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All issues Volume 83 / No 1 (July 2018) Eur. Phys. J. Appl. Phys., 83 1 (2018) 10902 Full HTML
Issue
Eur. Phys. J. Appl. Phys.
Volume 83, Number 1, July 2018
Materials for Energy harvesting, conversion and storage (Icome 2017)
Article Number 10902
Number of page(s) 5
Section Physics of Energy Transfer, Conversion and Storage
DOI https://doi.org/10.1051/epjap/2018180092
Published online 18 October 2018

© EDP Sciences, 2018

1 Introduction

Latent heat energy storage systems employing phase change materials (PCMs) have been considered one of the most effective methods to store thermal energy due to their high energy storage density and nearly isothermal characteristics [1]. State-of-the art reviews on the materials used as PCM for different engineering applications are available in [1–3]. The main drawback of the commonly used PCM, such as paraffin wax its low thermal conductivity particularly for the specialized applications where charging (melting) or discharging (solidification) time must be fast enough to avoid delays in plant operations [1,4]. In order to enhance the heat transfer during melting or solidification, several techniques have traditionally adopted, such as employing microencapsulated PCM [5,6], utilizing heat pipes [7,8], incorporating highly conductive nano-particles in the PCM [8,9], adding fins to augment the heat transfer area. The present study addresses the melting enhancement of a PCM placed inside a square cavity by placing a single fin at the heated wall. A literature search reveals that the enhancement in the melting rate by utilizing fins is feasible. Lacroix and Benmadda [10] studied the melting and solidification of a PCM from a finned vertical wall considering the number of fins, fin size and temperature of the heated wall. These authors concluded that having few long fins is more effective for enhancing the melting process than having many short fins. The same authors conducted another numerical study [11] to investigate the melting of a PCM inside a rectangular enclosure with vertical fins attached to the top or bottom walls. They reported that the melting process for the case of a top finned wall is slower than the case of a bottom finned wall. Fan et al. [12] examined experimentally the effect of the melting temperature and the presence of fins on the performance of a PCM-based heat sink for applications in the thermal management of electronic components. Based on the tests conducted, they concluded that by utilizing fins, the maximum temperature can be lowered by up to 10 °C for the finned heat sink. Even more, the performance of the heat sink is always invigorated regardless of the selected PCM. Sharifi et al. [13] developed a model to inspect the impact of the number of fins, the length and thickness of fins and the magnitude of the heated wall temperature on the melting process. It was reported that with horizontal fins, the melting is promoted in the early stages of phase change which is followed by a slow melting regime. Gharebaghi and Sezai [14] studied numerically the enhancement of energy storage rate of a thermal storage unit filled with a PCM incorporating different fin thicknesses and wall temperatures. They reported that the heat transfer rates can be boosted as much as 80 times as a result of adding a fin array into the PCM module. Conversely, the minimum enhancement rate attained was three times for fin arrays with widely spaced fins accounting for high temperature differences. A literature survey regarding enhancement in phase change process in latent heat energy storage systems by means of fins can be found in [15].

This study aims to investigate the influence of a single fin attached to the heated wall of a square cavity on the melting process of paraffin wax. The separate effects caused by the fin length and the orientation of the square cavity on the melting rate have been explored too.

2 Problem description

The schematic representation of the problem is given in Figure 1. The side of the square cavity W is 20 mm. The square cavity is heated from one wall and cooled from the facing wall while the other two sides are insulated. The heated and cooled walls are maintained at constant temperatures TH = 350 K and TC = 300 K, respectively. A single fin is attached to the midsection of the heated wall in the square cavity. The thermophysical properties of the fin material are: thermal conductivity k = 387.6 W/mK, density ρ = 8,978 kg/m3, specific heat capacity cp = 381 J/kgK. In order to examine the influence of the fin length (w) on the melting process, computations are performed for three fin lengths w = 4 mm, 7 mm and 10 mm, resulting in dimensionless fin lengths of w/W = 0.2, 0.35 and 0.5, respectively. The fin thickness is fixed at 0.5 mm for all the cases. The thermal properties of the PCM which are both phase (solid or liquid) and temperature dependent are listed in Table 1. The orientation of the heated wall on the melting process, namely, a) heating from the bottom and cooled from the top with orientation θ = 0° and b) heating from the vertical side wall and cooling from the facing vertical wall with orientation θ = 90° is also analyzed. Additionally, computations are carried out for a reference finless square cavity for the two orientations θ = 0° and θ = 90° in order to adequately quantify the enhancement produced by the fins. The initial temperature of the PCM is taken to be Ti = 300 K for all the cases under study.

The following assumptions are envisioned: (1) the heat transfer process is two-dimensional, (2) the PCM is homogeneous and isotropic, (3) the melted liquid is Newtonian, (4) the flow motion in the melted PCM is laminar and incompressible and (5) both viscous dissipation and volume expansion are negligible. According to the above description, the governing 2-D governing equations are:

Continuity equation: (1)

Momentum equation: (2)

Energy equation: (3) where ρ is the density, k is the thermal conductivity, μ is the dynamic viscosity, V is the velocity vector, T is the temperature. The symbol SM in equation (2) represents the momentum source term which is defined as [17]: (4)where ε is a small number (0.001) to prevent division by zero, Amushy is the mushy zone constant (108 kg/m3s) and f is the liquid fraction which is defined based on temperature as follows: (5)

The total enthalpy H of the PCM is computed as the sum of the sensible enthalpy, h and the latent heat, ΔH: (6) where (7)and href is the reference enthalpy, Tref is the reference temperature and cp is the specific heat at constant pressure. The latent heat content, written in terms of the latent heat of the PCM, L is: (8)

thumbnail Fig. 1

Schematic representation of the physical system.
Table 1

Thermophysical properties of the PCM [16].

3 Numerical procedure

The system of coupled partial differential equations is solved numerically by the finite volume method within the platform of the commercial code, ANSYS Fluent 15.0. For modeling the melting process and tracking the motion of the liquid-solid interface, the enthalpy-porosity approach [18] is utilized. For the discretization of the convective terms, the second order upwind differencing is activated. The velocity-pressure coupling is done by using the SIMPLE algorithm. Additionally, the temperature and the phase dependent thermophysical properties are implemented in the commercial code resorting to the User Defined Functions. To ensure that the numerical procedure is insensitive to the mesh size and the time step, a grid independent study was performed by refining the mesh size and testing different time steps. In this context, it was recognized that a uniform mesh having 201 × 201 nodes articulated with a time step of 0.01 s provides accurate results. The grid independency study was presented in [19,20] together with the validity of the model which was confirmed by comparing the computed numerical results with the available results published in the archival literature.

4 Results and discussions

Figure 2 shows the evolution of the streamlines and isotherms at different times for the case of heating from the left vertical wall. In the initial time of melting (t ≤ 100 s), the isotherms are almost symmetrical to each other on either side of the fin. The symmetrical structure of the isotherms manifests that heat diffusion is the dominant heat transfer mechanism during the early stages of the melting process. The PCM is melted only near the heated wall and also near the fin. As seen in Figure 2, there are two different unconnected melt zones at the upper and lower sides of the fin. The flow structure at both sides of the fin completely differs from each other. While Bénard rolls are formed at the upper surface of the fin, there is a single long circulation that appears at the bottom surface of the fin. As a direct result, the union of the melted fluid zones varies the heat transfer mechanism completely. The fluid heated by the hot wall begins to circulate in the whole liquid region and as a by-product, initiates the natural convection currents. At t = 900 s, these currents are merged into a primary circulating cell forcing the isotherms to become horizontal in the square cavity. The horizontal isotherms indicate the formation of temperature stratification which slows down the heat transfer rate and consequently the melting rate. It is further observed that even at a relative large time t = 1500 s, the PCM near the right bottom side of the cold wall remains solidus.

The streamlines and isotherms at the same time for the case of heating from the bottom with orientation θ = 0° are given in Figure 3. The melting has started along the heated wall and along the fin. Several Bénard cells are observed at t = 100 s. Both streamlines and isotherms are symmetrical according to the fin. For larger times (t = 900 s and 1500 s), the flow becomes chaotic which distorts the symmetrical structure of the flow. The chaotic flow randomly fluctuates the velocity field. Consequently, a swinging idle circulation region occurs in the middle of the melt region which prevents the heated fluid reaching directly to the solid surface at the top. Even if the flow field shows a chaotic behavior, the melting process is formed nearly symmetrically. A comparison between Figures 2 and 3 revealed that the melting process for the case with orientation θ = 0° is almost symmetrical at any time, contrarily to the case with orientation θ = 90° that indicates some asymmetricality.

The effect of fin length on the melting process is displayed in Figure 4. In the figure, the melting interface at different times for both orientations θ = 90° and θ = 0° is demonstrated. As can be seen from the figure, the fin length has a significant effect on the melting time in the early stages of melting for the two orientations of the heated wall. Gradual increments in the fin length enhance the melting, as expected. However for the long periods of heating, the benefit of having a long fin diminishes, particularly for orientation θ = 0° where the melting front for t = 1500 s nearly overlaps.

Instantaneous liquid fractions during the melting process are compared in Figure 5 for all the cases. In order to evaluate the benefits derived by the presence of fins, the liquid fraction for the case of the finless square cavity is also presented. As can be seen in the figure, the melting rate is much higher for the case of heating from the bottom when compared to the case of heating from the vertical side, particularly at the early stages of melting. For instance, the required time to reach 0.8 of liquid fraction is 1500 s for the case of heating from the vertical side. The melting time can be reduced down to 500 s by changing the orientation of the heated wall and adding the fin. For instance, while the required melting time to reach the 0.8 of liquid fraction is 500 s for a vertical fin of length 10 mm, it increases up to 900 s for the horizontal one while retaining the same fin length. It is also detected that the influence of fin length diminished after t ≥ 1100 s for the case of heating from the bottom while there is still a profound effect of the fin length on the melting rate for the case of heating from the side.

thumbnail Fig. 2

Streamlines and isotherms for a case with orientation θ = 90° and relative fin length w/W = 0.35.
thumbnail Fig. 3

Streamlines and isotherms for a case with orientation θ = 0° and relative fin length w/W = 0.35.
thumbnail Fig. 4

Temporal variation of the melting interface for the two orientations (left θ = 90° and right θ = 0°) of the heated wall of the square cavity.
thumbnail Fig. 5

Comparison of the instantaneous liquid fraction for various fin lengths and the two orientations of the heated wall of the square cavity.

5 Conclusions

In this study, the effect of a single fin attached to the heated wall of a square cavity during the melting process of paraffin wax was investigated numerically. The numerical computations are performed for three different dimensionless fin lengths (w/W = 0.20, 0.35 and 0.50) together with a pair of cavity orientations θ = 0° and θ = 90°. For completeness, numerical computations are also carried out for a finless square cavity which is taken as a reference case in order to assess the improvement provided by the fin. Numerical results demonstrated that utilizing a fin enhances the melting rates significantly for both orientations of the heated wall in the square cavity. This is a direct consequence of the appended heat transfer area. During the early stages of the melting process, higher melting rates are obtained for longer fins. However, after a certain period of melting process is surpassed, the effect of fin length on the melting rate diminishes particularly for θ = 0°. It was also observed that melting rates for θ = 0° is higher than that of θ = 90°; this behavior happens regardless of the fin length. By attaching a fin to the heated bottom wall, the required time to reach a given liquid fraction in the square cavity can be reduced significantly; up to three times when compared to the reference finless square cavity.

Nomenclature

Amush: mushy zone constant (kg/m3s)

f: liquid fraction

h: sensible heat (J/kg)

H: total enthalpy (J/kg)

ΔH: enthalpy of phase change (J/kg)

L: latent heat (J/kg)

w: length of fin (m)

W: Side of square cavity (m)

Subscripts and superscripts

C: cold

H: hot

i: initial

l: liquidus

ref: reference

s: solidus

Authors contribution statement

Müslüm Arıcı and Ensar Tütüncü conceived of the presented work and performed the numerical simulations. Hasan Karabay and Antonio Campo helped supervise the project and discuss the findings of the work. All authors discussed the results and contributed to the final manuscript.

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Cite this article as: Müslüm Arıcı, Ensar Tütüncü, Hasan Karabay, Antonio Campo, Investigation on the melting process of phase change material in a square cavity with a single fin attached at the center of the heated wall, Eur. Phys. J. Appl. Phys. 83, 10902 (2018)

All Tables

Table 1

Thermophysical properties of the PCM [16].

In the text

All Figures

thumbnail Fig. 1

Schematic representation of the physical system.
In the text
thumbnail Fig. 2

Streamlines and isotherms for a case with orientation θ = 90° and relative fin length w/W = 0.35.
In the text
thumbnail Fig. 3

Streamlines and isotherms for a case with orientation θ = 0° and relative fin length w/W = 0.35.
In the text
thumbnail Fig. 4

Temporal variation of the melting interface for the two orientations (left θ = 90° and right θ = 0°) of the heated wall of the square cavity.
In the text
thumbnail Fig. 5

Comparison of the instantaneous liquid fraction for various fin lengths and the two orientations of the heated wall of the square cavity.
In the text

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