Scholarly article on topic 'Experimental investigation of melting behavior of PCM by using coil heat source inside cylindrical container'

Experimental investigation of melting behavior of PCM by using coil heat source inside cylindrical container Academic research paper on "Mechanical engineering"

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Abstract of research paper on Mechanical engineering, author of scientific article — M.S. Tayssir, S.M. Eldemerdash, R.Y. Sakr, A.R. Elshamy, O.E. Abdellatif

Abstract The use of a latent heat storage system by using phase change materials (PCMs) is an effective method of storing thermal energy. This paper is carried out to study the melting behavior of PCM experimentally. The PCM used in the present study is paraffin wax and the heat transfer fluid, HTF is water. A test rig has been designed and constructed to store thermal energy in PCM contained in a vertical cylinder of 300mm inner diameter and 600mm height. A copper helical coil of 100mm outer diameter and 300mm height is fitted concentrically inside the cylinder and HTF is passed upward through the coil. Experiments were performed for different inlet temperatures of HTF 70°C, 80°C and 90°C and for different volume flow rates 5lpm, 10lpm and 15lpm. The transient variation of the molten fraction, the percentage of thermal energy storage and the average Nusselt number are obtained. A significant effect of the inlet HTF temperature more than that of volume flow rate on the paraffin melting process is observed. Also, empirical correlation for the molten fraction and percentage of heat stored are deduced in terms of the operating conditions.

Academic research paper on topic "Experimental investigation of melting behavior of PCM by using coil heat source inside cylindrical container"

Accepted Manuscript

Title: Experimental Investigation of Melting Behavior of PCM by Using Coil Heat Source inside Cylindrical Container

Author: M.S. Tayssir S.M. EldemerdashR.Y. Sakr A.R. Elshamy O.E. Abdellatif

PII: DOI:

Reference:

S2314-7172(16)30088-5 http://dx.doi.org/doi:10.1016/j.jesit.2016.10.008 JESIT 126

To appear in:

Received date: 4-7-2016

Revised date: 27-9-2016

Accepted date: 11-10-2016

Please cite this article as: {http://dx.doi.org/

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Experimental Investigation of Melting Behavior of PCM by Using Coil Heat Source inside Cylindrical Container

Tayssir, M.S., Eldemerdash, S. M., Sakr, R. Y., Elshamy, A. R., Abdellatif, O. E.

Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt.

Abstract

The use of a latent heat storage system by using phase change materials (PCMs) is an effective method of storing thermal energy. This paper is carried out to study the melting behavior ofPCM experimentally. The PCM used in the present study is paraffin wax and the heat transfer fluid, HTF is water. A test rig has been designed and constructed to store thermal energy in PCM contained in a vertical cylinder of 300mm inner diameter and 600mm height. A copper helical coil of 100mm outer diameter and 300mm height is fitted concentrically inside the cylinder and HTF is passed upward through the coil.

Experiments were performed for different inlet temperatures of HTF 70°C, 80°C and 90°C and for different volume flow rates 5 LPM, 10 LPM and 15 LPM. The transient variation of the molten fraction, the percentage of thermal energy storage and the average Nusselt number is obtained. A significant effect of the inlet HTF temperature more than that of volume flow rate on the paraffin melting process is observed. Also, empirical correlation for the molten fraction and percentage of heat stored are deduced in terms of the operating conditions.

Key words: PCM, Thermal energy storage, Melting, HTF

1. Introduction

The development of energy utilization, especially the renewable energy is greatly enhanced by the use of thermal energy storage systems. This results in an increase in energy saving and raising energy efficiency. The storage of thermal energy means to store thermal energy in a certain material for a time period and give an opportunity for using it later. There are two types of thermal energy storage: latent heat storage which is a storage system that utilizes a materials ability to change phase at almost constant temperature, sensible heat storage which involves the temperature variation of a material [1-4].

