#### Abstract

This paper presents a numerical study of melting of Nanoprticle-Enhanced phase change material (NEPCM) inside a shell and tube heat exchanger using RT50 and copper particles as base material and nanoparticle, respectively. In this study, the effects of nanoparticles dispersion (, 0.03, and 0.05) on melting time, liquid fraction, and penetration length are investigated. The results show that the melting time decreases to 14.6% and the penetration length increases to 146% with increasing volume fraction of nanoparticle up to .

#### 1. Introduction

In the recent years, due to the problems of fast depletion of conventional energy sources and ever increasing demand of energy, the implementation of proper thermal energy storage is one of the most important issues in energy conversion systems. There are three methods for storing the thermal energy: sensible, latent, and thermochemical heat or cold storage. Thermal storage systems, based on the latent heat storage, have been relevant, especially in solar thermal applications. Solid-liquid phase change during heat storage and recovery processes provides considerable advantages such as high storage capacity and nearly isothermal behavior during charging and discharging processes.

Zalba et al. [1] performed a detailed review on thermal energy storage that dealt with PCM, heat transfer studies, and applications. Farid et al. [2] also presented a review on the analysis of PCM, hermetic encapsulation, and application of PCM. Ettouney et al. [3] conducted an experimental study to investigate the solidification and melting on shell and tube arrangement. In their study, the heat transfer fluid (HTF) flows in the inner tube and the wax, as a phase change material, is stored on the shell side. The results showed that the melting and solidification process is dominated by natural convection and conduction, respectively. Seeniraj et al. [4] investigated the transient behavior of high temperature PCMs stored in shell and tube heat exchanger. They observed that if an unfinned tube is used, then some quantity of PCM nearer to the exit of the tube would remain in solid state. This is because nearer to the exit, the difference between HTF temperature and PCM’s melting point would be very small. It is also reported that the presence of a few number of annular fins maintains relatively high temperature difference between HTF and melting point, and thus melting could be found everywhere in the axial direction.

Hosseini et al. [5] investigated the effect of inlet temperature of the heat transfer fluid (HTF) on melting process in a shell and tube heat exchanger numerically and experimentally. They found that the melting front appeared at different times at positions close to the HTF tube and progressing at different rates outwards towards the shell. They obtained that by increasing the inlet temperature to 80°C, the melting time is decreased to 37%.

Vyshak and Jilani [6] numerically analyzed the effect of different configurations of latent heat thermal storage (LHTS) that having the same volume and surface area of heat transfer. They presented a comparative study of the total melting time of a phase change material (PCM) packed in three containers of different geometric configurations: rectangular, cylindrical, and shell and tube. Obtained results showed that cylindrical shell containers take the least time for equal amounts of energy storage, and this geometric effect is more pronounced with an increase in the mass of the PCM.

In order to enhance the heat transfer exchange during melting, Adine and Qarnia [7] studied the effect of multiple PCMs with different melting temperatures in shell and tube heat exchanger. They used two-PCM system (LHSU2) and single-PCM system (LHSU1) during charging process and compared the thermal performances of the latent heat storage units. Their results showed that when the mass flow rate was increased, the two-PCM system was efficient only for lowest HTF inlet temperature. Therefore, multiple-PCM unit is more efficient for low values of mass flow rate and inlet temperature of HTF.

However, the low thermal conductivity in PCM limits the heat transfer rates during both charging and discharging processes in the heat storage systems. To overcome this problem, a wide range of investigations were carried out aiming to enhance the thermal conductivity of the organic PCMs or increase the heat transfer performance. Using nanofluid to increase the heat transfer shows a great opportunity in storage system. The enhanced PCM (nanofluid) is found to exhibit lengthened melt times and shortened cool-down times.

