Hussein Hatem Saleh a, Munther Abdullah Mussaa, *
a Department of Mechanical Engineering, College of
Engineering, University of Baghdad, 10071 Baghdad, Iraq.
* Corresponding author.
Abstract: The study aims to find the optimal fin length
distribution for improved heat transfer during melting and
solidification in a tubular PCM heat exchanger designed for heat
storage. Three types of horizontal PCM tabular heat exchangers, all with
five longitudinal fins, were studied numerically. While maintaining a
constant heat transfer area, each model depicts a unique fin length
distribution design. The first model, which serves as the reference
design, has a homogeneous fin length distribution and each fin is 30 mm
long. The second model has shorter upper and side fins and longer lower
fins (20 mm for the upper fin, 25 mm for the side fins, and 40 mm for
the lower fins). The third model has long lower fins but shorter than
that of second model, short side fins and no change in upper fin length
with reference design (30 mm for upper fin, 25 mm for side fins and 35
mm for lower fins). The findings indicate that the second model exhibits
the best heat transfer performance for the melting process, while the
first model is most effective for solidification. Interestingly, the
third design emerges as the optimum choice for both melting and
solidification processes.
Key word: PCM heat exchanger, melting, solidification, optimum,
fin length distribution .
PCM : phase change material
H.E.: heat exchanger
H.T.F. : heat transfer fluid
CFD : computational fluid dynamic
Introduction
The increasing global demand for energy and the climate change crisis
have compelled countries to embrace renewable energy sources such as
wind and solar power. However, these energy sources are intermittent,
meaning they cannot consistently generate energy when required. This
mismatch between energy demand and the supply of renewable energy has
been highlighted (Joudi and Taha 2023). Consequently, this has prompted
the advancement of energy storage systems (Fathi and Mussa
2021).
Energy storage systems enable to
store surplus energy generated during periods of high production, such
as during sunny or windy weather, for later use when demand arises.
Various storage solutions are in use, with the most prevalent being
energy batteries, which find applications in electric vehicles and
large-scale energy storage for power plants. Additionally, there are
emerging technologies, including thermal and mechanical energy storage
systems. Thermal energy storage involves the accumulation of excess
thermal energy, often from solar collectors or other renewable sources,
within materials capable of retaining heat energy. This stored thermal
energy can be deployed as needed (Aneke and Wang 2016, Fathi and Mussa
2023).
Thermal energy storage can be accomplished using two primary methods:
sensible heat storage and latent heat storage (Nabhan 2015). Among
these, latent heat storage systems are particularly significant. These
systems store heat within materials during phase changes, including
processes such as melting, solidification, boiling, and condensation. In
latent heat storage, energy is stored and released at a constant
temperature. This characteristic enables stable energy charging and
discharging, thanks to the consistent temperature difference between the
phase change material (PCM) and its surroundings (Azim and Gupta 2020).
The applications of PCM storage systems include solar thermal energy
storage, building heating and cooling systems, spacecraft PCM heat
exchangers, and the use of PCM in human textile cooling systems,
providing a comfortable and efficient way to manage body heat. All these
applications used PCM inside heat exchanger (Nagar and Singh 2021).
PCM H. E. have shown significant potential in increasing energy
efficiency and reducing the environmental impact of different thermal
systems. One type of PCM H. E. that has received particular attention in
recent years is the PCM fin heat exchanger, which consists of a
PCM-filled fin that is attached to a heat transfer surface such as a
tube or a plate (Al-Mudhafar, Nowakowski et al. 2018). The design and
optimization of PCM fin H.E. pose several challenges, such as geometry,
and phase change material, as well as the analysis of the heat transfer
mechanisms and the evaluation of the performance metrics (Mehta, Vaghela
et al. 2020).
Numerical investigation of horizontal fin PCM H.E. with longitudinal
five fin, paraffin wax used as PCM due to high heat capacity, low
melting temperature and chemically stable but low thermal conductivity,
for this reason many research achieved to overcome this drawback
(Al-Ebadi and Abdullah 2022, Sadiq and Mussa 2022), water used as heat
transfer fluid H.T.F. due to high thermal conductivity and heat
capacity. Geometry of PCM H.E. has a great effect on PCM H.E., the full
understand of melting and solidification processes, where the natural
convection is dominated mode of heat transfer, that depend in density
change, and this natural convection up stream can restricted or enhance
by geometry of container (Huang, Yang et al. 2022). So, the length of
fin, fin density and fin angle are the main effects on PCM H.E., in
addition of shape and orientation of PCM H.E., these parameters can
enhance melting process but reduce solidification performance and vice
versa (Motevali, Hasandust Rostami et al. 2021).
