Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

54, 4, pp. 1285-1295, Warsaw 2016
DOI: 10.15632/jtam-pl.54.4.1285

A PCM-WATER HEAT EXCHANGER WITH POLYMERIC HOLLOW FIBRES

FOR LATENT HEAT THERMAL ENERGY STORAGE: A PARAMETRIC

STUDY OF DISCHARGING STAGE

Jiř́i Hejč́ık, Pavel Charvát, Luboḿir Klimeš

Brno University of Technology, Department of Thermodynamics and Environmental Engineering, Brno, Czech Republic

e-mail: hejcik@fme.vutbr.cz; charvat@fme.vutbr.cz; klimes@fme.vutbr.cz

Ilya Astrouski

Brno University of Technology, Heat Transfer and Fluid Flow Laboratory, Brno, Czech Republic

e-mail: astrouski@fme.vutbr.cz

The paper presents a theoretical parametric study into latent heat thermal energy storage
(LHTES) employing polymeric hollow fibres embedded in a phase changematerial (PCM).
The polymeric hollow fibres of five inner diameters between 0.5mm and 1.5mm are con-
sidered in the study. The effectiveness-NTU method is employed to calculate the thermal
performance of a theoretical LHTES unit of the shell-and-tube design. The results indicate
that the hollow fibres embedded in a PCM can mitigate the drawback of low thermal con-
ductivity of phase change materials. For the same packing fraction, the total heat transfer
rates between the heat transfer fluid and the PCM increase with the decreasing diameter
of the hollow fibres. This increase in the heat transfer rate and thus the efficiency of the
heat exchange to some extent compensate for the energy consumption of the pump that also
increases with the decreasing fibre diameter.

Keywords: polymeric hollowfibre, heat exchanger, latent heat thermal energy storage, phase
changematerials

1. Introduction

Thepolymeric hollow fibre heat exchanger (PHFHE) is a relatively novel type of heat exchanger
that employs thin-wall polymeric fibres for separation of heat transfer fluids. The hollow fibres
can be produced by the extrusion process from a variety of polymers such as polypropylene
(PP), polyethylene (PE), polyether ether ketone (PEEK) as well as from certain polymers with
increased conductivity. The PHFHEs are an alternative to conventional metal heat exchangers
for low temperature applications (Zarkadas and Sirkar, 2004).

A number of heat transfer devices was constructed and tested for both liquid and gaseous
heat transfer fluids. One of the most common designs of a PHFHE is the one similar to the
shell-and-tube heat exchanger. The PHFHEs have rather high ratios between the heat transfer
area and the volume (around 1400m2/m3). Zarkadas andSirkar (2004) reported the overall heat
transfer coefficients of these devices between 647W/m2K and 1314W/m2K for water-to-water
heat transfer application. It was shown that the overall conductance per unit of volume of the
PHFHE (around 1.2 ·106W/m3K) is larger than in the case of conventional metallic shell-and-
-tube exchangers and slightly less than in the case of the plate heat exchangers. Song et al.
(2010) presented a lab study aimed at the use PHFHEs in the thermal desalination process.
The metallic heat exchangers suffer from corrosive behaviour of salt water while the plastics
withstand salt water quite well. The two experimental lab-scale PHFHEs were of the shell-and-
-tube design and contained solid polypropylene hollow fibres (950 and 2750, respectively) with



1286 J. Hejč́ık et al.

the outer diameter of 0.58mm and the wall thickness of 0.075mm. The experimental PHFHEs
had large values of packing fraction (0.59 and 0.63, respectively) and the surface area/volume
ratios of 3061m2/m3 and 3290m2/m3, respectively. The heat transfer performance of the
PHFHEs was studied for a hot brine (80◦C to 98◦C) – cold water (8◦C to 25◦C) system as
well as for a steam (101◦C to 113◦C) – cold water (8◦C to 25◦C) system as these systems
are typically encountered in thermal desalination plants. The overall heat transfer coefficient
as high as 2000W/m2K was achieved, which was close to the limiting value imposed by the
PP wall thickness (2660W/m2K). The overall conductance per unit of volume was around
6.1 ·105-3.5 ·106W/m3K, which is higher than that of metallic shell-and-tube heat exchangers
and comparable with the best plate heat exchangers.