Masuda et al. [8] reported on enhanced thermal conductivity of dispersed ultrafine (nanosize) particles in liquids. Soon thereafter, Choi and Eastman [9] presented the benefit of using the nanoparticles dispersed in a base fluid for this new class of fluids with superior thermal properties. Rahimi et al. [10] numerically studied the natural convection of mixture of nanoparticles and water near its density maximum in a rectangular enclosure. They found that heat transfer rate considering a non-Boussinesq temperature-dependent density (inversion of density) undergoes a nonlinear trend with changes in nanoparticle volume fraction. Khodadadi and Hosseinizadeh [11] reported a numerical solution on improvement of thermal storage energy using nanoparticle-enhanced phase change material (NEPCM). They found that the resulting nanoparticle-enhanced phase change materials exhibit enhanced thermal conductivity in comparison to the base material. In addition, their numerical results showed reduction in the overall solidification time. Ranjbar et al. [12] investigated the influence of utilizing nanoparticle on enhancement of heat transfer in a three-dimensional cavity. They showed that the suspended nanoparticles substantially increase the heat transfer rate. Hosseinizadeh et al. [13] investigated numerically unconstrained melting of nanoparticle-enhanced phase change materials inside a spherical container. They used RT27 and copper particle as base material and nanoparticle that enhanced the thermal conductivity of base material. Their investigations showed that the nanoparticles cause an increase in thermal conductivity of NEPCM compared to conventional PCM. Khodadadi and Fan [14] utilized an analytic/integral approach to solve one-dimensional Stefan problem for a nanofluid that undergoes freezing. Their model accounts for the thermal property jumps between the liquid and solid phases and showed that the freezing time decreases as the volume fraction of the nanoparticle is raised. There are only few experimental data that are addressing the use of particles in order to enhance PCMs. Wu et al. [15] developed a new sort of nanofluid phase-change material by suspending a small amount of nanoparticles in melting paraffin. Nanoparticles of Cu, Al, and C/Cu were added to the melting paraffin to enhance the heat transfer rate of paraffin. They concluded that Cu nanoparticles have the best performance for heat transfer. Wu et al. [16] studied the potential of Al_{2}O_{3}–H_{2}O nanofluids as a new phase change material for the thermal energy storage of cooling systems. The thermal response test shows that the addition of Al_{2}O_{3} nanoparticles remarkably decreases the supercooling degree of water, advances the beginning freezing time and reduces the total freezing time. They showed that by adding 0.2 wt% Al_{2}O_{3} nanoparticles, the total freezing time of Al_{2}O_{3}–H_{2}O nanofluids can be reduced to 20.5%.

In the present study, the solidification behavior of the NEPCM and the effect of various volume fractions of nanoparticles (0, 0.03, and 0.05) on melting rate in a cylindrical shell container are numerically studied.

#### 2. Problem Statement and Boundary Conditions

Figure 1 presents the schematic of the physical model. The storage unit consists of two concentric tubes of 1 m length. The diameters of inside and outside tubes are 22.22 mm and 85 mm, respectively, and an annulus space is filled with NEPCM in solid phase. The thermophysical properties of the PCM based on a commercially available material, RT50 (Rubitherm GmbH), and nanoparticle which are used for simulation are given in Table 1. In addition, variable density is defined as for in the liquid state. Also water is used as the HTF that flows through the inner tube and exchanges heat with NEPCM. The initial temperature of the whole system is , and on the other hand, the lateral surface of the outer tube is insulated, while the HTF is at temperature .

#### 3. Mathematical Formulation

In order to simulate phase change of NEPCM in a shell and tube heat exchanger, enthalpy-porosity method [17, 18] is used. The flow is considered unsteady, laminar, incompressible, and three-dimensional. The viscous dissipation term is considered negligible, so that the viscous incompressible flow and the temperature distribution in annulus space are described by the Navier-Stokes and thermal energy equations, respectively. Considering the NEPCM as a continuous medium with thermal equilibrium between the base fluid and the solid nanoparticle, the governing equations for NEPCM are as follows.

Continuity:

Momentum:

Thermal energy:

The enthalpy of the material is computed as the sum of the sensible enthalpy,, and the latent heat, : where

The latent heat content can be written in terms of the latent heat of the material, : where may vary from zero (solid) to (liquid). Therefore, the liquid fraction, , can be defined as [19]:

The density of the nanofluid is given by

The heat capacities of the nanofluid and part of the Boussinesq term are

In above equations, is the volume fraction of the solid particles and subscripts, , and stand for base fluid, nanofluid, and solid particle, respectively. The effective dynamic viscosity of the nanofluid containing a dilute suspension of small rigid spherical particles given by Brinkman [20] is

The thermal conductivity of the stagnant (subscript 0) nanofluid is given by

The effective thermal conductivity of the nanofluid is

The thermal conductivity enhancement term due to thermal dispersion is given by

The empirically determined constant is evaluated following the work of Wakao and Kaguei [21].

Also the latent heat evaluated using [22] is

In (2), is the Darcy’s law damping terms (as source term) that are added to the momentum equation due to phase change effect on convection. It is defined as

The coefficient is a mushy zone constant. This constant is a large number, usually 10^{4}–10^{7}. In the current study, is assumed constant and is set to 10^{6}.

#### 4. Numerical Procedure and Validation

The SIMPLE algorithm [23] within a 3D in-house developed code [10] was utilized for solving the governing equations. The QUICK differencing scheme [24] was used for solving the momentum and energy equations, whereas the PRESTO scheme [24] was adopted for the pressure correction equation. By solving the governing equations at each time step, liquid mass fraction has been updated using (7). The computational grid was built of 300,000 cells and the time step in the calculations was as small as 0.05 s. The grid size was chosen after careful examination of the independency of the obtained results for grids of 200,000, 300,000, and 400,0000. Also, the time step for integrating the temporal derivatives was set to 0.05 s, following comparison of selected quantities obtained from simulations using 0.1, 0.05, and 0.01. Figure 2 shows the effects of grid size and time step on the variation of liquid fraction versus melting time at . The convergence was checked at each time step, with the convergence criterion of 10^{−7} for all variables.

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In order to validate the computational modeling of melting in our finite volume CFD code, an initial run was performed and compared with experimental data of Agyenim et al. [25] for a horizontal concentric tube heat exchanger incorporating a medium temperature phase change material (PCM) Erythritol, with a melting point of 117.7°C Figure 3 shows a comparison of average temperature profile in the PCM versus time between two works. The results of present calculation are in good agreement with those of Agyenim et al. [25].

#### 5. Results and Discussion

The contour of liquid fraction in melting process at various times for different volume fractions is shown in Figure 4. As it can be seen, melting process begins from contact surface of NEPCM and hot tube. At the beginning of the process, the molten region increases symmetrically and uniformly around the inner tube due to the conduction mechanism.

Then by advancing in time, the molten region develops due to raising of buoyancy effect; so the convection will be dominant heat transfer mechanism and molten region is no longer symmetrical.

As depicted in Figure 4, melted NEPCM adjacent to the hot tube moves upward and penetrates into solid region. The increase in molten region in the upper half of the heat exchanger is completely apparent after 60 minutes. On the other hand, due to the existence of solid NEPCM, the conduction heat transfer in lower half of the heat exchanger causes a temperature rise.

It should be mentioned that the rate of NEPCM melting increases as volume fraction increases. Figure 4 shows this phenomena clearly in and after 60 minutes.

Furthermore, progresses of melt front in midway along the length of heat exchanger are schematically shown in Figure 5. It can be observed that an increase in volume fraction of nanoparticle causes more penetration velocity of melt front.

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Pure PCM needs 8825.2 seconds for completing melting while by adding of nanoparticle from to and results in melting time reduction of 9.5% and 14.6%, respectively.

Also in this study, the effect of volume fraction of nanoparticle on liquid fraction is studied. Results indicate that at a particular time of melting process ( min) by increasing the volume fraction from to and , the liquid fraction in the heat exchanger rises from 29.5% to 44.2%. Consequently, by adding the amount of nanoparticle, a higher percentage of melting can be reached within a short time.

Due to the reduction of HTF temperature along the tube, temperature gradient between the NEPCM and HTF decreases which reduces melting at the downstream of the tube. Therefore, the effect of melting region penetration along the tube on the thermal energy is an important factor. In this study, the effect of this parameter is investigated, and the results are presented in Table 2 and Figure 6, respectively.

In order to study penetration length (Δ), the plane is chosen at position mm and along the axis of the tube at minutes. Also penetration length and the increasing rate of this parameter () are calculated in Table 2. The results show that with increasing the volume fraction of copper nanoparticle the penetration length of fluid increases.

#### 6. Conclusion

In this study, the effect of nanoparticle on melting process inside shell and tube heat exchanger is numerically investigated. Results reveal that the increment of volume fraction of nanoparticle causes more penetration velocity of melt front. Also, by increasing the volume fraction of nanoparticle up to , the total melting time is reduced to 14.6% and melt front penetration is increased to 146%. The present computations demonstrated that in a short time of the melting by increasing the volume fraction to , the liquid fraction is increased to 44.2%.

#### Nomenclature

: | Specific heat J/kg K |

: | Nanoparticle diameter m |

: | Gravitational acceleration m/s |

: | Sensible enthalpy J/kg |

: | Total enthalpy J/kg |

: | Thermal conductivity W/m k |

: | Latent heat J/kg |

: | Pressure Pa |

: | Source term |

: | Time s |

: | Temperature K |

: | Velocity vector m/s. |

*Greek Symbols*

: | Liquid fraction |

β: | Volumetric expansion coefficient 1/K |

: | Density kg/m |

: | Volume fraction of solid particles |

µ: | Dynamic viscosity Pa.s |

η: | Efficiency |

: | Penetration length m. |

*Subscripts*

eff: | Effective |

mush: | Mushy zone |

: | Melting |

: | Nanofluid |

0: | Stagnant |

: | Base fluids |

: | Solid |

ref: | Reference. |