Acta Polytechnica


https://doi.org/10.14311/AP.2022.62.0627
Acta Polytechnica 62(6):627–638, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence

Published by the Czech Technical University in Prague

THEORETICAL ANALYSIS OF THE INFLUENCE OF THE
CHEVRON INCLINATION ANGLE ON THE THERMAL

PERFORMANCE OF A GASKET PLATE HEAT EXCHANGER

Élcio Nogueira

State University of Rio de Janeiro, Department of Mechanic and Energy, Rio de Janeiro, Brazil
correspondence: elcionogueira@hotmail.com

Abstract.
Different models are applied for an experimental and theoretical determination of the thermal and

hydraulic performance of gasket plate heat exchanger. One of the relevant aspects of recent works is the
influence of the chevron inclination angle between the heat exchanger plates. This work aims to analyse
the impact of the chevron inclination angle by applying an effective concept in a sunflower vegetable oil
cooler. Comparisons are made with theoretical and experimental results from the literature for works
that consider angles of inclination equal to 30◦, 45◦, and 60◦. An analysis model that does not consider
the inclination angle as an explicit parameter is included for comparison purposes. In addition to the
angle of inclination, two other parameters, the mass flow rate of the cold fluid (water) and the number
of plates, are considered crucial for determining and analysing the results. Nusselt number, global
heat transfer coefficient, effectiveness, heat transfer rate, and outlet temperatures for hot and cold
fluids are presented in a graphical format. The results point to the need to improve models applied to
gasket plate heat exchangers concerning the influence of the inclination angle since there are significant
differences between those obtained and analysed in this work

Keywords: Gasket plate heat exchanger, chevron inclination angle, vegetable oil cooler, theoretical
analysis, second law of thermodynamics.

1. Introduction
Researchers have made numerous efforts to increase
the performance of gasket plate heat exchangers; how-
ever, regarding the influence of the inclination angle
of the chevron plates, there are different procedures
recommended for determining the performance of the
gasket plate heat exchanger. The work analyses three
of these procedures [1–3], which have different degrees
of refinement. The objective is to present the observed
differences and emphasize them so that the differences
between them are evident. To achieve the goal, two
aspects that strongly influence the performance of the
heat exchanger are included in the present analytical
model: the number of plates and the mass flow rate
of the working fluid. The inclusion of these two as-
pects, added to the inclination angle, emphasizes the
significant differences between the procedures under
analysis.

The present work theoretically analyses the influ-
ence of the three abovementioned parameters, but
with a greater emphasis on the aspect related to the
inclination angle. This parameter has been the object
of a recent analysis [1, 2] through different method-
ologies, that is, a model that applies computational
fluid dynamics (CFD) and another, more comprehen-
sive, that uses a semi-analytical model coupled to an
experimental procedure in an industrial plant. These
procedures contrast with many works in which the
influence of the angle of inclination is not considered

in determining the thermal performance of a gasket
plate heat exchanger. Instead, most works use the
Kumar correlation to determine the Nusselt number,
as mentioned by Kacaç et al. [3].

In summary, the present work aims to analyse the
impact of the chevron inclination angle on a Gasketed
Plate Heat Exchanger, applying the concept of effec-
tiveness in a sunflower vegetable oil cooler. The points
under analysis are equal to 30◦, 45◦, and 60◦.

The gasket plate heat exchanger consists of a pack-
age of thin corrugated metal plates pressed together,
with the plates of the heat exchanger arranged so that
the two fluids flow alternately in the channels. The
heat exchanger’s geometry enables high heat transfer
coefficients and has low fabrication and maintenance
costs. In addition, gasket plate heat exchangers have
a solid and robust structure and are very effective
for heat transfer. The search to improve the perfor-
mance of these types of exchangers continues today,
and experiments are carried out with the introduc-
tion of chevron-type plates. The improvement in the
thermal performance depends on reliable correlations
for Nusselt number determination and, consequently,
accurate determination of heat transfer coefficients
in the heat exchanger. This determination is vital
for the design of industrial plants and the analysis of
actual installations.

