage and all of them for high-temperature thermal storage. The specifications of the metal foams are listed in Table 2. Expanded graphite has a low bulk density and good mold ability, as well as a high surface energy. It can form a razor-thin liquid film that can stop the permeation of the media. Expanded graphite was tested and the results were compared with those of metal foams. To explore the influence of expanded graphite on the PCMs, the composites of paraffin and expanded graphite with a graphite mass ratio of 3%, 6%, and 9% were developed.

Experimental set up

The test facility consisted of the main test section, a power control system, and a data acquisition system (Fig. 1). The main test section was comprised of an infrared heater, a container, specimen, thermal insulations, and thermocouples. The power input to the heater and the thermocouple signals were recorded by the data acquisition system (IMP 3595). The thermocouples (T-type thermocouples for low temperature experiments and K-type thermocouples for high temperature experiments) were used to monitor the temperature variations at pre-selected different height locations in the specimen.

For low-temperature thermal storage, the experiment was conducted in a rectangular container (80 mm×50 mm×30 mm) made of synthetic glass (except the bottom surface) and in a copper plate with a rubber heater tightly attached. The external surfaces of the container were insulated with Styrofoam board to reduce heat loss from the sides and bottom to the surroundings. Therefore, the melting process can be regarded as a one-dimensional problem if the buoyancy-driven natural convection effect is not considered. Along the height of the container, three thermocouples were used to monitor temperature variations at pre-selected sites in the specimen (5, 10, and 15 mm away from the copper plate). The thermocouples were placed at the center of the sample to reduce the end effect. Another thermocouple was stuck on the copper plate by silver paint to precisely record the temperature of the heater.

For high-temperature thermal storage, the infrared heater was used. The experiment was performed in a cylindrical copper container with a 75 mm diameter. The containers were insulated with asbestos fabric more than 100 mm thick. Five thermocouples were put into the container (5, 15, 25, 35 , and 45 mm away from the heating surface) to measure the changes in temperature inside the samples. Another thermocouple was used to record the temperature of the heating surface.

A constant heat flux of 3.75 kW/m² was used for all low-temperature experiments and a constant heat flux of 13.6 kW/m² for all high-temperature experiments. The solidification/discharging processes of both low-temperature and high-temperature experiments were performed under natural ambient cooling. The temperature signals were recorded in the computer for further data processing.

Results and discussion

Low temperature

Figures 2 and 3 present the temperature variations with time for paraffin and calcium chloride hexahydrate, respectively. In the pure PCM experiments, calcium chloride hexahydrate exhibits heat transfer behaviors different from the paraffin. The temperature inside calcium chloride hexahydrate rises quickly and then stabilizes at the melting temperature, which is different from the sudden rising of temperature of paraffin around melting temperatures. One reason for this is that calcium chloride hexahydrate has a fixed melting temperature, whereas paraffin does not. A second reason is that the solid calcium chloride hexahydrate has a higher thermal conductivity resulting in faster heat conduction to the solid. Another possible reason is that the higher density of liquid calcium chloride hexahydrate results in a weaker natural convection.

Temperature difference is defined as \mathrm{\Delta }T=T_{\mathrm{h}}-T_{\mathrm{i}}, where T_{\mathrm{h}} is the temperature of the heating surface and T_{\mathrm{i}} is the local temperatures inside the samples. Figures 4 and 5 demonstrate temperature differences between the heater and local measuring points inside the PCMs, namely, the locations of the thermocouples 5 , 10, and 15 mm away from the bottom plate. The temperature differences of the samples with metal foams are lower than those without metal foams (Figs. 4 and 5). The temperature differences can be reduced to ~25% of the pure paraffin and to ~30% of the calcium chloride hexahydrate without metal foams. Lower temperature difference indicates higher heat transfer capability caused by the metal foam structures embedded in PCMs, such as high surface density and strong mixing capability of the fluid, which can significantly enhance the overall heat transfer.

Figure 6 describes the temperature variations in the cooling process of two samples of calcium chloride hexahydrate. Similar to the paraffin, at the beginning of the cooling process, the temperature of the sample without metal foam is slightly lower than that with metal foam. Solidification begins after 100 min for the sample with metal foams, and 175 min for that without metal foams.

Similar to the melting processes, some interesting differences between the two PCMs during the solidification process are observed. The temperatures of calcium chloride hexahydrate (for both with and without metal foams) decrease to their lowest and then increase sharply to their solidification point due to the inherent characteristic of severe subcooling (5°C for the sample with metal foams and 8°C for that without metal foams). Subcooling is one of the major shortcomings that limit the application of inorganic salts. Nevertheless, open-celled metal foams embedded in PCMs can considerably reduce the subcooling of calcium chloride hexahydrate, probably by providing the nucleation sites through the foam struts.

Figure 7 presents the comparison between the metal foam and expanded graphite. The results show that the metal foam can shorten the temperature difference by 25% of the pure paraffin, indicating the highest effective thermal conductivity of the metal foam; on the other hand, the composite with 9% graphite can only enhance heat transfer rate by 30%. The main difference lies in the continuous inter-connected structure of the metal foam, whereas the structure of expanded graphite is discontinuous and broken.

The main purpose of thermal energy storage is to store heat that can be used when required. Thus, volumetric heat fusion, which is thermal energy storage capability, is one of the most important parameters of thermal energy storage systems. The addition of metal foams certainly weakens the volumetric heat fusion of the system. Volumetric heat fusion decreases with the increase in porosity of the metal foam. By comparing paraffin with calcium chloride hexahydrate, the results reveal that when the volumetric heat fusion of pure PCM is higher, the stronger is the influence of the metal foam on the volumetric heat fusion of the system. In the composites of paraffin and expanded graphite, the results reveal that volumetric heat fusion decreases with the increase in the mass ratio of expanded graphite.

High temperature

PCM sodium nitrate (NaNO₃) was used in high-temperature storage experiment. Figure 8 shows the experimental results of the middle location T₃ of the sample for the heating process from solid state at 250°C to liquid phase at ~350°C, at which point the melting process occurs. Compared to other PCMs, NaNO₃ has two kinds of phase transition temperatures: solid-solid phase transition temperature at 276°C (labeled as 1-5) and solid-liquid phase transition temperature at 306°C (labeled as 6-10). When NaNO₃ reaches the solid-solid phase transition point, most of the energy is used to change the crystal lattice structure of NaNO₃. This variation leaves a little step in the temperature curves. As shown in Fig. 8, five clear turning points 1-5 occur in the curves of temperature difference \mathrm{\Delta }{T}_{\mathrm{3}}. In this regime, heat conduction is still the dominant heat transfer mechanism. The local NaNO₃ at T₃ with embedded metal foams or expanded graphite can absorb more heat than that without porous materials within the same heating period. Based on the measurements, the temperatures T₃ of the samples with porous materials are found to be higher than that without porous materials; this leads to a lower corresponding temperature difference \mathrm{\Delta }{T}_{\mathrm{3}} (Fig. 8).

After the solid-solid phase transition process, solid NaNO₃ was heated continuously to its melting point. In the phase change process, NaNO₃ has three regions in the container: liquid, mushy, and solid. Heat conduction and natural convection are the dominant heat transfer mechanisms in the solid region and the liquid region, respectively. Compared to the clear status of NaNO₃ in solid and liquid regions, the mushy region is a soft mixture layer of solid and liquid phase NaNO₃. Liquid phase NaNO₃ decreases from 100% at liquid-mushy surface to 0% at mushy-solid surface. Phase change of NaNO₃ happens inside this region, in which the temperature of NaNO₃ almost maintains a constant melting temperature with a little variation. During the melting process, the NaNO₃ mixture at the liquid-mushy surface becomes liquid whereas the solid NaNO₃ at mushy-solid surface changes. With the heat input, this region can continuously move to a higher level.

Below the mushy region, natural convection is more complicated in porous metal foam structures than that without metal foams. Although metal foam structures enhance conduction, natural convection can be weakened by metal foams. The pores of expanded graphite are so small that they strongly suppress natural convection inside the composite. In Fig. 8, these temperature profiles of T₃ and the corresponding temperature differences \mathrm{\Delta }{T}_{\mathrm{3}} are much more complicated than that of pure NaNO₃ after local NaNO₃ fully melts.

After the PCMs are fully melted, the structures of metal foam and expanded graphite may hinder overall heat transfer rate due to the effects of suppressed natural convection compared with that of pure PCMs. The average temperature difference between NaNO₃ and the heating surface can be used to characterize the overall heat transfer performance:

(1)\mathrm{\Delta }T=T_{\mathrm{6}}-(T_{\mathrm{1}}+T_{\mathrm{2}}+T_{\mathrm{3}}+T_{\mathrm{4}}+T_{\mathrm{5}})/\mathrm{5.0.}

As illustrated in Fig. 9, the average temperature differences between containers A and C are almost the same; the average temperature differences between containers B and D are also similar, whereas the average temperature difference of container E is in the middle of these four profiles. The average temperature difference between B and D is ~8°C higher than that between A and C. This means that the heat transfer rates of the pure NaNO₃ inside container A and the composite inside container C are higher than that of the composites inside containers B and D. This phenomenon indicates that the presence of metal foam suppresses natural convection inside containers B and D. This kind of negative effect is higher than that of positive effect generated by heat conduction through the metal strut. In container C, this positive effect (conduction) generated by lower porosity metal foams is nearly the same as its negative effect (natural convection). Therefore, an optimal metal foam structure should be developed for the overall heat transfer in PCMs. The heat transfer coefficient of 3% (wt) expanded graphite inside container E is higher than those inside containers B and D with a piece of 0.95 porosity metal foam, but is lower than that inside container C with a piece of 0.90 porosity metal foam. The results show that porosity for both porous materials is a dominant factor in enhancing heat transfer for heating liquid phase PCMs.

The weakening effect of natural convection at liquid zone caused by the porous materials (foams or graphite) is much smaller than the effects of paraffin and calcium chloride hexahydrate (Figs. 4 and 5). This observation can be attributed to the low viscosity of NaNO₃, which is ~10% of paraffin and calcium chloride hexahydrate, which in turn results in a much stronger natural convection. Hence, the weakening effect of porous materials is more significant.

Conclusions

In this paper, the feasibility of using metal foams and expanded graphite to enhance heat transfer capability in thermal energy storage systems was assessed. The results show that heat transfer can be enhanced by the use of these porous materials, thereby reducing the temperature difference among PCMs and shortening the charging/discharging period significantly. The structures of metal foam and expanded graphite can significantly enhance heat transfer in the solid region, but they can suppress the effects of natural convection in the liquid zone, particularly for the PCMs with low viscosities. The overall performance of metal foams is superior to that of expanded graphite. Given that heat transfer performance and heat storage capability vary at different regimes (solid, solid/liquid, and liquid regions) in low- and high-temperature storage systems, an optimal metal foam structure or expanded graphite fraction can be developed using PCMs for optimal overall thermal energy storage performance.

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