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Energy Procedia 75 (2015) 3091 - 3097

The 7th International Conference on Applied Energy - ICAE2015

Experimental and numerical study of heat transfer characteristics of a paraffin/metal foam composite PCM

Peng Zhanga*, Zhaonan Menga, Hua Zhua, Yanling Wangb, Shiping Pengb

aInstitute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China _bShanghai Radio Equipment Research Institute, Shanghai 200090, China_

Abstract

Paraffin as a phase change material (PCM) has a great potential to be applied in many energy-related applications due to its appropriate melting temperature and large latent heat. The heat transfer characteristics during phase change of paraffin play a very key role in determining the thermo-fluidic performance. However, the drawback of low thermal conductivity will hamper the broaden application. In this study, we use copper foam to enhance the thermal conductivity of paraffin, and an experimental setup is built to study the phase change heat transfer characteristics. A two-temperature energy equation is used to describe the heat transfer characteristics of the paraffin/copper foam composite. The evolvement of solid-liquid interface and temperature variation during the melting process are experimentally measured and compared with the numerical results. It is found that there is a quite large temperature difference between the paraffin and ligament of copper foam, which is due to the thermal non-equilibrium effect in heat transfer between two phases. The good agreement between the experimental and numerical results indicates that heat transfer characteristics can be well depicted by two-temperature energy equation, which can be further used to depict the heat transfer in thermal energy storage or temperature control using composite PCM. Keywords:metalfoam; paraffin; heat transfer; two-temperature energy model

1. Introduction

Energy consumption has drastically increased in recent years due to very rapid development of the economy and human society. Consequently, a lot of greenhouse gases, such as carbon dioxide, are emitted into atmosphere, which consequently contributes to the global warming. Therefore, there arises an issue of improving energy efficiency so as to decrease the energy consumption. Thermal energy storage is an effective way to balance the mismatch of the energy supply and energy demand; furthermore, renewable energy resources through energy storage can also be integrated into the energy system to make it more sustainable. There are in general three kinds of thermal energy storage methods, i.e., sensible heat storage, latent heat storage and chemical heat storage. Latent heat storage is considered to be effective and advantageous due to its large heat storage capacity by involving the latent heat of fusion and constant

* Corresponding author. Tel.: +86-21-34205505; fax: +86-21-34206814. E-mail address: zhangp@sjtu.edu.cn.

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Applied Energy Innovation Institute

doi: 10.1016/j.egypro.2015.07.637

temperature during phase change. So far, latent heat storage has been widely utilized in many applications, such as solar energy system, electricity peak-shaving and industrial waste-heat recovery. On the other side, the characteristic of constant temperature during phase change can also be used to realize the temperature control, which is very important and essential in such cases as electronic cooling and thermal management. The heat transfer characteristics are very essential in determining the thermo-fluidic performance of the energy system with phase change material as the heat transfer medium. However, the low thermal conductivity of phase change material always hampers its heat transfer performance, which requests that the thermal conductivity must be enhanced. For example, paraffin is a widely used PCM with a thermal conductivity of about 0.2-0.4 W/(m K). As a result, many researches have been conducted to find appropriate methods to enhance the thermal conductivity of the phase change material.

The widely used methods include adding high thermal conductivity matrix into PCM, installing fins on the wall of heat exchanger, encapsulation of PCM and fabricating PCM composites [1]. Among these methods, using metal foam as the thermal conductivity enhancer has been applied in various applications due to its abundant pores, which allows for a good fluidity of liquid PCM and large specific contact surface area between PCM and ligament of metal foam. Here we just mention a few typical recent results about the thermal conductivity enhancement by using metal foam and the investigation of the heat transfer characteristics. Xiao et al. [2] fabricated the composite PCMs using several metal foams and paraffin, and the measurement of thermal conductivities of the composite PCMs indicated that the thermal conductivity could be dramatically enhanced. For example, the thermal conductivities of the paraffin/copper foam composite with the porosity of 88.89% and pore size of 25 PPI was about forty-four times larger than that of pure paraffin [2]. Xu et al. [3] studied non-equilibrium heat transfer in metal foam solar collector with no-slip boundary conditions. They used Forchheimer/Brinkman/Darcy models in momentum equations and non-equilibrium/equilibrium for energy equations. They claimed that the metal foam duct presented both excellent thermal performance and great flow resistance. Li et al. [4] numerically and experimentally studied the melting phase change heat transfer of paraffin saturated in open-celled metallic foams. They investigated the effects of porosity and pore density on the temperature distribution. The velocity and solid-liquid interfaces at various times were studied. They concluded that the melting heat transfer was well enhanced by copper foam, although it would suppress local natural convection. The effective thermal conductivity of composite PCM was larger if porosity was smaller and natural convection was more functional if pore density was larger. However, the model was two-dimensional and the boundaries were considered adiabatic, which might be different from the practical situation. Since the composite PCM can be used for thermal energy storage and temperature control, the thermo-fluidic characteristics are apparently are the fundamental information for the application.