Phase change materials (PCMs) have a strong ability to store energy and have an excellent characteristic of constant temperature in the course of absorbing or releasing energy. Melting process involves the natural convection effect of the liquid phase. On the other hand solidification is normally considered as a pure conduction problem. A large number of PCMs have been reported in thermal energy storage reviews in temperature range suitable for heating and cooling [5-6]. PCMs can be classified into organic, inorganic and eutectics. The organic compounds include paraffin, Non-paraffin whereas inorganic include salt hydrates, metallic and eutectics include: inorganic-inorganic, inorganic-organic and organic-organic. Paraffin characteristics have been found to exhibit the thermal energy storage application as PCMs. The transition temperature ranges of paraffin 20-60oC and the range of heat of fusion 140-280 kJ/kg, its advantages reasonable cost, commercial availability, high heat of fusion, chemically inert and stable, low vapor pressure in the melting process and no phase change segregation [5, 7]. But there are some disadvantages such as low thermal conductivity and large volume change during phase change. The technical grade paraffins can be used for latent heat storage where the pure paraffins are very expensive, mixture of many hydrocarbons are used as technical grade of paraffins and it have a suitable melting temperature.

Nomenclature

As Coil surface area, m2 P Density, kg/m3

c Specific heat, J/kg K Subscripts

D Cylinder diameter i Initial

d Coil tube diameter, m l Liquid

g Gravity acceleration = 9.8 m/s2 PCM Pure PCM

H Height of cylinder PC Phase change

h Convective heat transfer coefficient, W/m2K s Solid

k Thermal conductivity, W/m. K S Surface

L Latent heat of fusion of PCM, kJ/kg. K w Wall

mo Mass of PCM inside the vertical cylinder, kg Abbreviations

mm Melted mass of PCM inside the vertical cylinder, kg PCM: Phase Change Material

q Surface heat flux HTF: Heat Transfer Fluid

T Temperature, oC TES Thermal energy storage

t Time, s LHTES Latent heat thermal energy storage

Vm Melted volume, m3 Dimensionless quantities

V- Actual HTF volume flow rate, LPM MF Molten fraction, —

v HTF velocity, m/s Ste Stefan number, —

Greek symbols Fo Fourier number, —

P Volumetric expansion coefficient, 1/K Gr Grashof number, —

A difference Nu Nusselt number, —

Dynamic viscosity, kg/m.s Re Reynolds number, —

El-Sawi et al [8] studied the long-term performance of a centralized latent heat thermal energy storage system that is integrated with a building mechanical ventilation system. Paraffin RT20 was used as a PCM and fins are used to enhance its performance. Artificial neural network ANN was used to relate the relationship between the input and outputs to reduce the computational time. The use of centralized LHTES system has high potential to reduce the cooling load with a wider range of phase change temperature. Also, it reduces the cooling load from 21% to 36% when the unit length is increased from 500 to 650 mm at a flow velocity of 1.5 m/s. Also, Prieto et al [9] examined the energy performance of a heating power micro-cogeneration system applied to 450 m2 office space. A hot water thermal energy system and two LHTES system based on PCM plate heat exchanger are compared and their performance are analyzed under dynamic conditions. Palm acid provides better results that RT60 paraffin, with higher heat transfer rates, more accumulated energy and less storage units needed to meet the heating demand.

Fornarelli et al [10] examined numerically using CFD simulations a LHTES system for concentrated solar plant CSP. A shell-and-tube geometry composed by a vertical cylindrical tank, filled by a PCM and an inner steel tube, in which the heat transfer fluid (HTF) flows, from the top to the bottom, is considered. The results showed that the enhanced heat flux, due to natural convective flow, reduce of about 30% the time needed to charge the heat storage. Guelpa el al [11] investigated numerically using CFD the design improvements of a shell-and-tube latent heat thermal energy storage unit using an approach based on the analysis of entropy generation. The different contributions to the local entropy generation rate are computed and presented for both un-finned and finned systems. Fin arrangement is then modified according with the analysis of entropy generation distribution in order to increase the efficiency of the system. The results showed that the improved system allows reducing PCM solidification time and increasing the second-law efficiency. Tay el al [12] conducted an investigation into characterizing and optimizing the useful latent energy that can be stored within a tube-in-tank phase change thermal energy storage system, with particular reference to off peak thermal storage applications for cooling buildings. The useful energy that can be stored within the PCM was determined using a validated effectiveness-NTU model. This storage effectiveness was

optimized delivering a storage effectiveness of 68% and 75%. It was found that tube-in-tank systems can store more than 18 times more useful energy than sensible storage systems per unit volume.

Rouault et al [13] designed and set up a real-scale LHTES device has been for air-cooling in the housing sector. The system uses the thermal gap between night-time and daytime outdoor air to refresh the indoor air. The air passes along a box-section horizontal tube bundle filled with paraffin wax as PCM. A 1-D model is proposed as a design tool. An enthalpy formulation is used for the PCM energy balance equation. An experimental study is performed which validates the modeling approach. Korti and Tlemsani [14] experimentally investigated three different types of paraffin as PCMs and water was used as heat transfer fluid HTF. The temperatures of PCM and HTF, solid fraction and thermal effectiveness are analyzed. The effects of inlet temperature of HTF, flow rate of HTF and the type of PCM used on the time for charging and discharging heat were discussed. Linga et al [15] investigated the performance of mannitol (melting temperature=166.7oC, enthalpy of phase change=323 kJ/kg) in storing solar thermal energy and producing hot water. Results showed mannitol can store high-level energy and the thermal energy storage and 14kg mannitol with latent heat activated can heat 100L water from 30 up to 50oC in 6 hours.

Iten and Lui [16] stated that the two main keys in the design of thermal energy storage, TES, are the selection of the appropriate PCMs and the heat exchanger formed by the PCM and the cold/hot heat sources. Weikl el al [17] investigated the application of two types of heat exchangers under molten salt service in thermal energy storage in a parabolic trough plant employing HTF-oil plants. A comparison of shell-and-tube and coil-wound type exchanger is presented. It is shown, that the coil-wound type exchanger can leverage its specific advantages as e.g. compactness, higher efficiency of heat transfer and inherent ability to withstand thermal shocks leading to a cost-effective and innovative solution which ultimately enhances operation of a thermal energy storage plant and reduces investment cost in various aspects. From the previous reviews, it is observed that there is a lack of studying LHTES systems using shell and coil heat exchanger. For this reason in this work, an experimental setup is designed to study the thermal behavior of paraffin was as a PCM during thermal energy charging (melting process) by using coil and shell heat exchanger.

2. Experimental Setup and procedure 2.1 Test Rig

The test rig used in the present work consists of water heating tank, test section, circulating pump of 1hp and control valves. These elements are interconnected via piping system which is made from propylene tubes of 25mm diameter as shown in Fig. 1. Hot water is used as a HTF which passes from the water tank into the test section coil to give heat to PCM, then drawn back into the tank by the circulating pump.

Figure (1): Photograph of the test rig

Figure (2): Schematic diagram of the test rig

The test section can be considered as a shell and coil heat exchanger, the shell is a vertical cylinder of internal diameter of 300mm and the height of 600mm and thickness of 2mm. The shell is made of clear Perspex. The coil is made from a copper tube which has an inner diameter of 17mm, outer diameter of 19mm and a length of 3250mm. The coil has an outer diameter of 100mm and inner diameter 62mm and pitch of 30mm the coil height is 300mm. The coil is placed concentrically inside the cylindrical shell; the entire cavity of test section is filled up to the coil height with paraffin wax which is used as phase change material (PCM). The thermophysical properties of the used paraffin wax are illustrated in Table (1). Due to symmetry, thirty calibrated K-type thermocouples each of diameter is 0.25mm and its length is 2m are fixed at the right half of test section only to record the temperature in both radial and axial directions. The thermocouples are distributed at six radial locations 15mm apart and five axial locations 75mm apart as illustrated in Fig.2. These thermocouples are connected to HT10X heat transfer service unit which is connected to interface device to record the temperature every 30 min on (PC).

The water flow rate through these test section is controlled via adjustable speed drive for single phase motor pump as depicted in Fig. (3). The water in the tank is heated by means of electrical resistance heater of 3kW. The water tank temperature is adjusted and controlled by using a thermal control unit. The specifications of test rig control unit components are illustrated in Table (2).

Figure (3): Schematic diagram of thermocouple distribution inside the cylindrical container

Figure (4): Schematic diagram for the drive system Table (1) Thermophysical properties of Paraffin wax

Specific heat kJ/kg K Thermal conductivity W/m. K Density kg/m3 Viscosity Pa. s Diffusivity m2/s Latent heat kJ/kg Melting Point oC

solid liquid solid liquid

2.1 2.5 0.2 927 827 167.82 9.7x10-8 167.82 60

Table (2): Test rig control unit component

Item No# Specification

Inverter (LG SV055iG5) 1 AC 200 - 230V , 1 HP

Logical Relay 6 24 Vdc Coil Voltage

Power Supply 1 24-Vdc , 1A

Circuit Breaker (MC 06A) 1 16A

Panel Meter(Voltmeter) 2 AC 500V

Panel Meter(Ammeter) 2 AC 10A

Pushbutton 5 AC 200 - 250V , 4 A

Alarm 1 AC 220V

Wire 0.5 mm 1 x 100 m 100m

DIN- rail (ro - bar) 2 Omega Bar

Duct 3 2.5 cm x4cm x 2 m

water flow rate is measured by flow meter with stainless steel float, in a range of 1.8-18 LPM with accuracy of ±5% of reading. A series of charging experiments are performed under different operating condition. The varied parameters in the present study are the heat transfer fluid temperature during charge process 70, 80, 90oC and the volume flow rates of 5, 10, 15LPM.

2.2 Experimental Procedure

1. Turn on the circuit breaker of the control unit.

2. The temperature is regulated by adjusting the thermal control unit (TCU) to certain prescribed heating temperature.

3. Switch on the electric heater in the hot water tank to get the desired hot water temperature.

4. The adjustable speed drive (inverter) frequency was adjusted to give the required pump speed, consequently the required water volume flow rate.

5. When the temperature control unit reach the desired temperature switch on the pump.

6. Measure the volume flow rate by using the flow meter and record the temperature reading through 12 hrs. for all experiments.

7. By using Tecplot software, the recorded temperature readings are utilized to draw the isotherms contours and the melted volume Vm, can be obtained from these contours.

2.3 Data Reduction:

The melted mass is calculated as mm = pj * Vm (1)

The melted mass fraction is calculated from; MF = mm/ Mo (2)

Where; the total PCM mass is Mo = pl*Vo

The accumulative thermal energy stored within the test section is given by:

Qst = ™m cs {TPC - Tt) + mmL + mt ct {Tl - TPC) + (M0 - mm)cs (Ts - Tt) (3)

The percentage of the thermal energy stored is calculated as:

% TES = Qst/Qst,max (5)

The surface heat flux, qs = AQst/(AsAt) (6)

Where;

As = n Do/ ; where Do outer diameter of the coil tube, l coil length

The heat transfer coefficient, h is given by: h = — (7)

Where; AT = Tw -Tpc, Tw= coil wall temperature which is taken as inlet HTF temperature, Tpc =phase change temperature.

Moreover, a number of non-dimensional parameters that govern the present problem are defined as follows:

Stefan number, Ste = q * (Tw - TPC)/L Grashof number, Gr = ^ p ^"^h3

Fourier number, Fo = kl 1

(pc)]H2

Reynolds number, Re = PHTF v Di

Nusselt number, Nu = —

3. Results and Discussions

3.1 Effect of varying inlet HTF temperature

3.1.1 Effect of varying inlet HTF temperature on molten volume fraction

Figure (5) shows the effect of inlet HTF temperature on the molten mass fraction, MF, for HTF flow rate of 5 LPM. It is observed from the figure that the melting process actually starts after about 100 min. from the process operation. This time is taken for raising the temperature of coil tube and overcome the contact resistance between the coil tube wall and the paraffin wax PCM for all inlet fluid temperatures. Also, it is shown that the effect of inlet HTF on the molten volume fraction increases as the time proceeds and this is may be due to natural convection

becomes significant. The effect of inlet HTF temperature for HTF flow rate of 10 LPM and 15 LPM is depicted in Figs. (6, 7) respectively. Less time used for heating the coil and overcome the contact resistance especially at HTF temperature of 80oC and 90oC respectively. Also, significant effect of inlet HTF temperature is observed during the experiment's time especially for HTF flow rate of 15 LPM.

T=70°C T=80oC A A A A A A A □ □ LJ . 0 0 0 0 0 ° A A

T=90°C A A m PI D A A A □ □

L □ □ □ o o

A A A □ o n o o I o O o o O O Q =5 LPM

300 400 500 Time (min)

Figure (5): Timewise variation of melted volume fraction at 5LPM with different THTF

T=70°C T=80°C AAA A A A A ^ □ □ □ A A □ □

T=90°C A A AD A A A □ □ □

A A A A D □ □ O * o A A A ADD □ □ □ □ >v A O ^ o O O O O

A D L D - = = Q = 10 LPM

300 400 500 Time (min)

Figure (6): Timewise variation of melted volume fraction at 10LPM with different THTF.

1.0 0.8 0.6 0.4 0.2 0.0

T=70°C A A A A A A A A A

T=80°C T=90°C A A A A A A A m □ □ □ D □ □ □ D . _ yv O O O □ □

A A A □ A A A D □ □ □ □ D ^ o o o □ □ □ o O

o o O o o V > r

Q =15 LPM

Time (min)

Figure (7): Timewise variation of melted volume fraction at 15LPM with different Thtf.

3.1.2 Effect of inlet HTF temperature on heat stored percentage

The effect of inlet HTF temperature on the percentage of heat stored for HTF flow rate of 5 LPM is illustrated in Fig. (8). It is obvious from the figure that the inlet HTF temperature is insignificant up to 350 min. Also, the maximum percentage of heat stored is about 70% for inlet temperature of 90oC. For HTF flow rate of 10 LPM and 15 LPM, the effect of inlet HTF temperature is depicted in Figs. (9 and10) respectively. The effect of inlet HTF temperature is observed from the beginning of the experiment and the maximum percentage of heat stored reached is 80% for inlet HTF temperature of 90oC and HTF flow rate of 15 LPM.

100 80

t/> UJ

40 20 0

0 100 200 300 400 500 600 700 800

Time (min)

Figure (8): Timewise variation of heat stored percentage at 5LPM with different Thtf. 100

40 20 0

0 100 200 300 400 500 600 700 800

Time (min)

Figure (9): Timewise variation of heat stored percentage at 10LPM with different Thtf 100 80

§5 60

t/> UJ

40 20 0

0 100 200 300 400 500 600 700 800

Time (min)

T=70°C T=80oC T=90°C

. A A A A A AAA □ □ □ □ □ □ □ A *

A A A A A □ □ □ □

□ u " O O o o o O O O o O o o

1 2 8 0 Q =5 LPM

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A A A § □ □ O A A A A £ □ A A A ADD 8880000 A A A □ □ □ □ □ A A

6 □ H ,A0<> o o o O O o o o o O O V

O ° Q } = 10 LPM

> □ o —1 —1 -1 II II II «MM o o o o o o « « n i A A A ] □ □ ° > O o O A A □ □

A A A A A A * n D 8S5S5** A A A AAA/

Aa A n A * A □ □ □ □ □ □ C o o o < I—I O O

_ □ g§o o o ^

=15 LPM

Figure (10): Timewise variation of heat stored percentage at 15LPM with different Thtf 3.1.3 Effect of varying inlet HTF temperature on Nusselt number

The effect of the inlet HTF temperature on the average Nusselt number for HTF flow rate of 5 LPM is illustrated in Fig. (11). It is observed that there is a sharp decrease of the average Nusselt number at the beginning of the experiment, then it nearly becomes constant during the rest of the experiment's time. This is may be due to the thinner thermal boundary layer at the start of the melting processes (conduction dominance mode) followed by natural convection dominance mode. Also, higher values of the average Nusselt number for lower inlet HTF temperature and lower HTF flow rates. The same behavior is illustrated in Fig. (12) for HTF flow rate of 10 LPM. But for HTF flow rate of 15 LPM the timewise variation has the same behavior but the average Nusselt number values is higher for higher inlet HTF temperature as depicted in Fig. (13).

z20 10 0

0 100 200 300 400 500 600 700 800

Time (min)

Figure (11): Timewise variation of Nusselt number at 5LPM with different Thtf 20

¿10 5 0

0 100 200 300 400 500 600 700 800

Time (min)

Figure (12): Timewise variation of Nusselt number at 10LPM with different Thtf

o T=70°C T=80°C

0 T=90°C

A A A Q = 1U LPM

° o o O o * s 0 0 0 0 B 0 000 ftftftftft ftft ft ft

10 8 6

> □ o —1 —1 —1 II II II CD 00 '—1 o o o o o o O O O

A □ A

A m □ A A □ □ ¿3 Q = 15 LPM

□ I S S 0 0 g g B H 0 o o o

° o o ° ° o O o O o a a a 0 a 0 ra o o O O O o o 0 0 O 5

100 200 300 400

Time (min)

Figure (13): Timewise variation of Nusselt number at 15LPM with different Thtf 3.2 Effect of varying HTF flow rate

3.2.1 Effect of varying HTF flow rate on molten volume fraction

A significant effect of HTF flow rate for inlet HTF temperature of 70oC is depicted in Fig. (14) after about 100 min from the starting of the experiments. Also, the figure shows that the maximum molten mass fraction reached after 12 h is 29%, 39% and 48% for HTF flow rate of 5, 10 and 15 LPM respectively. Also, increasing the flow rate by 200% reduces the charging time by 227%.

Figure

Q=5LPM

Q=10LPM

Q=15LPM

A A * A A *

A A A O O o A A ^ □ □ □ o o ° □ □ o o

THTF =70°C

400 Time (min)

(14): Timewise variation of melted volume fraction for different HTFflow rate at 70°C

Figure (15) illustrates the timewise variation of the molten volume fraction for different HTF flow rate of 5, 10 and 15 LPM and inlet HTF temperature of 80oC. It is observed that the maximum molten mass fraction ranges from 56% to 70% after 12.5 h charging time for HTF flow rate of 5 to 15 LPM. Similarly the same behavior is observed for the inlet HTF temperature of 90oC as shown in Fig. (16).

Q=5LPM Q=10LPM A a a a a a a ^ n n g _ n □ o o □ □ u . . a O a a 9 0

Q=15LPM a a a a a A □ * □ D □ □ □ d ^ a ° a a a □ □ □

a a A □ ° A o o o o o

A a J. „ □ , D A o ° ° o O O Thtf =80°C

300 400

Time (min)

Figure (15): Timewise variation of melted volume fraction for different HTFflow rate at 80oC

1.0 0.8 0.6 0.4 0.2 0.0

a a a a a a a a a

Q=5LPM Q=10LPM Q=15LPM

AAA A a a a _ □ □ □ „ n □ H o O O §8

a a □ a a a a a a a □ O S ♦ > o □ □ □ o O O u w o O O

D □ □ □ □ □ < o o °

□ o o o Thtf =90°C

0 100 200 300 400 500 600 700 800

Time ( min)

Figure (16): Timewise variation of melted volume fraction for different HTFflow rate at 90OC

3.2.2 Effect of varying HTF flow rate heat stored percentage

The timewise variation of heat stored percentage for different HTF flow rate at inlet HTF temperature of 70oC is illustrated in Fig. (17). Insignificant difference in TES for flow rate of 5 and 10 LPM while maximum difference in TES of 8% is observed for HTF flow rate of 15 LPM. A maximum value of TES percentage of 48% is reached for flow rate of 15 LPM and 70oC after about 12.5 h. So, it is not preferable to work the system under these conditions. Also, for inlet HTF temperature of 80oc and 90oC the same behavior is observed in Figs. (18 and 19) with maximum TES percentages of 63% and 81% respectively.

100 80

40 20 0

Thtf =70°c

300 400 Time (min)

Figure (17): Timewise variation of heat stored percentage for different HTFflow rate at 70oC

100 80 s5 60

UJ I—

40 20 0

5LPM 10LPM 15LPM

A A Q 9

A A 6 A A A A A D o o ° o*° ft ft 6 6 % 9 o O o O o

□ n □ A § a o □ B 6 $ O °

Thtf =80°c

400 500 Time (min)

Figure (18): Timewise variation of heat stored percentage for different HTFflow rate at 80oC

55 <s>

100 80 60 40 20 0

A A A A

0ee'095D

.¿"□□□□□So 0 0 0 °°

A □ A O

A A A A A

A A A A A _ „ U n Q 0 &

A A " _ n

A D000

□ 5 O

Thtf =90°c

300 400 Time ( min)

Figure (19): Timewise variation of heat stored percentage for different HTFflow rate at 90oC 3.2.3 Effect of varying HTF flow rate on Nusselt number

The timewise variation of the average Nusselt number for different HTF flow rate at inlet HTF temperature of 70oC is depicted in Fig. (20). A sharp decrease in the average Nusselt number at early times of melting process followed by nearly constant value (steady state) for the

average Nusselt number. Similarly, the same behavior is observed for inlet HTF temperatures of 80oC and 90oC is observed in Figs. (20 and 21) respectively. Also, insignificant effect for HTF flow rate of the constant value of the average Nusselt number.

20 16 12 8 4

o 5LPM

□ 10LPM 15LPM

1 rHTF =70°C

D n A A A 0 0 o c A A A L

A A A 3 □ □ □ ^ A A A □ □ □ AAA □ □ □ c AAA L 3 □ a □ 1 A A A □ 0 A A

100 200 300 400

Time (min)

Figure (20): Nusselt number at 70oC with different volume flow rate.