The selection of these parameters can be optimized to ensure the best
performance of both the melting and solidification processes or to
enhance one process over the other, depending on the purpose of the PCM
heat exchangers (PCM H.E.) and the intended application. Emphasis should
be placed on studying the fin length of tabular PCM heat exchangers.
Specifically, examining the effects of different length distributions on
the constant heat transfer area of the fin, and analyzing the heat
transfer mechanisms within PCM heat exchangers with these length
patterns.
Numerous studies have examined the impact of fin geometries on natural
convection during the melting and solidification of phase change
materials (PCM). For instance, (Rudonja, Komatina et al. 2016)
investigated the enhancement of heat transfer in a shell and tube PCM
heat exchanger designed for thermal energy storage. In this study,
paraffin wax E53 was used as the PCM, and longitudinal rectangular
copper fins were employed. A numerical analysis was conducted using a 3D
model built in Ansys FLUENT software. The results demonstrated that
increasing the ratio of heat transfer surfaces by raising the fin height
led to a decrease in melting time. Furthermore, the study found that the
number of longitudinal fins had a significant positive impact on melting
time. Similarly, (Mehta, Chaudhari et al. 2017) studied the thermal
performance of latent heat storage units filled with PCMs in various
shell and tube configurations: vertical, horizontal, and inclined (45°).
The investigation was carried out numerically using the enthalpy
porosity approach. To reduce computational time, a 2D slice of the PCM
heat exchanger was employed for modeling. It was observed from the
results that the PCM melting process occurred more quickly in the
inclined shell and tube configuration compared to the vertical and
horizontal configurations. Additionally, the impact of varying fluid
inlet temperatures on the thermal performance of the PCM heat exchanger
was examined. The results indicated that higher fluid inlet temperatures
led to a reduction in melting time. (Pizzolato, Sharma et al. 2017)
studied a new method for heat transfer fins design for shell-and-tube
heat exchanger used as thermal energy storage units, longitudinal fins
are used. The topology optimization and multi-phase computational fluid
dynamics used to design the optimal fin shape for a given PCM heat
exchanger set of design constraints. The results demonstrated that the
proposed method could identify fin shapes and designs that significantly
improved the heat transfer performance of the PCM heat exchanger. In a
separate study, (Kamkari and Groulx 2018) achieved experimental research
to enhance the melting rate of PCM by adding fins to rectangular
enclosures with different inclination angles. The findings revealed that
the melting rate increased as the inclination angle decreased, both for
unfinned and finned enclosures. Notably, in the case of a 3-fin
horizontal enclosure, the minimum melting time was observed, resulting
in the highest heat transfer rate. This study contributes to a better
understanding of the PCM melting process in differently inclined finned
enclosures and provides valuable benchmark data for future simulation
studies. (Shahid Afridi, Anthony et al. 2018), did a comparative study,
both experimentally and numerically, to evaluate the performance of
annular and longitudinal fins in thermal energy storage units utilizing
phase change materials (PCM). The results showed that longitudinal fins
are more effective than annular fins for PCM storage units because it
provides larger surface area of heat transfer, which contribute to
higher heat transfer rate and higher efficiency. (Aydin, Mete et al.
2018) studied the effect of attaching a fin to the bottom of the inner
tube in a horizontal shell-and-tube storage unit, that can enhance the
melting rate process of paraffin that used as PCM by up to 72.8%. that
because the fin intensifies the recirculation of melting paraffin or
natural convection currents in the lower half of the annulus of sell
side, that lead to increase the heat transfer rate. And the study
suggested that fins can be an effective improvement to enhance the
melting rate of paraffin wax in horizontal PCM shell-and-tube storage
units, which may be useful for different applications such as thermal
solar energy storage and building climate conditioning. (Deng, Nie et
al. 2019) studied a novel fin arrangement was proposed to enhance heat
transfer in latent heat thermal energy storage. Symmetrical fins were
placed along the lower vertical centerline, improving melting
significantly at specific angles. Effects of shell conductivity,
dimensionless fin length, and heat-transfer fluid temperature were
studied. Optimal angles reduced complete melting time by 66.7% with
increased fin length and by 53.1% with higher fluid temperature. Longer
fins exhibited more pronounced performance enhancement in latent heat
thermal energy storage in this configuration. Similarly, (Mahood, Mahdi
et al. 2020) conducted a numerical study to investigate the effect of
fin height and angle in the performance of a horizontal shell-and-tube
PCM heat exchanger. The results showed that increasing fin height
significantly improved the thermal performance of the PCM heat
exchanger, reducing melting time by 50% for a fin height equal to 0.8
of the hydraulic radius of the annulus shell. Additionally, the study
found that lower fin angles, when positioned below the horizontal axis,
provided better thermal performance by targeting the least efficient
heat transfer region within the PCM inside the heat exchanger shell.