In the present study, we investigate the heat transfer of a composite PCM both experimentally and numerically, where the paraffin is used as the phase change material and copper foam is used as the thermal conductivity enhancer. And the comparison between the experimental and numerical results is also conducted to understand the heat transfer characteristics and mechanisms, in particular the temperature difference between the copper foam ligament and PCM.

2. Experimental Setup

Fig. 1 shows the experimental setup to study the heat transfer characteristics of paraffin/metal foam composite PCM, which is consisted of three parts: rectangular cavity with the composite PCM, heating system and data acquisition system. In the experiments, the composite PCM with a size of about 100.0 mm*100.0 mm*10.0 mm is used, which is fabricated by infiltrating paraffin into copper foam with the porosity of 0.97 and pore size of 25 PPI, and the detailed fabrication process can be found in reference [2]. The composite PCM is encaged in a rectangular cavity made of plexiglass, and the left side of PCM is glued with a porcelain heater which is used to supply heating to melt PCM. A gap of about 5.0 mm between the top surface of composite and inner plexiglass cavity surface is left to accommodate the

volume expansion of melted paraffin. Furthermore, the plexiglass cavity was covered by the thermal insulation materials to reduce the heat loss to the surroundings. The heating is supplied by a DC voltage power supply. In the experiments, the electric voltage and current are measured to determine the heat flux supplied to the composite PCM.

In the experiments, the evolvement of the solid-liquid interface is observed to study the heat transfer characteristics of the phase change of composite PCM. We select one location to monitor the temperatures of the PCM and ligament of copper foam by using two pre-calibrated T-type thermocouples, where one thermocouple is inserted into PCM and the other is soldered on the surface of the ligament of copper foam to measure the temperature difference between PCM and copper foam. It is estimated the uncertainty of the supplied heat flux is about 3%, and that of the temperature is about 0.5 °C. The temperatures along with the electric voltage and current are recorded by the data acquisition system, and they are then stored in a computer for further analysis.

3. Mathematical Model

Fig. 2 shows the schematic illustration of the numerical model of paraffin/copper foam composite PCM. The length, width and height of unit are about 100.0 mm*10.0 mm*100.0 mm, respectively. The left side is subjected to a heat flux which can be approximately described as ^=6207.51-0.0108/ (W/m2). The following assumptions are used to simplify the numerical calculation:

(1) The liquid paraffin is considered as incompressible Newtonian fluid, and the density is subjected to the Boussinesq approximation.

(2) The copper foam is considered as homogeneous and isotropic, and the flow of the liquid PCM in copper foam is laminar flow subjected to Darcy's law.

Fig. 1 Schematic illustration of the experimental setup

PCM+Metal Foam

convection

Fig. 2 Schematic illustration of paraffin/copper foam composite PCM

+ V(pfU ) = 0 (!)

(3) Thermo-physical properties of both copper foam and paraffin are constant during phase change process.

(4) The heat loss is mainly due to the heat transfer between the composite PCM and the surrounding environment dominated by natural convection, and the heat transfer coefficient is considered as constant.

