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Energy Procedía 109 (2017) 385 - 392

International Conference on Recent Advancement in Air Conditioning and Refrigeration, RAAR 2016, 10-12 November 2016, Bhubaneswar, India

Thermal Modeling of Melting of Nano based Phase Change Material for Improvement of Thermal Energy Storage

B. R. Sushobhana, S. P. Kara*

aKIIT University, Bhubaneswar-751024, Odisha, India.

Abstract

A two dimensional numerical model is developed for melting of a nano based phase change material (PCM) such as n-octadecane with CuO nanoparticle in a square cavity. The governing equations are discretized using Finite Volume Method (FVM). The flow equations are solved using SIMPLER algorithm. Tri-Diagonal Matrix Algorithm (TDMA) is used to solve the corresponding algebraic equations. Enthalpy porosity technique is used to capture the position of the moving melt front. The melting of nano based phase change material with varying volume fractions of nanoparticles is studied to investigate the heat transfer enhancement during the melting process through dispersion of nanoparticles. The effect of some significant parameters, namely melting front progression, volume fraction of nanoparticle, heated left wall temperature, heat transfer rate and melting time are studied. The results obtained are represented graphically to study the nature and behavior of the parameters when are presented in terms of temperature, velocity profiles, moving interface position and solid fraction. Finally, it is concluded that addition of nanoparticles enhances the thermal conductivity as compared to conventional phase change material, resulting in a relatively higher heat transfer and a faster melting rate. In addition, with the rise in heat transfer rate of the nanofluid the melting time eventually decreased as the volume fraction of nanoparticles increased. Increase in difference between the melting temperature and the hot wall temperature fastened the melting process of the nano based PCM.

© 2017 The Authors. PublishedbyElsevierLtd. 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 the organizing committee of RAAR 2016. Keywords: Phase change material; Nanoparticle; Enthalpy method; Melting

* Corresponding author. Tel.: +91-9437263907 E-mail address: satyapkar@gmail.com

1876-6102 © 2017 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 the organizing committee of RAAR 2016. doi:10.1016/j.egypro.2017.03.035

1. Introduction

A number of experimental, analytical and numerical results have come forward for solid-liquid phase change problems [1-4] in the last few decades because of its growing demand and interest in the engineering field of Latent Heat Thermal Energy Storage (LHTES). In this technique the latent heat is stored during the melting process and releases the same when required during the freezing process. The ability of PCM to provide high-energy storage density and isothermal behaviour have brought them into force for applications in areas such as storage of food, temperature control inside buildings and refrigeration and air-conditioning applications [5-8].

As the PCMs have low thermal conductivity, hence many studies such as enhanced heat flux [9], inserting fins [10], and addition of nanoparticle [11] are found in the literature to enhance the thermal conductivity. Technical grade paraffins which are mixture of many hydrocarbons are used for latent heat storage instead of pure paraffin waxes which are very expensive. n-octadecane is a commercial paraffin wax used extensively for heat storage applications [12].

After a critical study of the literature, it is observed that no detailed model is available to study the effect of embedding nanoparticle in a PCM as a thermal conductivity enhancer to improve the thermal energy storage which has now-a-days a great demand. Further an elaborative analysis of role of nanoparticle in the heat transfer enhancement in particularly natural convection is not focused. The aim of this computational study is to investigate the natural convection effect using Copper oxide and n-octadecane Paraffin as nanofluid in an enclosure. A parametric study like the effect of volume fraction of nanoparticle on the melting rate of PCM is studied.

Nomenclature

t Time Subscripts

u x-velocity ref Reference value

v y-velocity s Solid

P Pressure 0 Stagnant

T Temperature d Thermal dispersion

g Acceleration due to gravity p Control volume

Sx Source term for x-momentum equation h Heated wall conditions

Sy Source term for y-momentum equation m Melting point

H Total Enthalpy c Cold wall conditions

Sh Source term for energy equation

Sc Source term for discretization equation Superscripts

Cp Specific heat at constant pressure n Iteration counter

K Thermal Conductivity

f Melt fraction during phase change Abbreviations

C Morphology constant PCM Phase Change Material

B Computational constant nf Nanofluid

L Latent heat of fusion FVM Finite Volume Method

b Empirically determined constant TDMA Tri Diagonal Matrix Algorithm

a Coefficients in the discretization equation TES Thermal Energy Storage

SIMPLER Semi Implicit Method for Pressure

Greek Symbols Linked Equation-Revised

0 Volumefraction

P Density

Dynamic viscosity

P Volumetric coefficient of thermal expansion

Under-relaxation factor

2. Mathematical Formulation

A two dimensional square enclosure with each side of 1 cm is considered as shown in fig. 1. The cavity is filled with CuO nanoparticle with n-octadecane paraffin which is Newtonian and incompressible. The top and bottom wall of the cavity are considered as adiabatic and the left and right vertical walls are exposed to a constant temperature of Th= 37°Cand Tc= 27°Crespectively. Initially the cavity is kept at room temperature 27°C which is below the melting temperature (Tm=28°C).