The present paper deals with a theoretical study aimed at application of PHFHEs in the
latent heat thermal energy storage. The polymeric hollow fibres embedded in a phase change
material (PCM) represent a way to increase the heat transfer rates between the heat transfer
fluid (HTF)andthePCM.Theanalysis hasbeenperformed for aPCM-water latentheat thermal
energy storage (LHTES) unit of the shell-and-tube designwhere the tubes are polymeric hollow
fibres and the shell is filled with a PCM.

2. Fluid flow and heat transfer in polymeric hollow fibres

The polymeric hollow fibres have the inner diameter of around 10−3m.Therefore, the fluid flow
andheat transfer in hollow fibres is essentially the fluidflowandheat transfer inminichannels as
classified byKandlikar andGrande (2003) where theminichannels were channels with diameter
between 200µm and 3mm. The fluid flow in minichannels is characterized by low Reynolds
numbers. A number of correlations for minichannels andmicrochannels can be found in Tullius
et al. (2012). It has been shown that the fluid flow and heat transfer in minichannels is in a
good agreement with the criteria established for channels of much larger diameters (Herwig and
Hausner, 2003; Celata et al., 2006; Dutkowski, 2008). A significant deviation could occur in
microchannels of very small diameters – only a few micrometers. Such channel diameters are
close to the free mean path of the molecules where the assumption of continuum in the case
of fluid flow no longer applies. However, the polymeric hollow fibres used in the PHFHEs do
not have the inner diameter of less than 0.1mm (100µm) and the assumption of the continuum
for heat and mass transfer is valid. Also, the decreasing diameter of a channel translates into
increasing pressure drop. Since the pressure drop significantly influences operating costs of heat
exchangers, the fluid velocities in the polymeric hollow fibres need to be rather small to achieve
reasonable pressuredrops.Figure 1 shows the pressuredropof 1meter length of the hollowfibres

Fig. 1. Pressure drop as a function of the channel diameter and water velocity



A PCM-water heat exchanger with polymeric hollow fibres... 1287

of five inner diameters between 0.5mm and 1.5mm. TheReynolds number for all the cases was
Re¬ 2000, whichmeans laminar flow. TheNusselt number in the case of the laminar flow only
depends on the boundary condition; a constant heat flux or a constant wall temperature. The
Nusselt number is defined as Nu= hd/k where h is the heat transfer coefficient, d is the inner
diameter and k is the thermal conductivity of the fluid. The Nusselt number for laminar flow
in a circular channel is Nu = 4.36 for the constant heat flux through the wall of the channel
and Nu = 3.66 for constant wall temperature (Incropera et al., 2006). It can be concluded
from the definition of the Nusselt number that the heat transfer coefficient increases rapidly for
channel diameters below 1mm (microchannels). However, it is important to not overestimate
the influence of heat transfer coefficient on the overall heat transfer rates.

3. Hollow fibres embedded in phase change materials

The phase change materials (PCMs) as the media for LHTES have received a lot of attention
in the last two decades (Oró et al., 2012; Sharma et al., 2009; Zalba et al., 2003). In contrast
to sensible heat storage, the phase change of a material offers a relatively high thermal storage
capacity and energy storage density in a narrow temperature interval around the temperature of
the phase change.Nonetheless, the practical application of thePCMs inLHTES is still relatively
limited. One of the reasons is rather low thermal conductivity of most PCMs (Jegadheeswaran
and Pohekar, 2009). Many possibilities to increase the heat transfer rates between the heat
transfer fluid (HTF) and the PCM have been proposed; from extended heat transfer surfaces
(Al-Abidi et al., 2014;Kozak et al., 2014) tometal foams (Zhao et al., 2010) and to nanoparticles
(RaamDheep and Sreekumar, 2014). This paper discusses the potential use of polymeric hollow
fibres embedded in a PCM as a way to increase the heat transfer rates between the PCM and
the heat transfer fluid. Five inner diameters of hollow fibres are considered: 0.5mm, 0.75mm,
1mm, 1.25mm and 1.5mm. The wall thickness of the fibres is proposed in a way to achieve
the same hoop stress in the wall of the fibre for the same HTF pressure. This assumption leads
to a constant ratio between the outer and the inner diameter of the fibre and consequently to
the same value of the thermal resistance of heat conduction through the fibre wall (per unit of
length).

Fig. 2. Polymeric hollow fibres embedded in the PCM

Figure 2 shows a schematic view of polymeric hollow fibres embedded in a phase change
material. The theoretical analysis presented in this paper focuses on the thermal performance of
such an arrangement in thermal energy storage. The hexagonal pattern of the hollow fibres was
considered as shown in Fig. 3. In this pattern, the distance between any two adjacent hollow
fibres is the same since the distances of the fibres are the sides of equilateral triangles. The
distance of the fibres, called the pitch andmarked PT in Fig. 3, is usually expressed in relation
to the diameter of the tube (polymeric hollow fibre in this case). The ratio between the pitchPT



1288 J. Hejč́ık et al.

and the outer fibrediameterD in thedesign of the conventional fluid-to-fluid shell-and-tubeheat
exchangers is between 1.25 and 1.5. This is equivalent to the packing fraction (the ratio of the
tube bundle cross section area to the shell cross section area) between 0.58 (for PT/D = 1.25)
and 0.4 (for PT/D=1.5).

Fig. 3. Hexagonal arrangement of the fibres

Various combinations of the fibre inner diameter d and the fibre pitch PT produce values of
the heat exchanger area density between 548m2/m3 and 2369m2/m3, see Fig. 4. The situation
inFig. 4 applies to fluid-to-fluidheat exhangers. It shows that it is possible to reach high thermal
performance with a small volume of the heat exchanger with the use of hollow fibres, because
a decrease in the fibre diameter leads to a simultaneous increase in the heat transfer coefficient
and the area density. However, the largest value of area density is reached for the combination of
theminimal fibre diameter and the smallest fibre pitch. Hence, a very small volume of the phase
changematerial remains around the fibres.This significantly reduces the overall thermal storage
capacity of LHTES units with this design. Therefore, the packing fraction of the shell-and-
-tube LHTES units with PCMs needs to bemuch smaller than in the case of the shell-and-tube
heat exchangers for fluid-to-fluid heat transfer. In the present study, the ratio PT/D=10 that
provides much larger volume and thus overall thermal capacity of the PCM is used. In general,
the smaller the PT/D ratio the higher overall heat transfer rates between the PCM and the
heat transfer fluid can be achieved. An optimal PT/D ratio would depend on the purpose and
operating conditions of the LHTES unit.

Fig. 4. Area density for different fibre diameters and PT/D ratios



A PCM-water heat exchanger with polymeric hollow fibres... 1289

Thepresentedparametric study takes into account both the heat transfer in the hollowfibres
and the amount of stored energy. Several assumptions and simplifications have been adopted
in the study. The phase change of the PCM is considered isothermal (taking place at constant
temperature). This assumption has frequently been adopted by other authors, e.g. Aadmi et
al. (2015), Hu and Patniak (2014), Zivkovic and Fuji (2001). The amount of the heat storage
material belonging to one hollow fibre has been calculated from the hexagonal section (grey area
in Fig. 3) and the length of the fibre. The thickness of the melted/solidified layer of the PCM
along the length of the fibre is considered to be constant. The analysis of the thermal behaviour
of hollow fibres in the LHTES unit has been based on the ε-NTU methodology (Tay et al.,
2012) where the thermal performance characteristics of a heat exchanger are described by the
equations

ε=1− e−NTU NTU= ln
( 1

1−ε

)

(3.1)

where ε is the heat exchanger effectiveness andNTU is theNumber of Transfer Units. Since the
phase change occurs at a constant temperature Tmelt, the medium with minimal heat capacity
rateCmin is theheat transferfluid.Theheat exchanger effectiveness thus represents the efficiency
of charging (ordischarging) ofheatbymeansof theHTF,and it canbeexpressedby the following
equation

ε=
Tin−Tout
Tin−Tmelt

(3.2)

where Tin is the HTF inlet temperature, Tout is the HTF outlet temperature and Tmelt is PCM
melting temperature. The heat transfer rate used for charging/discharging is calculated from
the parameter NTU, which is defined as