The follows are the equations used in the numerical investigation. Continuity equation:

dpL dr

Momentum equations:

PL du +Pf_ d(uu) + d(uv1 +d(uwy) = _dp+Ev2u _ E+p£ u | _ (1^ A u (2)

e dz £2 dx dy dz dx £ K k ft +

Pf dv , Pf td(vu) , d(vv) 5(vw) dp u 2 u Plc\\, (1 -Pf A , tt (3)

--+ 2 (-H--H--) =--H—^ v - (— + +/TM)v--3-Amv + pga(T - T0)

e dr e dx dy dz dy £ K K fi + a> m

PLdw (5Cwu) + d(wM) + 5(ww)) = _dp + Ey2w _ {E+PfC\w\)w _ (1 -^)2 A w (4)

£ dr £2 dx dy dz dz £ K K1/2,1 P3 +m m

Energy equations:

For PCM: ep (c + L—^)^ + Pfcf (u T + v T + w-% = (kd + ke )V2T + h a (7-Tf) (5)

Ff L —Tf dz LL dx dy dz td Le L sL sL ' L

For copper foam: d _ E)pfs K = kMVX _ hfasf T - Tf) (6)

Where, pf is the density of paraffin, kg/m3; e is the porosity of copper foam; ^ is dynamic viscosity, kg/m- s; m is the pore density, PPI; df and dp are fibre diameter and pore size, respectively, m; a is thermal expansion coefficient, K-1; p is liquid fraction; Am is a constant parameter, which is between 105 and 108; kf is thermal conductivity of fluid, W/m-K; C is inertial coefficient, m-1; K is permeability, m-2; cs is the specific heat capacity of copper foam, J/kgK; cf is the specific heat capacity of solid paraffin, J/kgK; ci is the specific heat capacity of liquid paraffin, J /kgK; Tm1 and Tm2 are the lower and upper limits of melting temperature of paraffin, K; Ts is the temperature of copper foam, K; Tf is the temperature of paraffin, K; L is the latent heat of paraffin, J/kgK. In the present study, the melting temperature and latent heat of paraffin are determined by differential scanning calorimetry (DSC), and the other thermo-physical properties are from reference [5]. The thermo-physical properties of copper foam can be estimated from the empirical equations shown in reference [6]. And the determination of the geometrical parameters of the copper foam can be found in reference [6]. The appropriate initial and boundary conditions are determined according to the experiments and used in the numerical calculation. 3D numerical calculation is conducted in the present study. We use grid size of about 231000 in the numerical calculation to compromise the accuracy and computational cost, and convergences of the solution are checked at each time step of the numerical calculation to guarantee the numerical stability.

4. Results and Discussion

Fig. 3 shows the evolvement of the solid-liquid interface of the composite PCM for both numerical and experiment results at 2000 and 4000 s, respectively. It can be seen that the paraffin at the top left corner melts more rapidly than that on the bottom due to natural convection, and the interface curves gradually. The numerical result agrees quite well with the experimental result. There is apparently a mushy region between the liquid area and solid area; in addition, the mushy region at the top is narrower than that on the bottom. However, it can be seen from the figure that paraffin in the numerical investigation melts slightly faster than that in the experiment, in particular for the top area of composite

PCM. This might be attributed to the fact that only heat losses of five surfaces are considered in 3D numerical calculation, and that for the heating surface is not included. Furthermore, the heat absorbed by the thermal insulation material is not considered in the numerical calculation. Therefore, the heat losses in the experiment are more than that in the numerical calculation, which leads to the discrepancy.

2000 s 4000 s 2000 s 4000 s

(a) (b)

Fig. 3 The results of the evolvement of solid-liquid interface, (a) numerical result, (b) experimental result

Fig. 4 shows the variation of the numerical and experimental results for the temperature and temperature difference at the monitor point with time. Due to the technical difficulty of mounting two thermocouples at the same location, the locations of the thermocouples in PCM and on the surface of ligament of copper foam shift slightly. Therefore, the location for the copper foam is chosen to be 55.0 mm from the left suface and 41.0 mm from the bottom, and the location for paraffin is chosen to be 57.0 mm from the left and 41.0 mm from the bottom. As shown in Fig. 4 (a), the numerical results agree reasonably with the experimental results. The temperature seems to increase very fast first in the sensible heat storage region. The temperature increase slows down at around 60.0 °C due to the effect of the phase change. After paraffin changes into liquid, the temperature continues to increase.

