Three-dimensional numerical studies were performed to investigate the effect of materials and fin arrangements in high-temperature latent heat thermal energy storage systems (HTLHTES). The HTLHTES is one of the most promising technologies in solar power generation using direct steam technology where water is used as a heat transfer fluid (HTF). The HTLHTES can contribute to solving the energy mismatch between the demand and the supply. The HTLHTES shows great potential in using renewable energy, offering high energy density, and releasing energy in latent heat. A latent heat storage using phase-change materials (PCM) provides much higher storage density, with minimal temperature variation during the charging and discharging processes, thus proving efficient in storing thermal energy. However, the PCM suffers from low thermal conductivity, affecting the overall efficiency of the HTLHTES. The study did investigations in a double-tube shell-and-tube latent heat thermal energy storage where fins were added to improve thermal conductivity. This study took different materials for the HTLHTES systems operating conditions from which NaNO3 was selected as a good material. The study also compared different fin arrangements to find out the best configuration to match the operating conditions. From the qualitative and quantitative analysis, the rectangular fin arrangement performs better. To solve the phase-changing processes the study used an enthalpy-porosity method. The three-dimensional simulation was done by using Finite Volume Method (FVM).

1. 1

2. Joy Raj Bhowmik
Reg. No: 2018339064
Md. Sojib Mia
Reg. No: 2018339006
Authors: Supervisor:
HM Toufik Ahmed Zisan
Lecturer
Department of Mechanical Engineering
Thermal Performance Enhancement of
Phase Change Material by Embedding Lower Fin
February 2024
SHAHJALAL UNIVERSITY OF SCIENCE AND TECHNOLOGY
2

3. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

4. INTRODUCTION
Solar Energy
Solar energy is the most common renewable energy resource to produce electricity. Solar thermal
powerplant is one of the technologies where solar radiation is used to generate electricity. The electricity
generation process in a solar thermal power plant is like a conventional power plant process.
The main drawback of solar thermal powerplant
Inability to maintain the consistency between the demand and the supply of energy. It faces problems,
especially during the winter weather or in the night.
Solution
Implementing TES into the solar thermal powerplant.
What is TES?
Thermal Energy Storage (TES) is a system that stores energy at a nearly constant temperature in
the form of latent heat.
1

5. INTRODUCTION
TES provides
Stores very large amounts of energy
in a small volume.
Solves the energy mismatch between
the energy demand and the energy supply.
Uses PCM as a storage medium.
What is PCM?
Phase-change material (PCM) undergoes the solid-liquid phase transformation which is called the
melting-solidification cycle. During melting the PCM charges by collecting heat from a heat transfer
fluid (HTF) and discharges by releasing heat to a cold fluid.
2

6. INTRODUCTION
The rate of heat transfer greatly depends on the thermal conductivity of the PCM.
Different enhancement techniques such as adding multi-tube shell-and-tube LHTES or embedding
different types or different arrangements of fins are employed to improve the thermal conductivity of the PCM.
3

7. OVERVIEW
Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

8. LITERATURE REVIEW
Authors PCM Enhancement techniques Model
Saleel Paraffin Added 1 mass % fraction of SiC nanoparticles with
paraffin.
A square enclosure where the bottom wall acts as a hot
wall and the top wall as a cold wall. The left and right
sides were considered adiabatic.
Soni V et
al.
Erythritol Added nanoparticles, such as copper, aluminum, silica,
and titania.
Exhaust section with embedded PCM capsule in waste
heat recovery system.
Hariss et
al.
n-eicosane Proposed different fin structures like the conventional
fin, the hexagonal Y-shaped, and the honeycomb fin.
A two-dimensional rectangular enclosure that was filled
with PCM and whose top and bottom parts were at
constant heat flux. And the side walls were adiabatic.
Guo and
Zhang
KNO3-NaNO3 Used aluminum foil embedded into the PCM. A typical foil-tube arrangement where Aluminum foils
were arranged orthogonal to the axis of the steam tubes
and the PCM fills the spaces between the foils and
tubes.
Park et al. n-eicosane Proposed eight arrangements of shell-and-tubes. The PCM in the shell side and the HTF into the tube.
Choudhari
et al.
Paraffin RT-42 Proposed different fin designs like a rectangular fin, I-
section fin, triangular fin, trapezoidal fin, and T-shaped
fin.
A Lithium-ion battery is surrounded by PCM. Equally
spaced fins were inserted into the PCM module.
Deng et al. Lauric acid Proposed arrangement of fins, straight fins, angled fins,
lower fins, and upper fins.
Single-tube LHTES was used in this study. The PCM
was filled in the annular space between the shell-and-
tubes.
Tao Y and
He Y
80.5% LiF and
19.5% CaF2
Designed different numbers of local finned. Shell-and-tube LHTES at where the PCM was in the
shell side and HTF flows into the tube. 4

9. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

10. OBJECTIVES
The objectives of the present study are described below:
To find out the most appropriate materials that can be used in TES.
To find out the most appropriate fin arrangements that can be used in TES.
5

11. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

12. PHYSICAL MODEL
PCM
HTF
HTF
Fin
Figure 1: Three-dimensional view of shell-and-tube TES with rectangular fin.
𝛅
do
di
Tube
Shell
Figure 2: Cross-sectional view of shell-and-tube system. 6

13. PHYSICAL MODEL
Fin type Cross-sectional area
a (m2)
Rectangle 2.42
Triangle 1.2834
I-Shaped 1.625
Table 1: Cross-sectional area for different fin types.
2 2
2 (14 )
o i
r l r l a l C
 
     equation:1
• The value of C in equation:1 is derived by
taking the values for the rectangle fin
configuration.
• Rectangle fin configuration is taken as an
ideal configuration.
• The inner radius of the tubes is taken as
constant.
3
,
4.5
30
sec
32865.676
o
i
where
r outer shell radius
r innertube radius mm
l lengthof the LHTES mm
a cross tional area of fin
C volumeof thePCM mm

 
 
 
 
7

14. PHYSICAL MODEL
Fin type Outer shell
diameter
do(mm)
Inner tube
diameter
di (mm)
Distance of tube
from shell
𝜹 (mm)
Without fin 39.457 9 5.3643
Rectangle 40 9 5.5
Triangle 39.95 9 5.487
I Shaped 39.822 9 5.456
Table 2: Dimensions of shell-and-tube for different fin configuration.
• From equation:1 the diameters of the outer
shell for different fin configurations are
derived.
• The total surface area for each fin
configuration is taken as constant which is
280.55mm2
8

15. PHYSICAL MODEL
Materials
Tm
(°C)
𝜌
(kg/m3)
K
(W/ m k)
𝛽
(k1)× 10−4
𝜇
(kg/m s)
× 10−6
Cp
(J/kg k)
L (J/kg)
Cost
Rs. /Kg
(₹)
Sn 232 730 15.08 0.013 9.8 2210 60500 ₹250
NaNO3 306 2260 0.5 1.2 2830 1440 179,240 ₹50-₹80
KNO3 335 2109 0.5 2 1.67 953 95,000
₹90-
₹120
n-eicosane 34.65 770 0.1505 9 3850 2460 247600 -
Aluminum - 2719 130 - - 871 -
₹180-
₹200
Table 3: Thermophysical properties for Sn, NaNO3, KNO3, n-eicosane, and Aluminum.
9

16. PHYSICAL MODEL
(a) (b)
(d)
(c)
Figure 3: Cross-sectional view of without fin condition (a), rectangle fin condition (b),
triangle fin condition (c), and I-section fin condition (d). 10

17. PHYSICAL MODEL
(a) (b) (c)
Figure 4: Three-dimensional view of shell-and-tube TES for without fin (a), triangle fin (b), and I-section fin (c).
11

18. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

19. MATHEMATICAL MODEL
.( ) 0
d
v
dt


  
Continuity equation:
2
( ) . ( ) ( )
ref
d
v v v P v g T T S
dt
   
        
Momentum equation:
( ) .( ) .( )
H vH k T
t
 

    

Energy equation:
The melting process of PCM is solved using enthalpy porosity techniques,
H h H
  
Governing equations
Enthalpy balance:
Latent enthalpy: H L

 
Here,
liquidfraction
totalenthalpy
sensibleenthalpy
velocityvector
specificheatatconst.pressure
latent heat of fusion
p
H
h
v
C
L
 





ref
T
p
T
h C dT
 
Sensible enthalpy:
12

20. MATHEMATICAL MODEL
0 ;when
;when
1 ; when
solidus
solidus
solidus liquidus
liquidus solidus
liquidus
T T
T T
T T T
T T
T T



 

  

 
2
(1 )
( )
mush
S A v

 



Momentum source term,
The value of liquid fraction can be,
solidus
Here,
mushyzoneconstant
constant with value 0.001
thermalexpansioncoefficient
referencetemperature
liquidfraction
= solidus temperature
liquidustemperature
mush
ref
liquidus
A
T
T
T









To consider natural convection, the buoyancy term,
( )
ref
g T T
 
The liquidus temperature is the temperature above which the system is
entirely liquid, and the solidus is the temperature below the system is
completely solid.
13

21. 14
MATHEMATICAL MODEL
o
r
PCM
n-eicosane
Constant hot wall
365.4 K
Adiabatic wall
PCM
NaNO3
Constant hot wall
623 K
Boundary condition
Figure 5: Boundary condition for
analysis of with fin and without fin.
Figure 6: Boundary condition for the comparison
of different fin configurations.
i
r
o
r
Adiabatic wall
i
r

22. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

23. SIMULATION PROCEDURE
Assumptions:
 Transient
 Incompressible
 Boussinesq approximation is taken
 Laminar
 Newtonian
Figure 7: Grid validation 15

24. SIMULATION PROCEDURE
Figure 8: Mesh generation
Mesh - Hexahedral and tetrahedron mesh.
Element size - 0.5904 mm.
Number of nodes – 245322.
Number of elements – 219200.
16

25. VALIDATION OF THE MODEL
Figure 9: Comparison of the temperature
of the present model with the result of
Saleel [1] for a square enclosure.
Figure 10: Comparison of the liquid
fraction of the present model with the
result of Park et al. [5] for circular shell
and tube.
17

26. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

27. RESULT AND DISCUSSION
Melting process of PCM for a rectangle fin system using
NaNO3 as PCM
18

28. RESULT AND DISCUSSION
Temperature variation of PCM for a squared finned system using
NaNO3 as PCM
19

29. Figure 12: Liquid fraction for 200 seconds
Without fin With fin
Figure 11: Distribution of temperature for 200 seconds
RESULT AND DISCUSSION
Melted portion (red)
Solid portion (blue)
Here,
The material is n-eicosane and the fin
is the rectangle fin.
Value of liquid fraction:
0 = The whole PCM is in a solid state
1 = The whole PCM is in a liquid state
Without fin With fin
20

30. RESULT AND DISCUSSION
Figure 13: Temperature magnitude vs time for
the without fin and the with fin (rectangle fin)
configuration for material n-eicosane.
Figure 14: Liquid fraction vs time for the without fin
and the with fin (rectangle fin) configuration for
material n-eicosane.
21

31. RESULT AND DISCUSSION
Figure 15: Temperature contour and liquid fraction contour for PCM materials (Sn, KNO3, and NaNO3)
Sn KNO3
NaNO3
At 100 sec At 100 sec At 100 sec
Temperature
contour
Liquid fraction
contour
22

32. RESULT AND DISCUSSION
Figure 16: Temperature distribution vs time
for different materials.
Figure 17: Liquid fraction vs time
for different materials.
• The temperature magnitude is higher for NaNO3
• The melting time is less for NaNO3.
23

33. RESULT AND DISCUSSION
Without fin Rectangle fin Triangle fin I section fin
Figure 18: Liquid fraction distribution for different periods for different fin configurations
10
sec
100
sec
24

34. RESULT AND DISCUSSION
Figure 19: Liquid fraction vs time for different
fin configurations.
531.18
262 246.5 240
0
100
200
300
400
500
600
Without fin Triangle I-section Rectangle
Time
(s)
Types of fin
Total melting time for different fin types.
Fin type Saved melting time
Rectangle 55%
I-section 53.5%
Triangle 50.5%
Table 5: Percent saved melting time comparison
with without fin condition.
25

35. RESULT AND DISCUSSION
Figure 20: Heat transfer rate vs time for different
fin configurations.
• The heat transfer rate is maximum for rectangle-
finned configurations and least for without-fin
configurations.
• Initially, the heat transfer rate is maximum, then
decreases and slightly increases due to natural
convection, and again it decreases with time.
26

36. RESULT AND DISCUSSION
Figure 21: Velocity magnitude vs time for different
fin configurations
• At t < 50 seconds, it is a strong conduction
zone.
• At 90 < t < 200 seconds, it is a strong
convection zone.
• At t > 200 seconds, it is a weak convection
zone.
• Velocity magnitude is maximum for the
rectangle fin configuration.
27

37. Mathematical Model
Introduction
OVERVIEW
Result and Discussion
Objectives
Simulation Procedure
Conclusion
Literature Review
Physical Model

38. CONCLUSION
CONCLUSION
 NaNO3 performs better as a phase change material for storing thermal energy than other
mentioned materials in terms of lower melting time, higher system temperature, and low
cost.
 Rectangle fin performs better.
28

39. CONCLUSION
FUTURE SCOPES
 Different configurations of other fins can be analyzed to enhance the heat transfer of the PCM.
 Proper ratio of the dimension (length and width) of the fin can be investigated to enhance the
melting of PCM.
 A proper shell-and-tube configuration can be designed to enhance the thermal performance of the
PCM.
29

40. 30
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41. Thank you