5LPM 10LPM

D 15LPM

T -onor

o ■HTF _ou

* § 5 8 * o e t >999 9 0 0 0 0 0 0 Q □ □ Q Q

300 400 500 Time (min)

Figure (21): Nusselt number at 80OC with different volume flow rate

12 10 8

0 100 200 300 400 500 600 700 800

Time ( min)

Figure (22): Nusselt number at 90°C with different volume flow rate

Empirical Correlations

The experimental data for the molten volume fraction, MF, is utilized to obtain the empirical correlations using least square method. This is done for different inlet HTF temperature of 70, 80, and 90oC which corresponding to Rayleigh number of 1.79x1010, 3.58x1010, and 5.36x1010 respectively; and Stefan number of 0.149, 0.298 and 0.447 respectively for HTF flow rate of 5, 10 and 15 LPM which corresponds to Reynolds number of 17570, 35140, and 52720 respectively.

For Re = 17570

MF = 8.2152 x 10~5Fo1-8235Ste0-636Ra0-204 (8)

1.0 0.9 0.8 0.7 0.6 | 0.5 0.4 0.3 0.2 0.1

0.0 0.2 0.4 0.6 0.8 1.0

Figure (23): Experimental data for the molten mass fraction vs. empirical correlation

at Re= 17570

For Re = 35140

MF = 4.458 x 10-2Fo°.769Ste0.6811Ra00569 (9)

D 5LPM

10LPM 15LPM

A □ □ A Thtf =90oC

o o O o

6 6 6 a a

1.0 0.9 0.8 0.7 0.6

| 0.5 0.4 0.3 0.2 0.1 0.0

0.0 0.2 0.4 0.6 0.8 1.0

Figure (24): Experimental data for the molten mass fraction vs. empirical correlation

at Re= 35140

For Re = 52720

MF = 1.2962 x 10-1Fo0-605Ste0-798Ra004485 (10)

1.0 0.9 0.8 0.7 0.6 | 0.5 0.4 0.3 0.2 0.1 0.0

Figure (25): Experimental data for the molten mass fraction vs. empirical correlation

at Re= 52720

Also, empirical correlations for the percentage of the energy storage for different Reynolds

number as follows:-

For Re = 17570

Q = 3.832 Fo0 ^Ste0265Ra0.0604 % (11)

Ra = 1.79e10, Ste = 1.49e-01 Ra = 3.58e10, Ste = 2.98e-01 Ra = 5.36e10, Ste = 4.47e-01 -Predicted Correlation (10) ___^ LAAA

0.5 MF

IS) 50

i— 40

Ra = 1.79e10, Ste = 1.49e-01 Ra = 3.58e10, Ste = 2.98e-01 Ra = 5.36e10, Ste = 4.47e-01 Predicted Correlation (11)

50 TES %

Figure (26): Experimental data for the percentage of heat stored vs. empirical correlation

at Re= 17570

For Re = 35140

Q = 47.309 Fo0 557Ste

,0.5059

-0.0255

<s> 50

i— 40

Ra = 1.79e10, Ste = 1.49e-01 Ra = 3.58e10, Ste = 2.98e-01 Ra = 5.36e10, Ste = 4.47e-01 -Predicted Correlation (12)

___ ♦ V

50 TES %

Figure (26): Experimental data for the percentage of heat stored vs. empirical correlation

at Re= 35140

For Re = 52720

Q = 1.275 Fo^Ste0 3616^001204 % (13)

Figure (27): Experimental data for the percentage of heat stored vs. empirical correlation

at Re= 52720

4. Conclusions

Experimental investigations have been carried out in order to study the thermal behavior of the paraffin wax during thermal energy charging (melting process) by using water as a HTF flowing in a helical copper coil placed concentrically in a vertical cylindrical container. The following conclusions can be obtained:-

1- The effect of the inlet HTF temperature on the molten mass fraction and the percentage of heat stored is higher than that the effect of HTF flow rate where the effect of HTF flow rate in noticeable only for inlet HTF temperature of 90oC.

2- There is a need to enhance the charging process when the HTF temperature is 70oC (ie. 10oC above the phase change temperature).

3- Useful empirical correlations for each HTF flow rate are deduced for estimating the molten volume fraction and the percentage of the thermal energy stored in terms of the operating conditions.

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