Beyond fin shape, fin spacing and height were also found to impact the
natural convection of melted PCM. (Soltani, Soltani et al. 2021)
conducted a numerical investigation into the combined effects of fins
and rotation on the melting and solidification processes of a latent
heat thermal energy storage heat exchanger. Radial fins were employed in
a shell and tube PCM heat exchanger. The results demonstrated that
rotational speed had a positive impact on both the melting and
solidification processes, reducing the solidification process time by
83.21% and increasing the heat transfer rate by 12.89 W. Furthermore,
an increase in rotational speed showed a direct correlation with the
enhancement of the heat transfer rate by 2.45 and 3.87 times during the
melting and solidification processes, respectively. In (Ali N. Abdul
Ghafoor 2020) study LHTES with paraffin wax, circular tubes outperformed
vertical and horizontal ovals, demonstrating superior efficiency and
longer heat absorption duration.
Overall, these studies illustrated that, the addition of longitudinal
fins can significantly enhance the thermal performance of PCM tubular
H.E., and the optimum number and geometry of fins depend on the specific
design and operating conditions of the heat exchanger.
The objective of this work to
select the optimum design from three fin length distribution designs,
the selected design, that gives heat transfer enhance for melting and
solidification processes, by implemented numerical simulation of these
designs in CFD and analyze the result obtained from simulation to
conclude the optimum design.
Mathematical and numerical model:
Mathematical model:
The typical heat exchanger (H.E.) problem is resolved by applying the
heat diffusion equation, combined with continuity, momentum, and energy
equations for steady-state conditions. In this context, each domain,
whether solid or liquid, is addressed separately using the respective
equations. However, the situation differs in the case of phase change
material heat exchangers (PCM H.E.), where the melting and
solidification processes change with time (transient), and the medium
undergoes phase transitions during operation. The heat diffusion is
transformed into an energy balance by include the PCM’s enthalpy change
during the phase change as following:
\(\rho C_{p}\frac{\partial T}{\partial t}=k\left(\frac{\delta^{2}T}{\delta x^{2}}+\frac{\delta^{2}T}{\delta y^{2}}+\frac{\delta^{2}T}{\delta z^{2}}\right)+\frac{\partial}{\partial x}(S\rho L)\)(1)
Where, \(\rho\) is the density of PCM, \(C_{p}\) heat capacity of PCM, K
thermal conductivity of PCM, S is liquid fraction and L laten heat of
phase change. Enthalpy-porosity theory can be used to include the impact
of phase-change materials in the energy equation as shown below:
(Arosemena 2018)
\(\rho C_{p}(\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z})=k\left(\frac{\delta^{2}T}{\delta x^{2}}+\frac{\delta^{2}T}{\delta y^{2}}+\frac{\delta^{2}T}{\delta z^{2}}\right)+\frac{\partial}{\partial x}(S\rho L)\)(2)
where u, v and w are the velocity components in x, y and z direction.
Solving these two equations analytically can be challenging, especially
for complex geometries like heat exchangers. Instead, numerical methods
are commonly employed, such as the finite element method, finite volume
method, and finite difference method. These numerical techniques enable
the simultaneous solution of the differential equations (D.E.) and
energy equations (E.E) for the same phase change material (PCM). A
combined approach is used, incorporating both equations and employing a
penalty method to eliminate undesired terms over time, corresponding to
the liquid state of the segment. Additionally, the momentum and
continuity equations are utilized to account for natural convection,
while the standard momentum, continuity, and energy equations are
applied for the heat transfer fluid. Numerous software applications are
available for solving numerical solutions, and one of the most renowned
ones is Fluent, part of the ANSYS package. In this study, ANSYS 21 was
utilized for numerical simulations.
Physical model: