Thermal performance of a solar latent heat storage unit using rectangular slabs of phase change material for domestic water heating purposes

Accepted Manuscript

Thermal performance of a solar latent heat storage unit using rectangular slabs of phase change material for domestic water heating purposes Radouane Elbahjaoui , Hamid El Qarnia PII: DOI: Reference:

S0378-7788(18)32378-8 https://doi.org/10.1016/j.enbuild.2018.10.010 ENB 8839

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

30 July 2018 6 October 2018 14 October 2018

Please cite this article as: Radouane Elbahjaoui , Hamid El Qarnia , Thermal performance of a solar latent heat storage unit using rectangular slabs of phase change material for domestic water heating purposes, Energy & Buildings (2018), doi: https://doi.org/10.1016/j.enbuild.2018.10.010

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ACCEPTED MANUSCRIPT Thermal performance of a solar latent heat storage unit using rectangular slabs of phase change material for domestic water heating purposes

Radouane Elbahjaoui*, Hamid El Qarnia

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Cadi Ayyad University, Faculty of Sciences Semlalia, Department of Physics, Fluid Mechanics and Energetic Laboratory, BP 2390 Marrakesh, Morocco

* Corresponding author

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Email address: [email protected] Phone: +212605706053 Fax: +212524436769

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Abstract

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In this paper, the thermal performance of a rectangular latent heat storage unit (LHSU) coupled with a flat-plate solar collector was investigated numerically. The storage unit consists of a number of vertically oriented slabs of phase change material (PCM) exchanging

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heat with water acting as heat transfer fluid (HTF). During the day (charging mode), the water heated by the solar collector goes into the LHSU and transfers heat to the solid PCM which

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melts and hence stores latent thermal energy. The stored thermal energy is later transferred to the cold water during the night (discharging process) to produce useful hot water. The heat

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transfer process was modeled by developing a numerical model based on the finite volume approach and the conservation equations of mass, momentum, and energy. The developed numerical model was validated by comparing the simulation results, obtained by a selfdeveloped code, with the experimental, numerical and theoretical results published in the literature. The numerical calculations were conducted for three commercial phase change materials having different melting points to find the optimum design of the LHSU for the meteorological conditions of a representative day of the month of July in Marrakesh city, Morocco. The design optimization study aims to determine the number of PCM slabs, water mass flow rate circulating in the solar collector and total mass of PCM that maximize the 1

ACCEPTED MANUSCRIPT latent storage efficiency. The thermal performance of the LHSU and the flow characteristics were investigated during both charging and discharging processes. The results show that the amount of latent heat stored in the optimum design of the storage unit during the charging process is about 19.3 MJ, 16.54 MJ, and 12.79 MJ for RT42, RT50, and RT60, respectively. The results also indicate that depending on the mass flow rate of HTF, the water outlet temperature during the discharging process varies within the temperature ranges 43.6°C-24°C,

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51.7°C-24°C, and 62.86°C-24°C for RT42, RT50, and RT60, respectively.

Keywords: Phase change material (PCM); Latent heat storage unit (LHSU); Solar collector; Heat transfer fluid (HTF); Melting; Solidification.

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Nomenclature collector area (m2)

cp

specific heat at constant pressure (J/kg K)

d

width of PCM slabs (m)

e

depth of the latent heat storage unit (e = 1 m)

f

liquid fraction

FR

collector heat removal factor

g

acceleration of gravity (m/ s2)

h

specific sensible enthalpy (J/ kg)

H

height of the PCM slabs (m)

IT

total incident radiation on solar collector

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PT

AC

m

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k

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Ac

thermal conductivity (W/ m K) total PCM mass filled in the storage unit (kg) HTF mass flow rate flowing in solar collector (kg/s)

Nc

number of PCM slabs (or number of HTF channels)

p

pressure (Pa)

Re

Reynolds number, Re  2m / ( f Nc ( w  e))

Su

source term for u momentum equation

Sv

source term for v momentum equation

Sh

source term for energy equation 2

T

temperature (K)

t

time (s)

u, v

velocity components (m/s)

UL

collector overall heat loss coefficient (W/m2 K)

x, y

Cartesian coordinates (m)

w

thickness of HTF channels (m)

Greek symbols thermal diffusivity (m2/ s),   k/ρcp



tilt angle of the solar collector (radian)

( )

average transmittance-absorptance product



hour angle (radian)



latitude (radian)



declination (radian)



dynamic viscosity (N s/ m2)

Δh

latent heat (J/ kg)



density (kg/ m3)



stream function (m2/ s)



dimensionless stream function,    /  m



coefficient of thermal expansion (1/K)

ambient

e

inlet

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lat

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a

f

M

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PT

Subscripts

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

heat transfer fluid (HTF) latent

m

PCM

melt

melting

o

outlet

P

node point

sen

sensible

solid

solidification

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1. Introduction Solar energy has become a reliable and popular alternative source of energy in several applications, especially in solar water heating systems which use a solar collector area to collect and convert solar radiation into thermal energy for water heating. Because the

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availability of solar radiation is irregular and intermittent in nature, the coupling of thermal storage systems with solar thermal collection systems is essential. It can improve the

reliability and the generation capacity of solar systems as well as the reduction of the

electricity consumption costs during periods of sunlight lack. Among the thermal storage systems, latent heat storage systems using phase change materials (PCMs) are at the center of

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focus due to their high thermal storage capacity and their isothermal behavior during phase change process. The research efforts on latent heat storage systems include numerical [1-3], experimental [4, 5] and analytical [6, 7] studies. PCMs have been employed in many practical applications, including solar cooling and heating [8-11], building envelopes [12-14] and electric cooling [15-17].

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In recent years, a number of numerical and experimental studies have been conducted to investigate the thermal performance of solar latent heat storage systems. Sharif et al. [18]

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presented a review of the previous studies on the thermal energy storage systems used in different parts of domestic hot water (DHW) systems and heating networks, including storage

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tanks, solar collector, packed beds, and specific heat exchangers. Seddegh et al. [19] conducted a review of the thermal energy storage technologies integrating phase change

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material (PCM) for solar DHW applications. Yang et al. [20] studied numerically a packed bed heat storage system connected with a flat-plate solar collector. The storage system

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consisted of spherical capsules filled with three kinds of PCM placed in series based on their melting point. They conducted numerical calculations to compare the storage performance of their proposed multiple-type PCM packed bed with the traditional single-type packed bed. The results revealed that the multiple-type PCM packed bed has higher exergy and energy transfer efficiencies compared to the single-type packed bed. El Qarnia [21] investigated numerically the thermal behavior and performance of a shell-and-tube latent heat storage unit (LHSU) coupled with a flat-plate solar collector during charging and discharging processes. Numerical calculations were conducted for three marks of PCM (n-octadecane, Paraffin wax, and Stearic acid) to get the optimum designs of the LHSU that maximize the thermal storage 4

ACCEPTED MANUSCRIPT efficiency. Nallusamy and Velraj [22] studied experimentally and theoretically the storage performance of a packed bed thermal storage system connected with a flat-plate solar collector during charging process. They evaluated the influence of HTF mass flow rate and porosity of the bed on the system performance. The results showed that the variation in the HTF mass flow rate affects significantly the charging rate of the thermal storage system. However, the results revealed that the variation in the bed porosity has less effect on the charging time of the storage system. Ledesma et al. [23] developed a numerical model based

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on the enthalpy method and the finite volume approach to study the thermal behavior of a LHSU consisted of a packed bed combined with a flat-plate solar collector situated in the south of Spain. The packed bed storage system is made of spherical capsules filled with PCM usable for a solar DHW system. The numerical simulations were conducted for the

meteorological data of several months in Malaga city to investigate the storage performance

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of the LHSU. Li et al. [24] developed a mathematical model based on finite-time

thermodynamics to investigate the overall exergetic efficiency of a thermal storage system composed of two PCMs (named PCM1 and PCM2) combined with a concentrating solar collector. They examined the effects of the melting temperatures and the number of heat

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transfer units of the both PCMs on the overall exergetic efficiency. The results showed that the use of two PCMs instead of a single PCM can lead to an increase of the overall exergetic efficiency between 19% and 53.8%. Osterman et al. [25] carried out an experimental and

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numerical study of a LHSU composed of 30 plates of PCM (Paraffin RT22HC) co-operating with a solar air collector for space heating during morning and evening hours in winter. The

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results revealed that due to the large amount of heat available in March, the important energy savings are obtained at this month. Saman et al. [26] developed a mathematical model to

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analyze the thermal performance of a LHSU composed of a number of horizontally arranged PCM slabs during charging and discharging processes. The studied LHSU is a part of a roof-