Time (s) Time (s)

(a) (b)

Fig. 4 Comparison of the numerical results with the experimental results. (a) temperature, (b) temperature difference

Shown in Fig. 4 (b) is the temperature difference between the copper foam and paraffin at the monitor point. It is seen that the temperature of copper foam is higher than that of paraffin, and temperature difference becomes larger as time elapses. And there are three stages for the temperature difference as follows. In the initial stage, heat conduction is the dominant heat transfer mode. The thermal conductivity of copper foam is much larger than that of paraffin, which results in higher temperature of copper foam than that of paraffin. Gradually, the temperature difference decreases as the temperature approaches the melting point. When the temperature of paraffin reaches melting temperature, paraffin will absorb much heat during phase change and the temperature tends to keep constant due to large latent heat of fusion. Therefore, the temperature difference increases again in this stage, as shown by the second peak in Fig. 4 (b). After phase change completes, natural convection gradually comes into play, which enhances the heat transfer between liquid paraffin and ligament of copper foam. Therefore, the temperature difference decreases again. Fianally, the temperature of paraffin approaches or might be even higher than that of the ligament of copper foam due to the effect of the natural convection. It can be seen

from Fig. 4 that the two-temperature energy equation can well describe the phase change heat transfer characteristics of paraffin/copper foam composite.

2000 s, Copper foam 2000 s, Paraffin 4000 s, Copper foam 4000 s, Paraffin

Fig. 5 Temperature fields of copper foam and paraffin

Shown in Fig. 5 are the temperature fields of copper foam and paraffin at 2000 and 4000 s, respectively. It can be seen that the temperature of copper foam is gernally higher than that of paraffin in solid region because heat conduction dominates heat transfer. However, the temperature difference between copper foam and paraffin is small due to the heat transfer enhancement by natural convection of the liquid after the paraffin is melted. With the elapse of time, the temperature of liquid paraffin becomes even higher than that of copper foam due to the dominant effect of natural convection, which can also be seen from Fig. 4 (b).

Conclusion

In the present study, the heat transfer characteristics of paraffin/copper foam composite PCM under heating are investigated both experimentally and numerically. The applicability of two-temperature energy equation is validated by comparison of the experimental and numerical results of the solid-liquid interface and the temperature variation. There is quite large temperature difference between the PCM and ligament of copper foam due to thermal non-equilibrium conditions of two phases, which must be taken into consideration in the modeling. Such heat transfer investigation can be further applied to the investigation of the thermal energy storage and thermal management.

Acknowledgements

This research is supported by the NSFC under the Contract No. U1137605, the MOST Program for International Cooperation under the Contract No. 2013DFG60080 and SAST Foundation (SAST201438).

References

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[2] Xiao X, Zhang P, Li M. Effective thermal conductivity of open-cell metal foams impregnated with pure paraffin for latent heat storage. Intt J Therm Sci 2014;81:94.

[3] Xu HJ, Gong L, Huang SB, Xu MH. Non-equilibrium Heat Transfer in Metal-foam Solar Collector with No-slip Boundary Condition. Int J Heat Mass Tran 2014;76:357-365.

[4] Li WQ, Qu ZG, He YL, Tao WQ. Experimental and Numerical Studies on Melting Phase Change Heat Transfer in Open-cell Metallic Foams Filled with Paraffin. Appl Therm Eng 2012;37:1-9.

[5] Zhang P, Ma ZW, Wang RZ. An overview of phase change material slurries: MPCS and CHS. Renew Sust Energ Rev 2010;14:598-614

[6] Zhang P, Xiao X, Li M. Experimental and numerical investigation of phase change heat transfer characteristics in open-cell metal foam infiltrated with eutectic salt for solar energy storage. Proc. of IHTC15 2014; paper No. IHTC15-8518

Biography

Dr. Peng Zhang is professor in Shanghai Jiao Tong University. His research is focused on heat transfer and fluid flow, such as thermal energy storage, flow and heat transfer of phase change material slurry and so on.