Fig. 1. Diagram for computational model

2.1. Governing equations

The governing equations are described below.

Continuity Equation: du dv

1T + 1T=0 ox oy

Momentum Equation:

x-direction: ôu ôu ôu 1 — +u—+ v—= — ot ox oy pnf

y-direction: dv dv dv 1 — +u—+ v—= — Ot OX oy Pnf

- — + ^nfV2v + (pß)nfg(T - Tref)

Energy Equation:

, , /dT 3T dT\ „

The source terms of the momentum and energy equations are given as:

cd-f)2

f3 + B

Sy^^^^v (6)

Sh = _pnf_dt~ ^

Here B= 1xl0-3 is used to avoid division by zero and C=1.6x106 mushy zone constant which signifies the

morphology of the melt front.

2.2. Initial conditions (t = 0)

u = 0,v = 0,T = 27°C atO< x < 0.01m and 0 < y < 0.01m

2.3. Boundary conditions (t > 0)

u = 0,v = 0,T = Th atx = 0 and 0 < y < 0.01m (8a)

u = 0,v = 0,T = Tcatx = 0.01m and 0 < y < 0.01m (8b)

u = 0,v = 0,^ = 0 aty = 0 and 0< x < 0.01m (8c)

u = 0,v = = 0 aty = 0.01m and 0< x < 0.01m (8d) The density of the nanofluid is expressed as:

Pnf = (1 - 0)Ppcm + 0PS (9) The heat capacity and the Boussinesq term are given as:

(pCp)nf = (1 - *)(pCp)pcm + 0(pCp)s (10)

CpP)nf =Cl-*)CpP)pcm + 0(pP)s (11)

The viscosity of the nanofluid is written as:

The latent heat is evaluated as:

CpX)nf=(i-*)CpX)pcm (13)

The effective thermal conductivity is given by:

keff = knfo + kd (14)

where, = ks + 2kpcm—2ct)(kpcm—kj Maxwell's model) (15)

kpcm ks + 2kpcm + 0(_kpcm — ksJ

and, kd = b(pCp)nf + Vu2 + v2 $dp (16)

Here 'b' is the empirically determined constant [13] and 'dp' is the nanoparticle diameter.

The above formulae are used to find out the values of the thermo physical properties which are mentioned in Tablel.

Table 1. Properties of the nanofluid and its constituents

Nanofluid and its constituents P (kg/m3) (Pa-sec) Cp (J/kg-K) K (W/m-K) a (m2/sec) ß (1/K) L (J/kg) Pr Fusion Point (°C)

Solid CuO nanoparticle 6510.00 - 540.00 18 5.12x10-6 - - - -

Basefluid, <| \>=0.000 770.00 3.85x10-3 2196.00 0.1480 8.75x10-8 9.10x10-4 243500 57.13 28

Nanofluid, < j)=0.025 913.50 4.11x10-3 1900.96 0.1591 9.16x10-8 6.46x10-4 200117 49.10 28

Nanofluid, < j)=0.050 1057.00 4.38x10-3 1686.00 0.1707 9.58x10-8 6.30x10-4 172949 43.26 28

3. Computational methodology

The governing equations are discretized using the finite volume method [14]. The equations obtained after discretization are solved by Tri-Diagonal Matrix Algorithm. The momentum equations are solved using SIMPLER algorithm. The convergence limit for the solution is set to 10-11. Before solving the energy equation, the enthalpy source term is calculated initially as described in the equation (7). Then the enthalpy update equation is solved iteratively for each cell as described below.

3.1. Enthalpy update technique

Implementation of enthalpy update [16] is accomplished as follows:

(AH)n+1 = (AH)n + (Tn - Tm) (17)

where 'X' is called as under-relaxation factor.

To avoid for melting more than one control volume during the iteration in a fixed time step, the following technique is adopted.

Set AH = 0 if AH < 0 Set AH = L if AH > L

Hence it can be deduced that when AH = L, the volume fraction is completely in liquid stage (or has fully melted) and when AH = 0 the domain is in a purely solid state; but if the value lies in the range of 0 <AH < L then it can be said that the contour is partly solid and partially liquid and the separating line of the two regions is termed as interface of the phase change material. So, the melt front can be captured at any instant of time.

3.2. Solution method

The solution procedure is described as follows.

1. The domain is discretized setting all the initial values.

2. The latent heat value of each control volume is assumed to be 0 as it is initially solid.

3. Increment the time step.

4. The source terms are calculated as per the equations (2-4).

5. The velocities and temperatures are calculated.

6. The latent heat value in each cell is updated using Eq. (17).

7. The convergence is tested. Otherwise repeat the steps from 4-7.

8. Finally, whether the required number of the time steps have been completed, is checked.

4. Results and discussions

The current model is validated with the experimental [15] and numerical result [16] found in the literature as shown in Fig. 2. It can be concluded that the proposed approach gives correct result.

Fig. 2. Validation (time = 6minutes)

Before proceeding further it is decided that there is a necessity of grid independent test and time-step independent test. Mesh sizes of 21x21, 41x41, 61x61, 81x81 and time-step sizes of 0.1, 0.01, and 1.0 are considered. A problem with 5% nanoparticle added to PCM is taken into consideration and the temperature distribution is taken along the central line of the cavity as shown in Fig. 3 (a) and (b). 61x61 grid size along with time step size of 1.0 is chosen for further representation of result.

Fig. 3. (a) Grid independent test (b) Time-step independent test

The movement of the melt front with and without adding nanoparticle at different time is shown in Fig. 4. It is observed that as the left wall is exposed to high temperature than the melting temperature, the melting starts form the left side. There is more melting in the upper side of the cavity due to the natural convection current. It is further found that adding nanoparticle improves the heat transfer.

The temperature distribution in the middle of the cavity at different volume fraction of nanoparticle after 1000 seconds of melting is shown in the Fig. 5. It is found that the difference in the temperature at different points along the horizontal line and the melting temperature is more in the extreme left side of the cavity which gradually decreases. It is seen that with the increase of volume fraction, more control volume melts. So, the heat transfer rate is enhanced.

To know the influence of adding nanoparticle on the duration of the melting, which is an important factor in the storage of thermal energy, the variation in the solid fraction over time for various volume fractions of nanoparticle is graphically represented in Fig. 6. As time of melting progresses, the volume of solid region decreases. However, as the volume fraction increases with addition of more nanoparticles, the volume of the solid region decreases at a fixed time of melting.

0.000'

n • / / ■ -Ф = 0; 250sec

//.' /f// -ф = 0; 500sec

r //,' /У ■ -ф = 0; 750sec

г г A ' -ф = 0; 1000sec

II.' П.' //.' Ir h • ' li- h • // - --ф = 0.025; 250sec --ф= 0.025; 500sec

i; h; --ф = 0.025; 750sec

A A' г- --ф = 0.025; 1000sec

г hAè' ■ - • ф = 0.050; 250sec

/ Lh,'//. ' rh/r ■ ■ ■ ф= 0.050; 500sec - - - ф = 0.050; 750sec • - • ф = 0.050; 1000sec

0.004 0.006

Fig. 4. Melting front progression with and without nanoparticle

Fig. 5. Temperature distribution along the cente line of cavity

Fig. 7. shows the velocity in the middle of the cavity at different volume fraction of the nanoparticle at 1000seconds. It is understood that as the volume fraction of the nanoparticle increases, the viscosity of the nanofluid increases due to which the velocity decreases.

5. Conclusion

A 2-D numerical model is developed to study the transport phenomena during the melting of n-octadecane with CuO nanoparticle. Enthalpy porosity technique is successfully implemented to capture the position of the melt front. The effect of addition of nanoparticle on the heat transfer rate is studied. It is found that more addition of nanoparticle helps to improve the thermal conductivity and thus the melting rate is enhanced due to high rate of heat transfer. So, the melting time is reduced if there is increase in the volume fraction of the nanoparticle. However, more addition of nanoparticle causes increase in the viscosity of the nanofluid which decreases the velocity. This may reduce the heat transfer rate. So, deciding the volume fraction of nanoparticle to be embedded with PCM plays an important role in the LHTES.

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