NTU=
UA

Cmin
(3.3)

whereU is theoverall heat transfer coefficient,A is theheat transferareaandCmin is theminimal
heat capacity rate, which is the product of mass flow rate ṁHTF and the specific heat cHTF of
the HTF,Cmin = ṁHTFcHTF.
TheUA parameter is derived from the thermal storage geometry and the physical properties

of theHTF and it is equal to the inverted value of the overall thermal resistance. Three thermal
resistances are taken into account in theparametric study.Thefirst one is the convective thermal
resistance inside the hollow fibre, based on the heat transfer coefficient for the fully developed
laminar flow with the constant wall temperature (Nu = 3.66). The second thermal resistance
is the conductive resistance of the fibre wall. Finally, the third resistance is the heat transfer
resistance through the solid PCM material which built up around the fibre surface during the
dischargeofheat fromthermal energy storage.Theresistanceof themeltedPCMaroundthefibre
surface would be used in the case of charging of the thermal storage. The thermal resistance of
themelting/solidification front is neglected and theUAvaluehasbeen calculated using following
equation

1

UA
=
∑

i

Ri =
1

hinπdL
+
lnD
d

2πkwL
+
lnDPCM

D

2πkPCML
(3.4)

where hin is the heat transfer coefficient inside the fibre, d is the inner diameter of the hollow
fibre,L is the fibre length, D is the fibre outer diameter, kw is the thermal conductivity of the
fibrewall,DPCM is the diameter onwhich themelting/solidification front is located and kPCM is
the thermal conductivity of the solid PCM surrounding the fibre.



1290 J. Hejč́ık et al.

4. Results and discussion

Quasi-steady-state thermal calculations have been carried out for comparison of several hollow
fibre diameters in the LHTES unit. The heat loss to the ambient environment is neglected as is
a common assumption in theoretical studies (Belusko et al., 2012; Pinnau and Breitkopf, 2015;
Daugenet-Frick et al., 2015). The study focuses on heat transfer between theHTFand thePCM
andnot on the overall thermal performance of an actual LHTESunit, so it has been justifiable to
assume an adiabatic shell of the unit. Nevertheless, it needs to be emphasized that the heat loss
to the ambient environment can significantly influence the real-life operation of LHTES units.
The internal volume of theLHTESunit is considered 1m3 and thePHFHEconsisted of 1m long
fibres that are assembled in the hexagonal pattern (Fig. 3)with the pitchPT/D=10.Therefore,
the packing fraction is the same for all fibre diameters and the LHTES unit contains the same
weight of PCM in all studied cases. The calculations start with the LHTES unit containing the
liquid PCM at the melting temperature. The heat stored in the unit is discharged by water
flowing through the hollow fibres (the water flow rate was 60ℓ/min). The initial condition is
DPCM =D at the time t = 0, which means the PCM thermal resistance is equal to zero. The
calculations have been performed with the time step∆t=30s. The input data for calculations
and the considered parameters of the LHTES unit are presented in Tables 1 and 2.

Table 1. LHTES unit parameters

Parameter
Simulation

1 2 3 4 5

d 0.5mm 0.75mm 1mm 1.25mm 1.5mm
D 0.7mm 1.05mm 1.4mm 1.75mm 2.1mm
PT 7mm 10.5mm 14mm 17.5mm 21mm
Number of fibres 23565 10473 5891 3770 2618

Table 2.Calculation inputs and parameters

PCMproperties

Melting temperature Tmelt 30
◦C

Latent heat 200kJ/kg
Density 760kg/m3

Thermal conductivity (solid) kPCM 0.2W/mK

HTF – water

Inlet temperature Tin 25
◦C

Flow rate ṁHTF 60ℓ/min

Fibre material

Thermal conductivity 0.18W/mK
Volume 1m3

Amount of PCM 753kg
Latent heat capacity 1.5GJ
Packing fraction 0.009

Figure 5 shows the time needed to discharge heat from the LHTES unit in the case of five
hollow fibre diameters. It is evident that the LHTES unit with the small diameter fibres is
more efficient as it takes less time to solidify all the PCM. This corresponds with the results
presented in Fig. 6 that shows the heat exchanger efficiency as a function of the solid fraction.
The heat transfer efficiency of the small diameter fibres remains high during the entire heat



A PCM-water heat exchanger with polymeric hollow fibres... 1291

Fig. 5. Time vs. solid fraction for different fibre diameters

Fig. 6. Heat exchanger efficiency and outlet water temperature as functions of the solid fraction

discharge process. It is the result of very high heat transfer area of the hollow fibres with the
small diameter which are surrounded by quite a thin layer of the PCM.

The efficiency of the heat exchanger influences the outlet temperature of thewater as can be
seen inEq. (3.2). Evenwhen the solidification of thePCMtakes place at a constant temperature,
as assumed in this study, theoutletwater temperature changesduringtheheatdischargeprocess,
see Fig. 6. This fact can have significant consequences for real-life operation of LHTES. One of
the advantages of LHTES is that heat is stored and released in a narrow temperature interval
around the melting point of the heat storage medium (PCM). If there is a certain requirement
on theminimumoutlet temperature of theHTF, the total thermal storage capacity of a LHTES
unit may not be utilized as the HTF outlet temperature drops below the required value during
discharge of heat.

A high efficiency of the heat exchanger with small diameter fibres is countered by a higher
pressure drop. The pressure drop in the case of 0.5mm hollow fibres is almost 9 times higher
than that in the case of 1.5mm fibres. This translates into an increase in the pump power for
the same water flow rates and the same packing fraction. Figure 7 shows the pump power as a
function of the flow rate for the considered LHTES unit. The pumppower has been obtained as

Pp =
V̇∆p

η
(4.1)



1292 J. Hejč́ık et al.

Fig. 7. Pump power as a function of the water flow rate

where V̇ is the volumetric flow rate,∆p is the pressure drop and η is the efficiency of the pump.
For the sake of comparison, a constant efficiency of the pump η=0.85 is considered in all cases.
Though the required pump power increases with the decreasing inner diameter of the fibre. A
better efficiency of the heat exchangers with small diameters of the fibres reduces the overall
energy consumed by the pump during a heat storage cycle. As can be seen in Fig. 5, the time
needed to discharge the heat from the heat storage unit is much shorter in the case of 0.5mm
fibres than in the case of 1.5mm fibres.

Fig. 8. Pump power as a function of the channel diameter

Figure 8 shows the energy consumedbyapumpduring theheat discharge period.The energy
is obtained as

E =

t
∫

0

Pp dt (4.2)

where t is the timeneeded for the discharge of the heat fromtheLHTESunit andPp is thepump
power given by Eq. (4.1). As can be seen in Fig. 8, the curves of energy consumption have a
minimum for certain diameters of the hollow fibres. A parameter similar to COP can be defined
as a ratio between the amount of heat charged into and/or discharged from the LHTES unit



A PCM-water heat exchanger with polymeric hollow fibres... 1293

and the energy consumed by the pump. Such a parameter can then be used in multi-criterion
optimization of the design of the LHTES units with polymeric hollow fibres.
The presented parametric study is relatively simple but it shows the potential of the poly-

meric hollow fibre heat exchangers in the latent heat thermal energy storage. There are many
obstacles to overcome in design and manufacturing of such units, e.g. LHTES units containing
tens of thousands of hollow fibres would be both difficult and costly to produce. For these re-
asons, the small units for short-term thermal energy storage with high heat storage and heat
release rates seem to be a more promising area of application of PHFHE than the large-scale
thermal energy storage. One area of application could be automotive industry where various
ways of LHTEShave been studied in the last several years (Kim et al., 2010; Javani et al., 2014;
Kauranen et al., 2010).

5. Conclusions

The polymeric hollow fibre heat exchangers (PHFHEs) provide a large surface area density
that can compensate for the small thermal conductivity of phase change materials (PCMs) in
the latent heat thermal energy storage (LHTES). Moreover, PHFHEs are resistant to corrosive
behaviour of somePCMsandheat transfer fluids.The results of the conducted parametric study
are in line with the expectations and they indicate strengths and weaknesses of the PHFHE in
LHTES in terms of heat transfer between the heat transfer fluid and the PCM.The efficiency of
the PHFHE in LHTES decreases with the increasing solid fraction of a PCM. For the constant
mass of a PCM, constant length of the hollow fibres and constant packing fraction, the heat
transfer rates and the efficiency increase with the decreasing diameter of the hollow fibres. An
increase in the packing fraction leads to an increase in the heat transfer rates but at the expense
of decreasing energy storage density. For a constant packing fraction, the diameter of the hollow
fibre can be found that provides the maximum ratio between the stored heat and the pump
energy.

Acknowledgement

The research leading to the presented results was supported by the Czech Science Foundation under

contract number P101/11/P538 andGA15-19162S.

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Manuscript received January 14, 2016; accepted for print March 3, 2016