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integrated solar heating system where air delivered by the flat-plate solar collector passes through the gap between the slabs and transfers heat to PCM. The results showed that the increase in the inlet temperature and the augmentation of air flow rate decrease the melting and solidification times during charging and discharging processes, respectively. Wu and Fang [27] investigated numerically the thermal characteristics of a LHSU composed of a packed bed filled with spherical capsules of myristic acid as PCM integrated into a solar heat storage system. They evaluated the effects of the HTF mass flow rate, HTF inlet temperature and packed bed initial temperature on the storage performance of the LHSU during the discharging process. The results showed that the increase in the HTF inlet temperature and the 5

ACCEPTED MANUSCRIPT mass flow rate enhances the heat release rate and reduces the time required for the complete solidification. Navarro et al. [28] presented an experimental study of a LHSU composed of a prefabricated concrete slab incorporating PCM in its hollows and coupled to a solar air collector. The results showed the high potential of the proposed LHSU to reduce the energy consumption and the environmental impact. Tao and He [29] developed a two-dimensional mathematical model to investigate the thermal performance of a shell-and-tube LHSU under non-steady state characteristics of HTF at the inlet. They evaluated the effect of the non-

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steady state inlet temperature and mass flow rate of HTF on the solid-liquid interface, melting fraction, thermal energy storage capacity, HTF outlet temperature, and heat transfer rate. The results showed that the time required for the complete melting of PCM decreases with

increasing initial HTF inlet temperature and mass flow rate. Elbahjaoui and El Qarnia [30] investigated the thermal performance of a shell-and-tube LHSU heated by a pulsed HTF flow

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during melting process. The effects of the pulsation frequency, pulsation amplitude, Reynolds number, and Stefan number on the thermal characteristics of the storage unit were numerically evaluated. The results showed that the pulsating parameters of HTF flow affect the melting time of PCM and the shorter melting time is obtained for a low pulsating

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frequency and high pulsating amplitude. Elbahjaoui et al. [31-33] studied the melting of PCM (Paraffin wax P116) dispersed with nanoparticles in a rectangular LHSU heated by a laminar HTF flow. The storage unit is made of a number of vertically arranged slabs of nanoparticle-

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enhanced phase change material (NEPCM) separated by a laminar flow of HTF (water). They investigated the effects of the volumetric fraction of nanoparticles, aspect ratio of NEPCM

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slabs, Reynolds number, and Rayleigh number on the storage performance and flow characteristics of the storage unit. They also developed a correlation including all the

unit.

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investigated parameters to estimate the time required for the complete melting of the storage

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In most of the studies published previously on latent heat storage systems coupled with solar collectors, the rectangular configuration of storage tanks using vertically oriented PCM slabs has not been researched before. Furthermore, in most of the previous works on the thermal performance of latent heat storage tanks co-operating with flat-plate solar collectors, the effect of natural convection in the liquid PCM has been neglected or described by an effective thermal conductivity in order to consider only the thermal conduction in the PCM and simplify the numerical modeling. In the proposed study, the thermal performance of a rectangular latent heat storage unit composed of several PCM slabs exchanging heat with a heat transfer fluid heated in a flat-plate solar collector has been numerically investigated. The 6

ACCEPTED MANUSCRIPT effect of natural convection is taken into account by resolving the momentum equations in the liquid PCM. The objectives of the proposed study are threefold. First, a two-dimensional numerical model has been presented for predicting the heat transfer and flow characteristics in the LHSU and flat-plate solar collector. Moreover, the developed numerical model has been validated by comparing the predicted results with the experimental, numerical and theoretical results

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available in literature. Second, the numerical calculations were carried out to evaluate the effect of the geometrical and operational control parameters for three commercial phase change materials having different melting temperatures. This parametric study aims to

determine the number of HTF channels, total mass of PCM and mass flow rate of HTF circulating in the solar collector that maximize the latent storage efficiency under the

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meteorological conditions of a representative day of the month of July in Marrakesh city, Morocco. Therefore, the optimal geometric design and operational parameters depending on the kind of PCM are given. Third, the thermal performance and flow characteristics of the optimal designs of LHSU have been investigated during charging and discharging processes. In addition, the effect of the mass flow rate of HTF on the thermal performance of the optimal

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2. System description

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storage units has been also evaluated during discharging process.

Fig. 1 shows the schematic diagram of the coupled solar collector LHSU investigated in the

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present study during charging and discharging processes. It consists of a flat-plate solar collector which is combined with a thermal storage tank containing vertical arranged slabs

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filled with PCM (Fig. 2a). The height of the PCM slabs, thickness of the HTF channels and collector area of the solar collector are fixed at 0.5 m, 6 mm and 2 m 2 , respectively. During the charging process, the water heated by the flat-plate solar collector flows through the

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rectangular tank and transfers the solar thermal energy to the PCM slabs which start gradually to melt. The solar thermal energy already stored in the PCM is thereafter transferred to cold water flowing in the storage tank (LHSU) to produce useful hot water during the discharging process. Initially, the storage tank is filled with solid PCM at the ambient temperature governing at the start moment of the charging process (6:00 a.m.). The temperature of the HTF (water) at the inlet of the flat-plate solar collector is initially assumed to be equal to the ambient temperature at the start moment of the charging process ( T f ,o = 19.4 °C). However, during the discharging process, the HTF inlet temperature to the LHSU is assumed equal to 7

ACCEPTED MANUSCRIPT the average temperature of the sanitary water network corresponding to the month of July for Marrakesh city (Morocco). Due to the symmetry considerations, the study of the thermal behavior of the overall storage tank can be reduced to the analysis of a repeating module composed of half a water channel and half a PCM slab, as illustrated in Fig. 2b. 3. Mathematical model

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3.1 Modeling of flat-plate solar collector

In steady state, the useful energy collected by a flat-plate solar collector is defined as the

difference between the absorbed solar radiation and thermal losses. It is expressed as follows [34]:

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Qu  Ac FR  IT ( )  U L (Tf ,o  Ta ) 

(1)

where Ac is the collector area, FR is the collector heat removal factor, IT is the total incident radiation on solar collector, ( ) is the average transmittance-absorptance product, U L is the

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collector overall heat loss coefficient, T f ,o is the water inlet temperature to the solar collector

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(water temperature at the outlet of the LHSU) and Ta is the ambient temperature. The total incident radiation on the tilted solar collector surface sloped toward the south is

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given as follows [34]:

1  cos  1  cos  IT  I b Rb  I d ( )  Ir g ( ) 2 2

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(2)

where I b is the beam radiation, I d is the diffuse radiation, I r is the total solar radiance on

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horizontal surface,  is the tilt angle of the solar collector and  g is the ground reflectivity. The geometric parameter Rb is given as follows [34]: Rb 

cos(   ) cos( ) cos( )  sin(   )sin( ) cos( ) cos( ) cos( )  sin( )sin( )

where  ,  and  stand for the latitude of Marrakesh city, the declination and the hour angle, respectively. The collector heat removal factor is calculated as [34]: 8

(3)

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FR 

m c p, f AcU L

(1  exp(

AcU L F ' )) m c p, f

(4)

where F ' represents the collector efficiency factor. It is given as follows [34]: F' 

1/ U L  1 1 W  U L  (W  D) F  D   Dhc , f

(5)

  

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with D is the diameter of the tubes of the solar collector in which the HTF circulates, W is the distance between two successive HTF tubes in the solar collector, F is the standard efficiency of the fin formed by the surface of the absorber, and hc , f is the heat transfer coefficient between the solar collector tubes and the HTF.

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The heat transfer coefficient between the tubes of the solar collector and the HTF, hc , f , is calculated using the correlations proposed respectively by Sieder and Tate [35] and Gnielinski [36] for laminar and turbulent HTF flows, respectively.

The parameter F representing the efficiency of the fin formed by the surface of the absorber

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 U  L tanh  (W  D) / 2   k p p  F  U  L (W  D) / 2    k p p 

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is given as follows [34]:

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(6)

where k p and  p represent the thermal conductivity and the thickness of the absorber surface,

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respectively.

The useful thermal energy collected can be also expressed in terms of the mass flow rate, the

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inlet and the outlet temperatures of water to the solar collector as [34]: Qu  mc p , f (T f ,e  T f ,o )

(7)

The flat-pate solar collector is assumed to be well thermally insulated. Therefore, the bottom and side losses can be neglected against the upper heat loss. In this study, the bottom and side thermal losses are ignored. However, the upper heat loss is calculated using the experimental expression of Klein [37] given as:

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ACCEPTED MANUSCRIPT    UL   m T  P

1

  Nv  (TP  Ta )(TP2  Ta2 ) 1    r 2 N v  n  1  0.133 p  Tp  Ta  hw  ( p  0.00591 N v hw ) 1   Nv  ( N  n)   c  v  

(8)

where TP represents the average temperature of the absorber, N v is the number of glass covers in the solar collector, hw is the wind heat transfer coefficient,  is the Stefan-

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Boltzmann constant (   5.67× 108 W / m2 K 4 ),  p is the emissivity of the absorber and  c represents the emissivity of the glass. The parameters m and n as well as the exponent r are given as follows: m  520(1  0.000051  2 )

r  0.43(1 

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n  (1  0.089 hw  0.1166 hw  p )(1  0.07866 Nv ) 100 ) Tp

(9) (10)

(11)

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The wind heat transfer coefficient, hw , is estimated using the given McAdams relation [38] as

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a function of the wind speed, Vw , as follows: hw  5.7  3.8Vw

(12)

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The values of the different characteristic parameters of the solar collector are displayed in

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Table 1.

The water temperature at the outlet of the solar collector can be calculated using Eqs. (1) and

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(7). It is expressed as follows:

T f ,e  T f ,o 

Ac FR  IT ( )  U L (T f ,o  Ta ) 

(13)

mc p , f

3.2 Modeling of heat transfer in LHSU The thermal behavior of the LHSU is modeled by considering the energy equation for HTF (water) circulating in rectangular channels between the PCM slabs, and the continuity, momentum and energy equations for PCM. The HTF and liquid PCM are assumed incompressible their flows are laminar. The HTF flow is assumed hydro-dynamically 10

ACCEPTED MANUSCRIPT developed. The thermo-physical properties of HTF and PCM are temperature independent. The Boussinesq approximation is used to taking into account the buoyancy in momentum equations. The enthalpy-porosity method [39] is used for the treatment of the solid-liquid phase change problem. Based on the above assumptions, the set of governing equations is expressed as follows:  

t

 (v f T f ) y



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T f

For HTF (water) [32]: T f T f   ( f )  ( f ) x x y y

where, 3 m x 2 (1  ( ) ) 2 Nc  f we w/ 2



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vf 

For PCM [32]:

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( mum ) ( m vm )  0 x y

(14)

(15)

(16a)

(16b)

( mvm ) ( mumvm ) ( mvmvm ) v v p        (  m m )  (  m m )  Sv t x y y x x y y

(16c)

( m h) ( mum h) ( m vm h)  km h  k h    ( ) ( m )  Sh t x y x c p ,m x y c p ,m y

(16d)

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where,

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PT

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( mum ) ( mumum ) ( mvmum ) u u p        ( m m )  ( m m )  Su t x y x x x y y

h   c p ,m dTm

(17a)

Su  C

(1  f )2 um ( f 3  b)

(17b)

Sv  C

(1  f )2 vm  m g (Tm  Tmelt ) ( f 3  b)

(17c)

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Sh   m h

f t

(17d)

where f is the local liquid fraction, h is the specific sensible enthalpy, C is a mushy zone constant that cancels velocity in solid PCM ( C  1.6 106 kg m3 s 1 ), b is a small constant introduced to avoid the division by zero ( b  0.001) when PCM is in the solid state ( f  0).

t  0:

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The initial and boundary conditions are given as follows [31]:

Tf  Tm  Ta , um  vm  0

x kf

T f x

 km

Tm , um  vm  0 x

Tm v  0, um  0, m  0 x x

x  w / 2  d / 2: T f

y  0:

(18b)

Tm  0, um  0, vm  0 x

(18c)

(18d)

(18e)

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x



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x  w/ 2:

0

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T f

x  0:

(18a)

yH:

Tm  0, um  0, vm  0 x

(18f)

PT

T f  T f ,e ,

It is worth noting that the HTF temperature at the inlet of the LHSU, T f ,e , is equal to that of

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the water at the outlet of the flat-plate solar collector during the charging process. However, during the discharging process, it is equal to the average temperature of the sanitary water

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network in the month of July ( T f ,e  24°C). 4. Numerical solution and validation

The set of governing equations are integrated using the finite volume approach over each control volume. The convection terms in governing equations are treated adopting the power law scheme. The pressure-velocity coupling in momentum equations is resolved using the SIMPLE algorithm. And the resulting algebraic equations are solved using the iterative Tridiagonal Matrix Algorithm (TDMA).

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ACCEPTED MANUSCRIPT The developed numerical model has been implemented into an in-house Fortran code to carry out the numerical simulations. The iterative calculation process continues, for each time step, until convergence is declared. The latter is declared when the following criteria are satisfied [33]:

Max

(T f ) P k  (T f ) P k 1 (T f ) P

k 1

 106 ,

(19)

Qf

 5 103 ,

where,

e (i, j )  um (i, j )y  vm (i, j )x   o (i, j )  um (i  1, j )y  vm (i, j  1)x 



N

 m ( f (i, j)  f 0 (i, j)) h x y 

ED

M

M

M1 N m c p , f (T f ,e  T f ,o )t    f c p , f (T f (i, j )  T f 0 (i, j )) x y 2 Nc i 1 j 1

Qf 

i  M 11 j 1

M1 i 1

f

N

 

i  M 11 j 1

c

m p ,m

(Tm (i, j )  Tm 0 (i, j )) x y

(20)

(21)

(22)

(23)

(24)

( x, y  0, t )x

f

M1

(25)

 v x f

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T f ,o 

v T

M

PT

Qm 

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Q f  Qm

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Max e (i, j )  o (i, j )  108 ,

i 1

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In order to determine the suitable grid size and time step for numerical simulations, four grid sizes (M×N: 20×60, 30×140, 30×300 and 35×350) and five time steps ( t  60 s, 30 s, 20 s, 10 s and 5 s) are tested for a typical simulation characterized by the following control parameters values: m  0.5 kg/s, Nc  10 and M  200 kg. The impacts of varying the grid size and time step on the melting fraction of RT42 as PCM at the end of the charging process (At 6:00 p.m.) are displayed in Tables 2 and 3, respectively. The analysis of these results reveals that the relative deviation of melting fraction between the grid sizes 30×300 and 35×350 is only 0.0513 %. Furthermore, the relative deviation of melting fraction between the time steps 10 s and 5 s is only 0.16 %. Consequently, the grid size 30×300 and the time step 13

ACCEPTED MANUSCRIPT 10 s provide independent results and they are adopted in numerical calculations. It should be noted that similar grid size and time step independent studies were conducted for other values of control parameters ( Nc  10 or M  200 kg) and other kinds of PCM (RT50 and RT60). As a first step before carrying out the numerical simulations, the reliability of the developed numerical model has been tested by comparing our obtained results with the experimental, numerical and theoretical data available in the literature. Three validations were carried out.

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In the first validation, the melting of gallium as PCM inside a differentially heated rectangular enclosure has been studied experimentally by Gau and Viskanta [40] and investigated

numerically by Brent et al. [41] and Khodadadi and Hosseinizadeh [42]. The width and height of the gallium enclosure is 9.89 cm and 6.35 cm, respectively. The left and right walls of the enclosure are maintained at temperatures 38 °C and 28.3 °C, respectively. However, the

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horizontal walls are thermally insulated. The solid-liquid interface positions at t  2 min, 6 min, 10 min and 17 min predicted by the present numerical model were compared with those obtained by the experimental and numerical studies cited above as shown in Fig. 3. The average and maximum errors between the results obtained by the current model and the experimental data are 8.9% and 23.4%, respectively. From this figure, it can be concluded that

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a reasonably agreement exists between the experimental and numerical results.

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A second validation was carried out by comparing the results of the current model with the data of a benchmark study performed by Bertrand et al. [43] for the melting of PCM in a differentially heated square enclosure. The latter is initially filled with solid octadecane at the

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melting point. The right wall of the enclosure is fixed at the melting point, while the left vertical wall is maintained at 10°C higher than the melting temperature. The horizontal walls

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are thermally insulated. The results predicted by the current model were compared with the numerical models of “Lacroix”, “LeQuere”, “Gobin-Viera” and “Binet-Lacroix” for the

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melting front positions at times Ste  Fo  0.002, 0.006 and 0.01 as shown in Fig. 4(a), (b) and (c), respectively. The maximum errors between our results and those obtained by the numerical model of “Binet-Lacroix” using the enthalpy-porosity method are 11.2%, 22.8% and 19% at times Ste  Fo  0.002, 0.006 and 0.01, respectively. The analysis of the results of this figure reveals that a good agreement exists between the current developed model and the other numerical models of “Lacroix”, “LeQuere”, “Gobin-Viera” and “Binet-Lacroix” [43]. In the last validation, the heat transfer by laminar forced convection in a rectangular channel in which circulates a downward HTF is numerically investigated. Such a validation is useful 14

ACCEPTED MANUSCRIPT for testing the robustness of the developed numerical model in this part of latent heat storage unit. Two boundary conditions were studied: constant temperature and constant heat flux at the wall. The distribution of the local Nusselt number predicted by the current numerical model is illustrated in Fig. 5 for the both considered boundary conditions. The obtained results show that the local Nusselt number reaches its asymptotic values of 8.23 and 7.54 when the flow becomes thermally developed for a constant heat flux and a constant temperature wall, respectively. These results are in good agreement with the literature data

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[44]. 5. Results and analysis

The numerical calculations were performed to investigate the storage performance and

thermal behavior of the LHSU coupled with a flat-plate solar collector for three kinds of

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PCM: RT42, RT50 and RT60. The melting temperature of the PCMs used in this study for storing collected solar energy are 41 °C, 49 °C and 60 °C for RT42, RT50 and RT60, respectively. The thermo-physical properties of PCMs are obtained from the manufacturer [45], and they are displayed as well as those of HTF [36, 46] in Table 4.

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The storage unit’s performance was evaluated under the meteorological data of a representative day of the month of July in Marrakesh city, Morocco. The ambient

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temperature, Ta (°C), and the total solar radiation on horizontal surface, I r ( W / m2 ), are shown in Fig. 6. The charging time of the LHSU is fixed at 720 min for all kinds of PCM.

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Accordingly, the circulation pump was switched on at 6:00 am to trigger charging process and it was turned off at 6:00 pm.

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5.1 Optimization study

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Before analyzing the thermal behavior of the LHSU, an optimization study of the design of the storage unit has been carried out to determine the optimum values of the control parameters that lead to the maximum storage of the solar thermal energy by latent heat in PCM during charging process. Therefore, the latent storage efficiency is defined and evaluated to quantify the storage performance of the LHSU. It is expressed as the ratio between the amount of solar thermal energy stored by latent heat and total solar radiation absorbed by the solar collector absorber plate as follows [21]:

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t

f M h c

I

T

(26)

( ) Ac dt

0

where f represents the total liquid fraction of PCM at the end of the charging process and

M stands for the total mass of PCM contained in the LHSU. It is worth noting that for a given meteorological data, the latent storage efficiency depends on

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the kind of PCM (RT42, RT50 or RT60), number of HTF channels (number of PCM slabs),

N c , total mass of PCM, M , and mass flow rate of HTF circulating in the solar collector, m . The melting fraction of PCM at the end of the charging process is an important indicator

when optimizing the storage unit. Consequently, the melting fraction of the optimal design of

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the LHSU resulting from the optimization study should be close to the value 1. The

optimization strategy aims to determine for each kind of PCM the optimum values of PCM mass, number of HTF channels and mass flow rate that maximize the latent storage efficiency. It is based on a parametric study in which only one control parameter is varied in each simulation series.

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Fig. 7 shows the effect of the mass flow rate of HTF on both latent storage efficiency and liquid fraction for RT42 as PCM. The number of HTF channels and the total mass of PCM are

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kept constant at Nc  10 and M  200 kg, respectively. The latent storage efficiency and the liquid fraction increase with increasing mass flow rate of HTF to reach their maximum value

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and decrease thereafter. The maximum value of latent storage efficiency and liquid fraction are 0.5155 and 0.4758, respectively. It is obtained for a HTF mass flow rate equal to 0.07 kg/s

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( m  0.07 kg/s). Therefore, the value 0.07 kg/s is considered as a first optimum value of the HTF mass flow rate and will kept constant when evaluating the effect of the number of HTF

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channels and the total PCM mass. Fig. 8 shows the effect of the number of HTF channels on the behavior of both latent storage efficiency and liquid fraction for M  200 kg and m  0.07 kg/s. It should be noted that the number of HTF channels is varied while maintaining the same total mass of PCM. Thus, the augmentation or diminution of the number of HTF channels leads to the decrease or increase in the thickness of the PCM slabs, respectively. In addition, the number of the HTF channels affects the mass flow rate flowing through each HTF channel separating two PCM slabs ( m / Nc ), while the total mass flow rate circulating in the solar collector remains constant. The 16

ACCEPTED MANUSCRIPT analysis of Fig. 8 reveals that the maximum value of the latent storage efficiency and liquid fraction is achieved for a number of HTF channels equal to 6 ( Nc  6). The maximum values of the latent storage efficiency and the liquid fraction are 0.5253 and 0.4849, respectively. Consequently, the value 6 is taken as a first optimum value of the number of HTF channels and will be kept constant at this value when evaluating the effect of the total PCM mass. Fig. 9 shows the effect of the total PCM mass on the latent storage efficiency and the liquid

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fraction for m  0.07 kg/s and Nc  6. In this case, it should be noted that the variation of the total PCM mass causes the change of the thickness of PCM slabs. The latent storage

efficiency increases with the augmentation of the total PCM mass until it reaches a maximum value and decreases thereafter. However, the liquid fraction differs in behavior from the latent storage efficiency. For a low value of PCM mass ( M  100 kg), the PCM is completely

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melted at the end of the charging process and the value of the liquid fraction is equal to the value 1. As the PCM mass increases, the thermal energy stored augments while the liquid fraction at the end of the charging mode decreases. The maximum value of the latent storage efficiency is about 0.5988 and it is reached for a total PCM mass equal to 124 kg ( M  124 kg). This value of the total PCM mass will be kept constant in the two next series of

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simulations when evaluating the effect of the mass flow rate and the number of HTF channels.

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The simulation series of the optimization study continues until there is no change in the optimum values of the control parameters. Table 5 displays the final optimum values of the

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control parameters resulting from the optimization study. Therefore, the final optimum values of the HTF mass flow rate, number of HTF channels and total mass of PCM are 0.13 kg/s, 7 and 122 kg, respectively. It is worth noting that the optimum thickness of PCM slabs

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composing this optimal design of the LHSU is about 4.25 cm ( d / 2  2.125 cm). In addition, the Reynolds number corresponding to the HTF mass flow rate flowing in the channels of the

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optimal design of the storage unit is about 64 ( Re  64). The same optimization strategy has been adopted to find the optimum control parameters for the other kinds of PCM (RT50 and RT60). The results are shown in Table 6. The analysis of such results reveals that the highest latent storage efficiency is achieved for the PCM having the low melting temperature (RT40). This behavior can be explained by the fact that low melting temperature causes early and rapid melting and hence increases the melted total PCM mass. This can improve the amount of latent heat energy stored in LHSU at the end of the charging process. It is worth noting that the optimum values of HTF mass flow, number of 17

ACCEPTED MANUSCRIPT HTF channels and total PCM mass decrease with using PCM having higher melting temperature. 5.2 Thermal behavior analysis during charging process Fig. 10 shows the instantaneous streamlines representing the flow structure in liquid PCM at times: t  300 min (at 11:00 a.m.), 360 min (12:00 p.m.), 420 min (1:00 p.m.), 480 min (2:00 p.m.), 540 min (3:00 p.m.), 600 min (4:00 p.m.), 660 min (5:00 p.m.) and 720 min (6:00 p.m.)

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for the optimal design of the LHSU filled with RT42 as PCM. These results are obtained for the optimum values of HTF mass flow rate, number of HTF channels and total PCM mass as displayed in Table 5. From the beginning moment of the charging process (6:00 a.m.), the HTF circulating in the flat-plate solar collector starts to receive solar thermal energy collected by the absorber area. A portion of this solar thermal energy received by HTF is next

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transferred to PCM by forced convection through the heat exchange wall. During the early hours of the storage process (before 11:00 a.m.), the heat transfer by thermal conduction within PCM is predominant and it allows the gradual increase in the temperature of PCM initially at the ambient temperature. At t  300 min (11:00 a.m.), the PCM starts to melt and

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natural convection begins to develop in the left upper part of the slab near the heat exchange wall. At this stage, the melting convective flow consists of a single cell separating both liquid

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and solid phases of PCM. As time progresses ( t  360 min), the convective cell widens in volume and covers the entire heat exchange wall. It is worth noting that the effect of natural convection remains weak at this stage and the tilted shape of the solid-liquid interface is

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mainly due to the high temperature difference between HTF and melting point at the inlet region ( y  H). At t  420 min, the effect of natural convection on the melting process begins

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to intensify and the solid-liquid interface becomes more tilted in the upper part. Although the melting convective flow remains clockwise and mono-cellular, it becomes more intensified.

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This behavior is described by an increase in the maximum dimensionless streamline function from the zero value to the value 20 (  max  20). In fact, the liquid PCM heated near the heat exchange wall moves up and impinges on the solid-liquid interface. This causes the rapid melting of PCM in the top part of the slab and consequently leads to the tilted shape of the melting front. As time elapses further ( t  480 min and 540 min), the liquid PCM widens further in volume and the melting convective flow continues to intensify over time. In addition, the maximum streamline function increases from the value 45 (  max  45) to the value 60 (  max  60) when time progresses from t  480 min to 540 min. At this stage, the 18

ACCEPTED MANUSCRIPT solid-liquid interface reaches the right side of the slab and appears more deformed in the top section. From t  600 min, the melting convective flow becomes bi-cellular and a new counterclockwise cell develops in the upper section of PCM slab. As heating continues ( t  660 min and 720 min), the new counterclockwise cell expands, while the clockwise one occupying the bottom section reduces in volume. The counterclockwise convective flow appeared in the upper section intensifies with increasing time. This behavior is reflected in the augmentation of the maximum dimensionless streamline function over time (  max  10, 20

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and 30 at t  600 min, 660 min and 720 min, respectively). Moreover, the convective flow intensity of the clockwise cell occupying the bottom section of PCM slab decreases with time. In this case, the maximum dimensionless streamline function decreases over time (  max  60, 50 and 35 at t  600 min, 660 min and 720 min, respectively).

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Fig. 11 illustrates the instantaneous temperature distribution in the computational domain (PCM and HTF) for the optimal design of LHSU filled with RT42 at the same previously mentioned moments. At the early hours of the storage process and before 11:00 a.m., the heat transfer within PCM is dominated by the thermal conduction. At this stage, the PCM stills solid and the heat transferred by HTF to PCM through the heat exchange wall only serves to

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gradually increase its temperature over time. From t  300 min (11:00 a.m.), the melting

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begins to take place in PCM slabs near the heat exchange wall. At this stage, the heat transfer by conduction remains predominant and the temperature contours appear slightly tilted in the upper section of the slab due to the high HTF temperature at the inlet region. As time

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progresses, natural convection begins to develop in the molten region and starts to affect the heat transfer within PCM. Due to natural convection movements, the liquid PCM heated at

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the heat exchange wall moves to the upper section of the slab and impinges on the solid-liquid interface. In fact, the melting convective flow transports the hot liquid PCM to the upper

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section of the slab and causes the non-uniform temperature distribution in this section. As a result, the higher PCM temperature takes place in the upper section of the slab. It is interesting to note that from t  540 min (3:00 p.m.), the higher PCM temperature decreases with time progress. As shown in Fig. 11, the maximum PCM temperature is 47°C, 46°C, 45°C and 44°C at t  540 min, 600 min, 660 min and 720 min, respectively. This behavior is mainly due to the decrease in the total solar radiation which passes from 780 W / m2 at

t  540 min (3:00 p.m.) to 272 W / m2 at t  720 min (6:00 p.m.) as illustrated in Fig. 6.

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ACCEPTED MANUSCRIPT Fig. 12 shows the temporal variation of the liquid fraction for the three optimal designs of the LHSU during charging process. For all kinds of PCM, the liquid fraction behavior goes through two distinct stages over time. In the first stage, the PCM remains at its initial solid state and no phase change takes place in slabs. Consequently, the liquid fraction remains constant at the zero value during this stage. The heat transferred by HTF to PCM is stored by sensible heat in the LHSU and it only serves to increase the temperature of PCM up to the melting point. The time duration of the first stage is about 274 min, 299.33 min and 328.5 min

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for RT42, RT50 and RT60, respectively. The analysis of these results reveals that the time duration of the first stage increases with the use of PCM having higher melting point. Such a behavior is due to the fact that more sensible heat is needed to start the phase change process for higher melting point of PCM. In the second stage of behavior, the liquid fraction increases over time to reach its optimum value at the end of the charging process (at t  720 min). This

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optimum value of liquid fraction is slightly higher for PCM having higher melting point.

Indeed, the value of the liquid fraction at the end of the charging process is about 0.9092, 0.9287 and 0.945 for RT42, RT50 and RT60, respectively.

Fig. 13 illustrates the temporal variation of the HTF temperature at the outlet of the LHSU for

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the three kinds of PCM (RT42, RT50 and RT60). The temporal variation of the HTF temperature at the inlet of the LHSU is illustrated in Fig. 14. The HTF inlet and outlet

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temperatures behavior can be divided into two different stages. In the first stage, the collected solar thermal energy starts to gradually increase the temperature of HTF. Consequently, the

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HTF temperature at the inlet and outlet of the storage unit increases with increasing time for all PCM kinds. In fact, the HTF temperatures curves are similar during the early minutes of

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the charging process and they begin to differ gradually with time progress. Toward the end of the first stage, the HTF inlet and outlet temperatures are higher for the optimum LHSU filled with PCM having greater melting point. The second stage starts when the HTF temperature

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becomes very close to the PCM melting point. The slope of the HTF inlet and outlet temperature curves undergoes a sudden decrease at the beginning of this stage. Furthermore, the HTF temperature undergoes a slightly increase to reach its maximum value and remains almost constant in the vicinity of this value. It is worth noting that the maximum value of HTF temperature for each kind of PCM is relatively higher than the PCM melting point. At this stage, the LHSU stores the collected solar thermal energy by latent heat and the liquid PCM resulting from the melting process is at a nearly constant temperature. It should be noted that during this stage, the temperature of HTF at the inlet of the LHSU is much higher than that at the outlet. It is also interesting to note that the HTF temperature starts to decrease 20

ACCEPTED MANUSCRIPT toward the end of the charging period. Such a behavior is due to the low solar radiation just before t  720 min (6:00 p.m.) which makes the flat-plate solar collector unable to absorb solar energy. Fig. 15 shows the temporal evolution of the sensible heat stored in the optimum design of the LHSU for the three kinds of PCM (RT42, RT50 and RT60). As shown in this figure, the sensible heat stored in the LHSU goes through two distinct stages. In the first one, the amount

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of sensible heat charged in the storage unit increases with time progress. Moreover, the sensible heat stored is the same for all kinds of PCM. This is reflected by substantially

identical sensible heat curves. During this stage, the heat transferred by HTF to PCM is only stored by sensible heat and no phase change takes place in the PCM slabs. The first stage extends until the PCM temperature reaches the melting point. As it can be seen at the end of

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this stage, the higher amount of sensible heat is stored in the PCM having higher melting point. In the second stage, the phase change begins to occur in the PCM slabs and the storage of solar thermal energy by latent heat prevails. In this stage, the sensible heat stored increases to achieve its maximum value and undergoes thereafter a slightly decrease when the charging period approaches to its end. It is interesting to note that, at the end of the charging process (at

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6:00 p.m.), the higher amount of sensible heat is stored in the optimum design of the LHSU filled with RT60. In fact, the amount of sensible heat stored at the end of the charging process

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is about 5.872 MJ, 6.855 MJ and 8.21 MJ for RT42, RT50 and RT60, respectively. Fig. 16 illustrates the temporal evolution of the latent heat stored in the optimum design of the

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LHSU for the three kinds of PCM (RT42, RT50 and RT60). The evolution of the latent heat charged in the storage unit also goes through two distinct stages. During the early hours of

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storage process, the PCM stores heat only by sensible heat. Thus, no latent heat is charged in the LHSU during this stage. The time duration of the first stage is the same as indicated for

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the liquid fraction. At the beginning of the second stage, the PCM temperature reaches the melting point and the phase change starts to occur in the LHSU. During this stage, the amount of latent heat charged in the storage unit undergoes a nonlinear increase to achieve its maximum value at the end of the charging process. It is worth noting that due to the higher latent heat of fusion, ∆h, and the larger PCM melted mass, the higher amount of latent heat is charged in the LHSU for the PCM having lower melting point. Consequently, the amount of latent heat stored in the LHSU at t  720 min (6:00 p.m.) is about 19.30 MJ, 16.54 MJ and 12.79 MJ for RT42, RT50 and RT60, respectively.

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ACCEPTED MANUSCRIPT 5.3 Effect of the HTF mass flow rate during discharging process The effect of the HTF mass flow rate on instantaneous liquid fraction during discharging process is illustrated in Figs. 17, 18 and 19 for RT42, RT50 and RT60, respectively. The numerical calculations relating to the evaluation of the impact of the HTF mass flow rate were carried out for the optimum designs of the LHSU. From t  720 min, the cold HTF flows in the LHSU and receives the heat already stored during the charging process from PCM which

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starts to solidify. The liquid fraction decreases over time until reaching the zero value when the PCM becomes completely solid. For all kinds of PCM, the liquid fraction decreases more rapidly with increasing HTF mass flow rate. This behavior is due to the fact that the

augmentation of the HTF mass flow rate intensifies heat transfer along the heat exchange wall and increases the heat extraction rate from PCM. For the optimum design of the LHSU filled

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with RT42, the PCM becomes completely solid at t  925.17 min, 987.33 min, 1095 min, 1316.17 min, and 1439 min for m  0.1 kg/s, 0.04 kg/s, 0.02 kg/s, 0.01 kg/s, and 0.008 kg/s, respectively. For the optimum design of the storage unit filled with RT50, the PCM is completely solidified at t  856.17 min, 898.67 min, 973.17 min, 1126.67 min and 1204.17 min for m  0.1 kg/s, 0.04 kg/s, 0.02 kg/s, 0.01 kg/s, and 0.008 kg/s, respectively. It is worth

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noting that for m  0.004 kg/s, the two kinds of PCM (RT42 and RT60) are partially solidified at the end of the discharging process (i.e. at t  1440 min). In fact, the liquid

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fraction at t  1440 min is about 0.425 and 0.17 for RT42 and RT50, respectively. For the optimum design of the LHSU filled with RT60, the PCM becomes completely solid at t 

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825.33 min, 851.83 min, 899.83 min, 1001.83 min, 1054 min and 1318 min for m  0.1 kg/s, 0.04 kg/s, 0.02 kg/s, 0.01 kg/s, 0.008 kg/s, and 0.004 kg/s, respectively. It is interesting to

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note that contrary to the cases of RT42 and RT50, the RT60 is completely solidified at the end of the discharging process for m  0.004 kg/s. The analysis of these results reveals that the

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solidification time of PCM during discharging process is significantly decreased by increasing the mass flow rate of HTF. It is also worth noting that for a given HTF mass flow rate, the PCM filled in the optimum design of the LHSU is early solidified for that having higher melting/solidification point. The effect of the HTF mass flow rate on the time-wise variation of the temperature of HTF at the outlet of the storage unit during discharging process is shown in Figs. 20, 21 and 22 for RT42, RT50 and RT60, respectively. For all PCM kinds, the HTF outlet temperature undergoes a rapid decrease to reach the PCM solidification temperature and remains constant for a certain period of time before decreasing more significantly over time until it achieves the 22

ACCEPTED MANUSCRIPT HTF inlet temperature when the thermal equilibrium establishes between PCM and HTF. For m  0.02 kg/s, the time duration during which the HTF outlet temperature stills constant at the

PCM solidification temperature increases significantly with decreasing mass flow rate of HTF. However, this time duration virtually disappears for high mass flow rate of HTF (m

0.02 kg/s). It is interesting to note that for a given low mass flow rate, the time duration

during which the HTF outlet temperature is equal to the solidification temperature appears shorter for the PCM having higher solidification temperature. During the discharging process,

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the HTF outlet temperature varies according to the mass flow rate of HTF within the

temperature ranges 43.6°C-24°C, 51.7°C-24°C and 62.86°C-24°C for RT42, RT50 and RT60, respectively. It should be also noted that for m  0.004 kg/s, the HTF outlet temperature

remains equal to the solidification temperature until the end of the discharging process for RT42 and RT50. This case of HTF mass flow rate is not beneficial in the practice because the

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amount of thermal energy stored in LHSU during the charging process has not been totally removed from the PCM during the discharging process. However, the optimum design of the LHSU filled with RT60 seems to be more suitable for lower mass flow rate ( m  0.004 kg/s).

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6. Conclusion

The thermal performance of a rectangular latent heat storage unit coupled with a flat-plate

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solar collector was studied numerically for three kinds of PCM (RT42, RT50 and RT60). A numerical model based on the finite volume approach and the conservation equations of mass, momentum, and energy was developed and validated by comparing the present simulation

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results with the experimental, numerical and theoretical results previously published in the literature. The developed numerical model was then used to optimize the latent heat storage

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unit during charging process and under the meteorological data of a representative day of the month of July in Marrakesh city, Morocco. Therefore, the optimum HTF mass flow rate,

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number of PCM slabs, and total PCM mass filled in the storage unit were estimated for each kind of PCM. The storage performance and flow characteristics of the optimum designs of the storage unit were investigated during the charging process. The effect of the HTF mass flow rate on the water outlet temperature and liquid fraction during the discharging process was also evaluated. The results show that the amount of latent heat stored in the optimum design of the storage unit during the charging process is about 19.3 MJ, 16.54 MJ, and 12.79 MJ for RT42, RT50, and RT60, respectively. The results also indicate that depending on the HTF mass flow rate, the water outlet temperature during the discharging process varies within the

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ACCEPTED MANUSCRIPT temperature ranges 43.6°C-24°C, 51.7°C-24°C, and 62.86°C-24°C for RT42, RT50, and RT60, respectively. Conflict of Interest The authors declare no conflict of interest Acknowledgement

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We extend our sincere thanks to the Joint International Laboratory LMI-TREMA (http://trema.ucam.ac.ma) for providing us the meteorological data.

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[1] Jourabian M, Farhadi M, Sedighi K, Darzi A R, Vazifeshenas Y. Simulation of natural convection melting in a cavity with fin using lattice Boltzmann method. International Journal for Numerical Methods in Fluids (2012); 70: 313-325. [2] Darzi A R, Farhadi M, Jourabian M. Lattice Boltzmann simulation of heat transfer enhancement during melting by using nanoparticles. Iranian Journal of Science and Technology. Transactions of Mechanical Engineering (2013); 37: 23. [3] Jourabian M, Farhadi M, Darzi A A R. Simulation of natural convection melting in an inclined cavity using lattice Boltzmann method. Scientia Iranica (2012); 19: 1066-1073. [4] Kasaeian A, bahrami L, Pourfayaz F, Khodabandeh E, Yan W-M. Experimental studies on the applications of PCMs and nano-PCMs in buildings: A critical review. Energy and Buildings (2017); 154: 96-112. [5] Wang C, Huang X, Deng S, Long E, Niu J. An experimental study on applying PCMs to disaster-relief prefabricated temporary houses for improving internal thermal environment in summer. Energy and Buildings (2018); 179: 301-310. [6] Bechiri M, Mansouri K. Exact solution of thermal energy storage system using PCM flat slabs configuration. Energy Conversion and Management (2013); 76: 588-598. [7] Bechiri M, Mansouri K. Analytical study of heat generation effects on melting and solidification of nano-enhanced PCM inside a horizontal cylindrical enclosure. Applied Thermal Engineering (2016); 104: 779-790. [8] Singh R, Lazarus I J, Souliotis M. Recent developments in integrated collector storage (ICS) solar water heaters: A review. Renewable and Sustainable Energy Reviews (2016); 54: 270-298. [9] Brancato V, Frazzica A, Sapienza A, Freni A. Identification and characterization of promising phase change materials for solar cooling applications. Solar Energy Materials and Solar Cells (2017); 160: 225-232. [10] Pintaldi S, Perfumo C, Sethuvenkatraman S, White S, Rosengarten G. A review of thermal energy storage technologies and control approaches for solar cooling. Renewable and Sustainable Energy Reviews (2015); 41: 975-995. [11] Elbahjaoui R, El Qarnia H, Naimi A. Thermal performance analysis of combined solar collector with triple concentric-tube latent heat storage systems. Energy and Buildings (2018); 168: 438-456. [12] Kuznik F, David D, Johannes K, Roux J-J. A review on phase change materials integrated in building walls. Renewable and Sustainable Energy Reviews (2011); 15: 379391. [13] Šavija B, Schlangen E. Use of phase change materials (PCMs) to mitigate early age thermal cracking in concrete: Theoretical considerations. Construction and Building Materials (2016); 126: 332-344. [14] Panayiotou G P, Kalogirou S A, Tassou S A. Evaluation of the application of Phase Change Materials (PCM) on the envelope of a typical dwelling in the Mediterranean region. Renewable Energy (2016); 97: 24-32. [15] Wang S, Li Y, Li Y-Z, Wang J, Xiao X, Guo W. Transient cooling effect analyses for a permanent-magnet synchronous motor with phase-change-material packaging. Applied Thermal Engineering (2016); 109, Part A: 251-260. [16] Javani N, Dincer I, Naterer G F, Yilbas B S. Exergy analysis and optimization of a thermal management system with phase change material for hybrid electric vehicles. Applied Thermal Engineering (2014); 64: 471-482. [17] Tang Z, Zhu Q, Lu J, Wu M, Study on various types of cooling techniques applied to power battery thermal management systems, in: Advanced Materials Research, 2013, pp. 1571-1576. 25

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[18] Sharif M K A, Al-Abidi A A, Mat S, Sopian K, Ruslan M H, Sulaiman M Y, Rosli M A M. Review of the application of phase change material for heating and domestic hot water systems. Renewable and Sustainable Energy Reviews (2015); 42: 557-568. [19] Seddegh S, Wang X, Henderson A D, Xing Z. Solar domestic hot water systems using latent heat energy storage medium: A review. Renewable and Sustainable Energy Reviews (2015); 49: 517-533. [20] Yang L, Zhang X, Xu G. Thermal performance of a solar storage packed bed using spherical capsules filled with PCM having different melting points. Energy and Buildings (2014); 68, Part B: 639-646. [21] El Qarnia H. Numerical analysis of a coupled solar collector latent heat storage unit using various phase change materials for heating the water. Energy Conversion and Management (2009); 50: 247-254. [22] Nallusamy N, Velraj R. Numerical and Experimental Investigation on a Combined Sensible and Latent Heat Storage Unit Integrated With Solar Water Heating System. Journal of Solar Energy Engineering (2009); 131: 041002-041002. [23] Ledesma J T, Lapka P, Domanski R, Casares F S. Numerical simulation of the solar thermal energy storage system for domestic hot water supply located in south Spain. Thermal Science (2013); 17: 431-442. [24] Li Y-Q, He Y-L, Wang Z-F, Xu C, Wang W. Exergy analysis of two phase change materials storage system for solar thermal power with finite-time thermodynamics. Renewable Energy (2012); 39: 447-454. [25] Osterman E, Butala V, Stritih U. PCM thermal storage system for ‘free’ heating and cooling of buildings. Energy and Buildings (2015); 106: 125-133. [26] Saman W, Bruno F, Halawa E. Thermal performance of PCM thermal storage unit for a roof integrated solar heating system. Solar Energy (2005); 78: 341-349. [27] Wu S, Fang G. Dynamic performances of solar heat storage system with packed bed using myristic acid as phase change material. Energy and Buildings (2011); 43: 1091-1096. [28] Navarro L, Gracia A d, Castell A, Cabeza L F. Experimental study of an active slab with PCM coupled to a solar air collector for heating purposes. Energy and Buildings (2016); 128: 12-21. [29] Tao Y B, He Y L. Numerical study on thermal energy storage performance of phase change material under non-steady-state inlet boundary. Applied Energy (2011); 88: 41724179. [30] Elbahjaoui R, El Qarnia H. Numerical Study of a Shell-and-Tube Latent Thermal Energy Storage Unit Heated by Laminar Pulsed Fluid Flow. Heat Transfer Engineering (2017); 38: 1466-1480. [31] Elbahjaoui R, Qarnia H E, Ganaoui M E. Melting of nanoparticle-enhanced phase change material inside an enclosure heated by laminar heat transfer fluid flow. Eur. Phys. J. Appl. Phys. (2016); 74: 24616. [32] Elbahjaoui R, El Qarnia H. Transient behavior analysis of the melting of nanoparticleenhanced phase change material inside a rectangular latent heat storage unit. Applied Thermal Engineering (2017); 112: 720-738. [33] Elbahjaoui R, El Qarnia H. Thermal analysis of nanoparticle-enhanced phase change material solidification in a rectangular latent heat storage unit including natural convection. Energy and Buildings (2017); 153: 1-17. [34] Duffie J A, Beckman W A, Solar engineering of thermal processes, John Wiley & Sons, 2013. [35] Sieder E N, Tate G E. Heat transfer and pressure drop of liquids in tubes. Industrial & Engineering Chemistry (1936); 28: 1429-1435. [36] Incropera F P, Lavine A S, Bergman T L, DeWitt D P, Fundamentals of heat and mass transfer, Wiley, 2007. 26

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[37] Klein S A. Calculation of flat-plate collector loss coefficients. Solar Energy (1975); 17: 79-80. [38] McAdams W H, Heat transmission, in, 1954. [39] Voller V, Cross M, Markatos N. An enthalpy method for convection/diffusion phase change. International journal for numerical methods in engineering (1987); 24: 271-284. [40] Gau C, Viskanta R. Melting and solidification of a metal system in a rectangular cavity. International Journal of Heat and Mass Transfer (1984); 27: 113-123. [41] Brent A D, Voller V R, Reid K J. Enthalpy-porosity technique for modeling convectiondiffusion phase change: Application to the melting of a pure metal. Numerical Heat Transfer (1988); 13: 297-318. [42] Khodadadi J M, Hosseinizadeh S F. Nanoparticle-enhanced phase change materials (NEPCM) with great potential for improved thermal energy storage. International Communications in Heat and Mass Transfer (2007); 34: 534-543. [43] Bertrand O, Binet B, Combeau H, Couturier S, Delannoy Y, Gobin D, Lacroix M, Le Quéré P, Médale M, Mencinger J, Sadat H, Vieira G. Melting driven by natural convection A comparison exercise: first results. International Journal of Thermal Sciences (1999); 38: 5-26. [44] Kays W M, Crawford M E, Convective Heat and Mass Transfer, McGraw-Hill, New York, 1970. [45] Rubitherm Technologies GmbH, www.rubitherm.de. [46] Ait Adine H, El Qarnia H. Numerical analysis of the thermal behaviour of a shell-andtube heat storage unit using phase change materials. Applied Mathematical Modelling (2009); 33: 2132-2144.

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Table 1: values of the different characteristic parameters of the flat-plate solar collector [34] W

D

Nv

kp

p

p

c



0.15 m

0.01 m

1

240 W/m K

0.0008 m

0.1

0.88

45°

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Table 2: Impact of the grid size change on the melting fraction of RT42 as PCM at the end of the charging process (At 6:00 p.m.) for m  0.5 kg/s, Nc  10 and M  200 kg f

Deviation (%)

20×60

0.4760

-

30×140

0.4659

2.12

30×300

0.4651

35×350

0.4648

AN US

M×N

0.175

0.0513

Table 3: Impact of the time step change on the melting fraction of RT42 as PCM at the end of

M

the charging process (At 6:00 pm) for m  0.5 kg/s, Nc  10 and M  200 kg Time step, ∆t

f

60 s

0.4050

22.92

30 s

0.4418

9.12

0.4583

3.72

0.4651

1.48

0.4643

0.16

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20 s

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10 s 5s

Deviation (%)

28

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Table 4: Thermo-physical properties of HTF [36, 46] and PCMs [45] Water

RT42

RT50

RT60

Melting temperature, Tmelt (°C)

-

41

49

60

Solidification temperature, Tsolid (°C)

-

42

50

61

Density, ρm (kg/m )

989

820

880

780

Specific heat, cp (J/kg/K)

4180

2000

2000

2000

Thermal conductivity, k (W/m K)

0.64

0.2

0.2

0.2

Latent heat, ∆h (kJ/kg)

-

174

168

144

Dynamic viscosity, μ ( kg/m s)

5.77×10-4

2.534×10-2

2.75×10-2

2.89×10-2

Thermal expansion coefficient, ξ (K-1)

-

1.0×10-3

1.0×10-3

1.0×10-3

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3

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Propriety

29

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m (kg / s)

Nc

M (kg )



m (kg / s)

0.07

10

200

0.5155

0.4758

Nc

0.07

6

200

0.5253

0.4849

M (kg )

0.07

6

124

m (kg / s)

0.12

6

124

Nc

0.12

7

124

-

-

-

-

-

-

-

-

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Table 5: Results of the optimization strategy for RT42 as PCM

Final

0.13

7

Optimum

f

Variable

0.8915

0.5997

0.8928

0.6006

0.8942

-

-

-

-

0.6008

0.9092

AN US

0.5988

122

Table 6: Optimum control parameters for RT50 and RT60

m (kg / s)

M (kg )



6

106

0.5148

5

94

0.3982

Nc

0.1

RT60

0.08

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RT50

ED

PCM

M

Optimum

30

d (cm)

Re

0.9287

4.015

57.4

0.9451

4.82

55.1

f

AN US

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Figure 1: Schematic diagram of the coupled solar collector latent heat storage unit during (a)

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the charging and (b) the discharging processes

31

M

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Figure 2: Schematic of (a) the storage unit and (b) the symmetric computational domain

32

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 2 min

17 min

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 6 min 10 min





Current model Brent at al. Khodadadi and Hosseinizadeh Gau and Viskanta















M



AN US

y (m)









ED

x (m)

Figure 3: Melting front position at t  2 min, 6 min, 10 min and 17 min: Comparison between

PT

the current numerical model, the numerical studies of Brent et al. [41] and Khodadadi and

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Hosseinizadeh [42], and the experimental work of Gau and Viskanta [40].

33

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(b)









Y



Y











Current model 'Lacroix' 'LeQuere' 'Gobin-Vieira 'Binet-Lacroix'











X

(c) 









X

M







AN US



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(a)

Y

ED





Current model 'Lacroix' 'LeQuere' 'Gobin-Vieira 'Binet-Lacroix'















X

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

Figure 4: Melting front positions at times Ste  Fo  0.002 (a), 0.006 (b) and 0.01(c): Comparison between the current developed model and the numerical models of “Lacroix”, “LeQuere”, “Gobin-Viera” and “Binet-Lacroix” [43].

34

Current model 'Lacroix' 'LeQuere' 'Gobin-Vieira 'Binet-Lacroix'





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12.0 11.5 11.0

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Constant heat flux Isothermal wall

10.5

Nu

10.0 9.5 9.0 8.5

AN US

Nu = 8.23

8.0 Nu = 7.54

7.5 7.0

0

2

4

6

8

10

ED

M

y(m)

Figure 5: Distribution of the local Nusselt number for a downward HTF flow in a rectangular channel with a constant temperature and a constant heat flux wall for a Reynolds number of

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100

35

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1000 34 32

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2

30

Ambient temperature ( °C )

Total solar radiation (W / m )

800

600

28 26

400

24

0

5

6

7

8

9

10

AN US

Total solar radiation Ambient temperature

200

11

12

13

14

15

16

22 20

17

18

19

18

M

Time ( h )

ED

Figure 6: Hourly variation of the total solar radiation on a horizontal surface and ambient

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temperature of a representative day of the month of July in Marrakesh city

36

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0.518

0.50

0.516

0.512

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0.48

0.510

0.47

0.508 0.506

0.46

0.502 0.500 0.498 0.0

0.1

0.2

0.3

AN US

0.504

0.4

0.5

0.6

Liquid Fraction

Latent storage efficiency

0.49

Latent storage efficiency Liquid Fraction

0.514

0.45

0.7

0.44 0.8

ED

M

Mass flow rate ( kg / s)

Figure 7: Effect of the mass flow rate of HTF circulating in the flat-plate solar collector on the

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latent storage efficiency and the liquid fraction using RT42 as PCM for Nc  10 and M  200

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kg

37

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0.530

0.500

Latent storage efficiency Liquid Fraction

0.525

0.495 0.490

CR IP T 0.485

0.515

0.480

0.510

0.475

0.500

3

4

5

6

7

AN US

0.470

0.505

0.495

Liquid Fraction

Latent storage efficiency

0.520

8

9

10

11

12

0.465 0.460 13

14

ED

M

Number of HTF channels

Figure 8: Effect of the number of HTF channels on the latent storage efficiency and the liquid

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fraction using RT42 as PCM for M  200 kg and m  0.07 kg/s

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0.66 1.0

0.64

Latent storage efficiency Liquid Fraction

0.62

0.9

CR IP T

0.58

0.8

0.56 0.54

0.7

0.52 0.50

0.46 0.44 80

100

120

AN US

0.6

0.48

0.42

Liquid Fraction

Latent storage efficiency

0.60

140

160

180

0.5

200

0.4

ED

M

Total PCM mass ( kg )

Figure 9: Effect of the total mass of PCM on the latent storage efficiency and the liquid

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fraction using RT42 as PCM for m  0.07 kg/s and Nc  6

39

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(b) (11:00 a.m.)

(c)



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(d)



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(e)



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

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-20



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0



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y ( m)

y ( m)

y ( m)



















   x (m)

   x (m)

(f)

   x (m)

(g)



(4:00 p.m.)

   x (m)

(h)



(5:00 p.m.)



(6:00 p.m.)



30

   x (m)



5



   x (m)



-35

-50





y ( m)

PT



AC

5

0

CE



0

y ( m)



-60

y ( m)



ED

0

30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 -55 -60

M

5

20



   x (m)



10



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y ( m)



0

AN US

y ( m)

-60

0

0

   x (m)

Figure 10: Flow structure in the liquid PCM at times: (a) t  300 min ( 11:00 a.m.), (b) 360 min (12:00 p.m.), (c) 420 min (1:00 p.m.), (d) 480 min (2:00 p.m.), (e) 540 min (3:00 p.m.), (f) 600 min (4:00 p.m.), (g) 660 min (5:00 p.m.) and (h) 720 min (6:00 p.m.) for the optimum design of the storage unit filled with RT42 as PCM

40

ACCEPTED MANUSCRIPT (b) (11:00 a.m.)

(c)



(12:00 p.m.)

(d)



(1:00 p.m.)

(e)



46

(2:00 p.m.)

(3:00 p.m.)

47





 41

41



41

40





47

41



44

(a)





















   x (m)

   x (m)

(f)

   x (m)

(g)



(4:00 p.m.)

   x (m)

(h)



(5:00 p.m.)



(6:00 p.m.)

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39

41

y ( m)



y ( m)



y ( m)



y ( m)



y ( m)



   x (m)

T (°C)

y ( m)

M



PT



y ( m)

46





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

y ( m)



          

45

   x (m)



   x (m)

 44

 41

CE AC



41



41



   x (m)

Figure 11: Temperature distribution in PCM slabs at times: (a) t  300 min ( 11:00 a.m.), (b) 360 min (12:00 p.m.), (c) 420 min (1:00 p.m.), (d) 480 min (2:00 p.m.), (e) 540 min (3:00 p.m.), (f) 600 min (4:00 p.m.), (g) 660 min (5:00 p.m.) and (h) 720 min (6:00 p.m.) for the optimum design of the storage unit filled with RT42 as PCM

41

ACCEPTED MANUSCRIPT

1.0

RT42 RT50 RT60

CR IP T

0.6

0.4

0.2

0.0 0

100

200

300

AN US

Liquid Frcation

0.8

400

500

600

700

800

ED

M

Time (min)

Figure 12: Temporal evolution of the liquid fraction for the three optimal designs of the latent

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heat storage unit during the charging process

42

ACCEPTED MANUSCRIPT

70 65

RT42 RT50 RT60

CR IP T

55 50 45 40 35 30 25 20 15

0

100

200

300

AN US

HTF outlet temperature ( °C)

60

400

500

600

700

800

ED

M

Time (min)

Figure 13: Temporal evolution of the HTF temperature at the outlet of the LHSU for the three

AC

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optimal designs of the storage unit during the charging process

43

ACCEPTED MANUSCRIPT

70 65

RT42 RT50 RT60

60

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50 45 40 35 30 25 20 15

0

100

200

300

AN US

HTF inlet temperature ( °C)

55

400

500

600

700

800

ED

M

Time (min)

Figure 14: Temporal evolution of the HTF temperature at the inlet of the LHSU for the three

AC

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optimal designs of the storage unit during the charging process

44

ACCEPTED MANUSCRIPT

0.9

RT42 RT50 RT60

0.7

CR IP T

7

Sensible heat stored in LHSU (10 Joule)

0.8

0.6 0.5 0.4

0.2 0.1 0.0 0

100

200

300

AN US

0.3

400

500

600

700

800

ED

M

Time (min)

Figure 15: Temporal evolution of the sensible heat stored in the LHSU for the three optimal

AC

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designs of the storage unit during the charging process

45

ACCEPTED MANUSCRIPT

RT42 RT50 RT60

CR IP T

1.5

1.0

0.5

0.0

0

100

200

300

AN US

7

Latent heat stored in LHSU (10 Joule)

2.0

400

500

600

700

800

ED

M

Time (min)

Figure 16: Temporal evolution of the latent heat stored in the LHSU for the three optimal

AC

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designs of the storage unit during the charging process

46

ACCEPTED MANUSCRIPT

RT42

1.0

.

m = 0.004 kg/s . . m . = 0.008 kg/s m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

CR IP T

0.8

0.4

0.2

0.0

720

800

880

960

AN US

Liquid Fraction

0.6

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 17: Effect of the HTF mass flow rate on the temporal evolution of the liquid fraction

AC

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for RT42 during the discharging process

47

ACCEPTED MANUSCRIPT

RT50 1.0

.

m = 0.004 kg/s . m = 0.008 kg/s . m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

CR IP T

0.8

0.4

0.2

0.0

720

800

880

960

AN US

Liquid Fraction

0.6

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 18: Effect of the HTF mass flow rate on the temporal evolution of the liquid fraction

AC

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for RT50 during the discharging process

48

ACCEPTED MANUSCRIPT

RT60

1.0

.

m = 0.004 kg/s . m = 0.008 kg/s . m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

CR IP T

0.8

0.4

0.2

0.0

720

800

880

960

AN US

Liquid Fraction

0.6

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 19: Effect of the HTF mass flow rate on the temporal evolution of the liquid fraction

AC

CE

PT

for RT60 during the discharging process

49

ACCEPTED MANUSCRIPT

RT42 48

m = 0.004 kg/s . m = 0.008 kg/s . m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

36

32

28

24

20 720

800

880

960

CR IP T

.

40

AN US

HTF outlet temperature (°C)

44

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 20: Effect of the HTF mass flow rate on the temporal evolution of the HTF

AC

CE

PT

temperature at the outlet of the storage unit for RT42 during the discharging process

50

ACCEPTED MANUSCRIPT

RT50 60 56

.

m = 0.004 kg/s . m = 0.008 kg/s . m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

CR IP T

48 44 40 36 32 28 24 20 720

800

880

960

AN US

HTF outlet temperature (°C)

52

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 21: Effect of the HTF mass flow rate on the temporal evolution of the HTF

AC

CE

PT

temperature at the outlet of the storage unit for RT50 during the discharging process

51

ACCEPTED MANUSCRIPT

RT60 68 64

.

m = 0.004 kg/s . m = 0.008 kg/s . m = 0.01 kg/s . m = 0.02 kg/s . m = 0.04 kg/s . m = 0.1 kg/s

52 48 44 40 36 32 28 24 20 720

800

880

960

AN US

HTF outlet temperature (°C)

56

CR IP T

60

1040

1120

1200

1280

1360

1440

ED

M

Time (min)

Figure 22: Effect of the HTF mass flow rate on the temporal evolution of the HTF

AC

CE

PT

temperature at the outlet of the storage unit for RT60 during the discharging process

52