The work carried out by Skočilas and Palaziuk [1]
applies computational fluid dynamics (CFD) to de-
termine heat transfer through a chevron plate. They

627

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Élcio Nogueira Acta Polytechnica

provide expressions for tilt angle-dependent Nusselt
number and use experimental results from the litera-
ture and results obtained by a numerical simulation to
compare with the developed model. They state that
the model of turbulent water flow between two corru-
gated chevron plates can provide relevant information
about the momentum transfer and thermal diffusivity
process. They fit the developed model using a nu-
merical model and experimental data. They consider
that the model can predict essential performance char-
acteristics in plate heat exchangers concerning the
dimensions, angles of inclination of the corrugations,
etc. In addition, they claim that the performed simu-
lation demonstrates the advantages of using chevron
ripples as compared to using smooth plates since they
allow high heat transfer coefficients. They conclude
by saying that the simulation results can help find
geometries with the lowest possible value of hydraulic
resistance.

Neagu and Konsag [2] validate Lévêque’s semi-
analytical model using experimental data obtained
in four heat exchangers of different sizes. The model
considers the flow in the cell’s sine duct in the furrow
direction, and Nusselt numbers are calculated consid-
ering the construction of the channels. The model was
validated for corrugation inclination angle relative to
vertical direction equal to 30º. The analysis of rela-
tive errors and the statistical analysis concluded for
predicting Nusselt number in gasket plate exchangers,
showed promising results.

The correlation for the Nusselt number independent
of the chevron plate inclination angle obtained by
Kumar, referenced by Kakaç et al. [3], was also used
in the analysis.

Élcio Nogueira [4] uses the concept of entropy gener-
ation to analyse the thermo-hydraulic performance of
a gasket plate heat exchanger for cooling vegetable oil
and uses volumetric fractions of non-spherical nanopar-
ticles in a water-ethylene glycol mixture as a coolant.
He concludes that it is possible to work with relatively
low flow rates using non-spherical nanoparticles, em-
phasizing platelet-shaped nanoparticles. The analysis
of thermal entropy generation versus viscous entropy
generation shows that high flow rates dissipate a large
part of the valuable energy available and do not con-
tribute to oil cooling, increasing the operating cost of
the heat exchanger.

Tovazhnyanskyy et al. [5] present the development
and study of constructing a specially welded plate
heat exchanger. They investigate heat transfer and
hydraulic performance in a single-pass model under
laboratory conditions, and propose an equation that
relates the effectiveness and the number of thermal
units. They develop a mathematical model for multi-
pass heat exchangers from the results obtained, and
validate the model through results obtained in an
industrial prototype confirming the reliability and effi-
ciency of the heat exchanger under analysis compared
to a tubular heat exchanger. In addition, they devel-

oped a method that makes it possible to determine the
height of the undulations and the number of passes
for specified operating conditions.

Nguyen et al. [6] present a study where nickel, cop-
per, and silver electrolytic coating is applied to stain-
less steel plate heat exchangers to improve the thermo-
hydraulic performance. An experiment was conducted
where the efficiency was evaluated using the global
heat transfer coefficient, friction factor, number of
transfer units, and effectiveness. It was found that all
coated plate heat exchangers showed an increase in
performance, especially for silver, followed by copper
and nickel. Finally, they pointed out that the study
shows a potential regarding applications in environ-
ments of severe and corrosive wear or with hygiene
requirements.

Kumar and Singh [7] conducted an experimental
study on a plate heat exchanger and presented ther-
mal and hydraulic performance results with Reynolds
numbers ranging between 800 and 5900. They use a
chevron plate with an angle equal to 60◦ in isothermal
or non-isothermal conditions. They compare the Nus-
selt number developed based on experimental data
with analytical and numerical expressions from the
literature, and conclude that the global heat transfer
coefficient increases with the Reynolds number and
decreases with the number of plates. They state that
considering uniform flux distribution for many plates
is undesirable.

Grigore et al. [8] present a theoretical and experi-
mental study and perform a numerical simulation for
a counterflow plate heat exchanger using the finite
element method. They develop an iterative model
that considers characteristics related to the channel
geometry and determines heat transfer and fluid flow
results. They conclude that the developed model
agrees with experimental results, despite being a com-
plex and labour-intensive simulation and presenting
an excessive consumption of computational resources.
In addition, they claim that the numerical simulation
does not capture the influence of the angle and height
of the ripple. However, the model offers a good un-
derstanding of the temperature distribution and fluid
flow in turbulent conditions.

Jamil et al. [9] developed a theory to analyse heat
exchangers through exergoeconomic concepts and nor-
malised sensitivity analysis. The model allows the in-
vestigation of thermodynamic effects associated with
fiscal parameters and is more comprehensive and sig-
nificant than the conventional thermodynamic or eco-
nomic analyses used separately. They present a practi-
cal example in a plate exchanger used in a desalination
system. The sensitivity analysis demonstrates that
the most critical input variables for determining the
heat transfer rate are the mass water flows and the
salinity. Essential variables of input for the cost of
operation are the mass flow rates of hot and cold flu-
ids, followed by the cost of electricity, interest rate,
and pump efficiency. The parametric analysis demon-

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vol. 62 no. 6/2022 Theoretical analysis of the influence of the chevron . . .

strates that the h/∆P ratio decreases with increasing
Reynolds number and that the cold stream outlet cost
is higher for β = 30◦ than for β = 60◦.

D. dos S. Ferreira et al. [10] study the application
of the Wilson-Plot method for analysis and verify
if the fluid inlet temperatures significantly influence
the thermal behaviour of a plate heat exchanger. The
research is performed by varying the inlet temperature
and the mass flow of the hot fluid with the mass flow of
the cold fluid, fixed. The experimental data presented
a relative error of less than 15 %, within the scope
of uncertainties of the analysed correlations. It is
concluded that the Wilson plotting method is highly
effective for analysing the thermal behaviour of a plate
heat exchanger.

Mota et al. [11] present two methods for analysing
the thermal and hydraulic performance. The first
simulates a configuration of a heat exchanger oper-
ating in a steady state. The parameters considered
in the analysis are the number of channels, number
of passes, the locations of the connections, and the
type of flow. The second model applies to multi-pass
heat exchangers with a large number of plates, which
can be reduced to a single pass. In this particular
case, they established that most multi-pass plate heat
exchangers are equivalent to combinations of single-
pass exchangers. They observed that the first model
is limited to heat exchangers with a large number of
plates and that industrial heat exchangers have more
than 40 thermal plates. They highlight the advantage
of using the first model as it has an applicability to
any configuration. However, the implementation is
highly complex, contrary to the second approach.

Anusha and Kishore [12] present an experimental
work in a heat exchanger with 249 stainless steel
welded metal sheets used in hydraulic cooling. They
determine the correlation for Nusselt number as a
function of Reynolds number, Prandtl number, and
chevron angle. They get results for the heat transfer
coefficient, overall heat transfer coefficient, and effec-
tiveness. Graphical results are used to demonstrate
the performance of the Gasket Plate Heat Exchanger.
They conclude that the maximum effectiveness for
counterflow arrangement is equal to 0.949 and that
with increasing Reynolds number from 20 to 60, the
Nusselt number increased by 10.01 %, the friction
factor decreased by 25.7 %, the overall heat transfer
coefficient increased by 10.44 %, and the effectiveness
increased by 12.53 %.

Khond et al. [13] worked to optimise the perfor-
mance of the plate heat exchanger by reducing the
number of plates and, for that, they present a math-
ematical model that allows to reach the optimum in
certain operational restrictions. The results obtained
through applying the mathematical model demon-
strate that the effect of the initial and final plates
and the transverse flow distribution are considerable
and affect the performance of the heat exchanger.
They conclude that the model proposed in the work

meets the thermal and hydraulic demand and makes
it possible to determine the smallest number of plates
necessary for the adequate performance of the heat
exchanger. However, they note that a more advanced
algorithm is needed to achieve greater precision in
determining the minimum number of plates.

In this context, the present work aims to analyse
the impact of the chevron inclination angle in a Gas-
ket Plate Heat Exchanger by applying the effective
concept in a sunflower vegetable oil cooler. The tips
under analysis are equal to 30◦, 45◦, and 60◦.

2. Methodology
The geometric characteristic and physical parameters
of the heat exchangers used in the present work were
those tested by Neagu and Koncsag [2]. The rele-
vant fact regarding the models is that Skočilas and
Palaziuk [1] used water as the working fluid and two
chevron plates for the numerical simulation (CFD).
The work developed by Neagu and Koncsag [2] was
theoretical and experimental in an industrial plant,
using water and vegetable oil as working fluids, and
presented comparisons with relative errors below 20 %.

The fluids that exchange heat are water and sun-
flower vegetable oil. The water at 30◦ is used to cool
vegetable oil that enters the heat exchanger at a tem-
perature of 110◦. The heat exchanger used for the
analysis uses 63 plates, and the original chevron plate
has an angle of inclination equal to 30◦. The empiri-
cal expressions used to determine the Nusselt number
were taken from three independent works [1–3]. Sun-
flower properties were taken from numerical tables
provided in the literature [13] and determined through
3rd and 4th-degree polynomial interpolations (Equa-
tions (1)–(5)). Angles of 45◦ and 60◦ were introduced
in the analysis for comparison purposes. The results
independent of the inclination angle are arbitrarily
referenced as the angle of inclination equal to 0◦. Two
parameters independent of the angle of inclination, the
flow rate of the cold fluid and the number of plates of
the heat exchanger, are predominant for determining
the thermal performance. Therefore, their variations
were included in the analysis.

Figure 1 shows geometric features of a chevron-type
plate. Recent works [1, 2] use the chevron angle, β,
the corrugation depth, b, and the corrugation wave-
length, l, to look for local influences that can improve
empirical expressions for the Nusselt number, which
generally depends on the Reynolds number and the
Prandtl number. In the present work, fixed values are
adopted for b and l. In contrast, in most simulations,
empirical expressions for Nusselt number are used in
which the chevron angle appears explicitly.

Table 1 presents properties for the fluids used in this
work as a function of average temperatures. Water
is used to cool the vegetable oil in the case under
analysis.

Tci = 30 ◦C and Thi = 110 ◦C are the inlet tem-
peratures of water and vegetable oil. Tc = 35 ◦C,

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Élcio Nogueira Acta Polytechnica

ρ [kg/m3] k [W/(m K)] Cp [J/(kg K)] µ [kg/(m s)] ν [m/s2] α [m/s2] Pr
Water 993.80 0.610 4186 0.725 · 10−3 7.29 · 10−7 1.47 · 10−7 4.96
Sunflower 913.00 0.163 2346 11.54 · 10−3 1.26 · 10−5 0.76 · 10−7 166

Table 1. Physical properties for cold (water) and hot (sunflower vegetable oil) fluids.

Figure 1. Basic geometrical dimensions of chevron
corrugated plate heat exchanger [2].

Th = 75 ◦C and T W = 55 ◦C.

ρh = 920.8893939 − 0.09046037296 T h

− 0.0003712121212 T h
2

+ 2.331002331 · 10−6 T h
3
,

(1)

µh = 0.144681007 − 0.00571479528 T h

+ 9.81172771 · 10−5 T h
2

− 7.880585664 · 10−7 T h
3

+ 2.402607809 · 10−9 T h
4
,

(2)

µW = 0.144681007 − 0.00571479528 T W

+ 9.81172771 · 10−5 T W
2

− 7.880585664 · 10−7 T W
3

+ 2.402607809 · 10−9 T W
4
,

(3)

kh = 0.1595212121 + 7.626262626 · 10−5 T h

− 5.303030303 · 10−7 T h
2

+ 2.5252525 · 10−9 T h
3
,

(4)

Cph = 2046.651515 + 3.511130536 T h

− 0.005606060606 T h
2

+ 9.906759907 · 10−6 T h
3
,

(5)

where ρh is the specific mass (density) of the hot fluid,
µh is the dynamic viscosity of the hot fluid, µW is the
dynamic viscosity of the hot fluid at the surface, kh is

the thermal conductivity of the hot fluid and Cph is
the specific heat of the hot fluid.

νh is the kinematic viscosity or momentum diffusiv-
ity of the hot fluid and αh is the thermal diffusivity
of the hot fluid and Prh is the Prandtl number of the
hot fluid:

νh = µh

ρh
, (6)

αh = kh

ρhCph
, (7)

Prh = νh

αh
. (8)

Rfc = 0.00018 and Rfh = 0.00053 are the fouling
factors of the cold and hot fluids, respectively. Nt = 63
(original value) is the number of plates used in the
reference work [1], ρc = 993.8 kg/m3 is the specific
mass (density) of the cold fluid, µc = 0.725·10−3 is the
dynamic viscosity of the cold fluid, kc = 0.610 is the
thermal conductivity of the cold fluid and Cpc = 4183
is the specific heat of the cold fluid.

νc is the kinematic viscosity or momentum diffusiv-
ity of the cold fluid and αc is the thermal diffusivity
of the cold fluid and Prc is the Prandtl number of the
cold fluid:

νc = µc

ρc
, (9)

αc = kc

ρcCpc
, (10)

Prc = νc

αc
. (11)

LV = 1.070 is the vertical distance between centres of
ports, Lp = 0.858 is the plate length between ports,
Lw = 0.450 is the plate width, Lh = 0.238 is the
horizontal length between centres of ports, DP =
0.212 is the port diameter, δW = 0.6 ·10−3 is the plate
thickness, kW = 17.5 is the thermal conductivity of
the plate, LC = 175.56 · 10−3 is the compressed plate
pack length. Pit is the plate pitch:

Pit = LC

Nt
, (12)

b is the corrugation depth:

b = Pit − δW , (13)

φ = 1.17 is the surface enlargement factor, Dh is the
hydraulic diameter:

Dh = 2b

φ
, (14)

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vol. 62 no. 6/2022 Theoretical analysis of the influence of the chevron . . .

Ach is the channel cross-sectional free flow area:

Ach = bLW , (15)

Ne is the effective number of heat transfer plates:

Ne = Nt − 3, (16)

Np = 1 is the number of fluid passes, Ncp is the
number of channels for one pass:

Ncp = Nt − 1
2Np

. (17)

A1 = 0.331 is the heat transfer area for a plate, Ae

is the heat transfer total area:

Ae = A1Ne, (18)

Reh = 30.0 (fixed) is the Reynolds number for hot
fluid, Gch is the mass velocity:

Gch = Rehµh

Dh
, (19)

ṁch is the mass flow rate per channel:

ṁch = GchAch, (20)

ṁh is the total mass flow rate of the hot fluid:

ṁh = ṁchNcp. (21)

Gcc = Recµc

Dh
. (22)

Rec is the Reynolds number for cold fluid.

ṁcc = GccAch, (23)
ṁc = GcAch, (24)
Cc = ṁCpc, (25)
Ch = ṁCph, (26)

where mc is the total mass flow rate of the cold fluid
and Ch is the thermal capacity of the hot fluid. Cmin

is the minimum thermal capacity between the hot and
cold fluids:

C∗ = Cmin

Cmax
. (27)

Equations (1)–(27) include the physical property de-
termination and mass flowrates needed for the Nusselt
calculation. In Table 2, the parameters determined by
Skočilas and Palaziuk [1] and for Kumar correlation [3]
are presented.

2.1. Equations for no explicit angle in
the expressions of Nusselt number

This section presents the Equations (28)–(38) that
depend only on the coefficients and exponents shown
in Table 2. Nuc is the Nusselt number for cold fluid:

Nuc = c2Ren
c Prm

c

(
µc

µW

)x

, (28)

Nuh = c2Ren
hPrm

h

(
µh

µW

)x

. (29)

β C2 n m x

No angle
(Kumar) 0.348 0.663 1/3 0.17

30◦ 0.14 0.64 0.39 0.1
45◦ 0.14 0.645 0.395 0.1
60◦ 0.14 0.65 0.40 0.1

Table 2. Coefficient and exponents for the expres-
sion of Nusselt [2] determined by Skočilas and Palaz-
iuk [1].

hh is the coefficient of heat convection for hot fluid:

hc = Nuckc

Dh
, (30)

hh = Nuhkh

Dh
. (31)

Uo is the global heat transfer coefficient:

Uo = 1
1
hc

+ 1
hh

+ δW

kW
+ Rfc + Rfh

. (32)

NT U = UoAe

cmin
, (33)

where NTU is the number of thermal units associated
with the heat exchanger and Ae is the total heat
transfer area, established by Equation (18). εT is the
thermal effectiveness:

εT = 1 − e−NT U(1−C∗)

1 + C∗e−NT U(1−C∗) . (34)

Q̇ is the actual heat transfer rate and Qmax is the
maximum heat transfer rate:

Q̇ = εT Cmin(Thi − Tci), (35)
Q̇max = Cmin(Thi − Tci). (36)

Tco and Tho are the outlet temperatures for cold and
hot fluids, respectively:

Tco = Tci + Q̇

ṁcCpc
, (37)

Tho = Thi + Q̇

ṁhCph
, (38)

3. Equations for explicit angle in
the expressions of Nusselt
number

This section introduces several parameters (39)–(55)
that explicitly depend on the chevron inclination angle,
emphasizing the Nusselt numbers (56) and (57).

β is the chevron inclination angle:

β = πβ

180 , [rad], (39)

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Élcio Nogueira Acta Polytechnica

l is the corrugation wavelength:

l = Pit sin β, (40)

Lfurr and Llong are the furrow and longitudinal flow
components:

Lfurr = l

sin 2β
, (41)

Llong = l

sin β
. (42)

XX is the ratio corrugation depth:

XX = b

P it
. (43)

Dh sin e is the hydraulic dynamic diameter of a sine
duct:

Dh sin e = (0.149 XX3 − 0.623 XX2

+ 1.087 XX − 0.0014)l, (44)

Ach sin e is the channel cross-section transverse to the
furrow:

Ach sin e = Ach cos β. (45)

usin ec = ṁcc

ρcAch sin e
, (46)

usin eh = ṁch

ρhAch sin e
, (47)

Resin ec = 2usin ecDh sin e

νc
, (48)

Resin eh = 2usin ehDh sin e

νh
. (49)

C = 2.6624 XX4 − 10.586 XX3

+ 11.262 XX2 − 1.036 XX + 9.6,
(50)

Keinf = 5.888 XX4 + 9.4611 XX3

− 4.248 XX2 − 0.1333 XX + 2.648,
(51)

Kdinf = 1.7237 XX4 + 2.7669 XX3

− 1.2651 XX2 − 0.0097 XX + 1.512,
(52)

Kinf = 2(Keinf − Kdinf), (53)

B = KinfDh sin e

4lfurr
. (54)

fappc is the apparent friction coefficient:

fappc = C

Resin ec
+ B. (55)

Nuc sin e

= 0.40377
(

4fappcRe2
sin ec + Prc

Df sin e

lfurr

)1/3
,

(56)

Nuh sin e

= 0.40377
(

4fapphRe2
sin eh + Prh

Df sin e

lfurr

)1/3
.

(57)

Then, the overall thermal transfer coefficient Uo sin e,
number of transfer units NTUsin e, thermal effective-
ness εT sin e, and thermal flux Q̇sin e, can be calculated
with Equations (58)–(65)).

hc sin e is the coefficient of heat convection for cold
fluid and hh sin e is the coefficient of heat convection
for hot fluid:

hc sin e = Nuc sin ekc

Dh sin e
, (58)

hh sin e = Nuh sin ekh

Dh sin e
. (59)

Uo is the global heat transfer coefficient and εT sin e

is the thermal effectiveness:

Uo = 1
1

hc sin e
+ 1

hh sin e
+ δW

kW
+ Rfc + Rfh

. (60)

NTUsin e = Uosin eAe

Cmin
, (61)

εT sin e = 1 − e−NT Usin e(1−C∗)

1 + C∗e−NT Usin e(1−C∗) . (62)

Q̇sin e is the actual heat transfer rate:

Q̇sin e = εT sin eCmin(Thi − Tci). (63)

Tco and Tho are the outlet temperatures for cold and
hot fluids, respectively:

Tco = Tci + Q̇sin e

ṁcCpc
, (64)

Tho = Thi + Q̇sin e

ṁhCph
. (65)

4. Results and discussion
The results presented in this work are strongly depen-
dent on the experimental parameters determined by
Neagu and Koncsag [2]. In addition to the physical
and geometric parameters, the most significant influ-
ence on obtaining the results are Reynolds number,
inlet temperatures, and heat exchanger plates. The
Reynolds number range adopted for cold fluid is ob-
tained from Table 5 of reference [2], i.e. Rec = 979 <
Re < Rec = 1530. The Reynolds number for the
hot fluid was kept fixed, equal to 30. The original
number of plates, taken from Table 1, equals to 63.
The inlet temperatures of the hot and cold fluids are
equal to 110 ◦C and 30 ◦C, respectively. The angle of
inclination used in the experiment is equal to 30 ◦C.

Figure 2 presents the apparent friction factor as a
function of the Reynolds number. The angles under
analysis are equal to β = 30◦, β = 45◦, and β =
60◦. The highlight is for the angle equal to 30◦ since
the friction factor variation range is compatible with
the results of Figure 3 of reference [2]. The results
graphically presented in reference [2] show that the

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vol. 62 no. 6/2022 Theoretical analysis of the influence of the chevron . . .

Figure 2. Apparent friction coefficient versus
Reynolds number with slope angles as parameters.

Figure 3. Resine versus Reynolds number for cold
fluid (Experimental Ref. [2]).

lower limit value for the friction factor is equal to
fapp = 0.2. In this specific situation (chevron angle
equal to β = 30◦), the smallest value for the Reynolds
number is equal to Rec = 60, and the largest is equal
to Rec = 1530. The values obtained for angles equal
to β = 45◦ and β = 60◦ show a slight variation
concerning the reference angle but are compatible
with the values and the trend presented by this one.

The relationship between the Reynolds numbers
used in the expressions to determine the Nusselt num-
bers is shown in Figure 4, for a number of plates equal
to NT = 63. The Reynolds Resin e number is depen-
dent on the chevron in the inclination angle. The
graph shows the relationship for the Reynolds number
between Rec = 60 and Rec = 1530. The experimen-
tal values are taken from the reference [2], within

Figure 4. Nusselt number versus Reynolds number
for cold fluid [1, 2].

the Reynolds number range between Rec = 979 and
Rec = 1530, for an inclination angle equal to β = 30◦.
The β = 46◦ and β = 60◦ angles are included in
the analysis to compare and analyse the theoretical
model.

The Nusselt number as a function of the Reynolds
number, with slope angles as parameters, is repre-
sented in Figure 4. The models under analysis, al-
ready described above, were developed by Skočilas
and Palaziuk [1], Neagu and Koncsag [2], and Ku-
mar (in [3]). In Figure 4, the experimental values for
an angle of β = 30◦ and Reynolds number in the range
of Rec = 979 to Rec = 1530 are highlighted. The re-
sults obtained through the Skočilas and Palaziuk [1]
model do not show great dispersion concerning the
angles of inclination and present values significantly
lower than the other models. Regarding the model
developed by Neagu and Koncsag [2], a significant dis-
persion can be observed between the values obtained
for the angles under analysis. In this case, the values
for the Nusselt number increase with the angle of incli-
nation. Regarding the Kumar correlation, regardless
of the angle of inclination, it can be observed that the
Nusselt number surpasses the other two models under
analysis.

Figure 5 shows the global heat transfer coefficient
for the models under analysis. It is noteworthy that
the global heat transfer coefficient carries information
related to the hot fluid and has a value for a Reynolds
number equal to Reh = 30. The results obtained
through reference [3] do not present great numerical
dispersion within the wide range of values obtained by
the models. The highlight is the Kumar correlation,
with intermediate values between the two models.
There is a great difference between the models.

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Élcio Nogueira Acta Polytechnica

Figure 5. Global heat transfer coefficient versus
Reynolds number for cold fluid [2].

Figure 6. Thermal effectiveness versus Reynolds
number for cold fluid [1, 2].

As expected, thermal effectiveness, represented by
Figure 6, presents a behaviour similar to that ob-
tained for the global heat transfer coefficient. Again,
the attention is drawn to the great dispersion between
the models, with significantly high values obtained
through the reference model [1] concerning the refer-
ence values [3]. The effectiveness obtained by Neagu
and Koncsag [2] is practically double that of the effec-
tiveness obtained by the model developed by Skočilas
and Palaziuk [1]. The Kumar model presents inter-
mediate values, slightly closer to the results obtained
through the reference [1].

Figure 7 shows the heat transfer rate and demon-
strates, as already observed in Figure 5, that for plates
equal to Nt = 63 and within the analysed flow rate,
the maximum rate theoretically possible is signifi-
cantly different from the values obtained by the model

Figure 7. Heat transfer rate versus Reynolds number
for cold fluid [2].

Figure 8. Outlet temperatures versus Reynolds num-
ber for cold fluid [2].

associated with reference [2], the least conservative of
the three under analysis.

Figures 8 and 9 show outlet temperatures for the
fluids. The temperatures represented in Figure 8
demonstrate that the model developed and presented
through reference [2], with an angle of 30◦ and plate
number equal to Nt = 63, is close to the best possible
result of the analysed heat exchanger. However, the
model developed by Kumar tends to approach these
results for higher flow rates. Figure 9 shows the outlet
temperature for the hot fluid and demonstrates that
the trend presented by the profiles is similar for all
of them. The highlight for the model developed by
Kumar shows intermediate values to the other two
models. The flow variation is more significant as
an influence on the thermal performance of the heat
exchanger than the angle of inclination.

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vol. 62 no. 6/2022 Theoretical analysis of the influence of the chevron . . .

Figure 9. Outlet temperature for cold fluid versus
Reynolds number for cold fluid.

Figure 10. Thermal effectiveness versus Reynolds
number for cold fluid with number of plates as a pa-
rameter.

Figure 10 shows the effectiveness for number of
plates equal to Nt = 49, Nt = 98, and Nt = 150,
and an inclination angle equal to β = 30◦. It can
be observed that the differences between the models
decrease with the increase in the number of plates.
For example, with plates, in the case of the model
developed by Neagu and Koncsag [2], the effectiveness
is very close to 1, i.e., the heat transfer rate is very
close to the maximum theoretically possible value.

The results shown in Figure 11 corroborate what
was observed for effectiveness. The heat transfer rate
increases with the number of plates and approaches
the maximum theoretically possible for a plate number
equal to Nt = 150 and a Reynolds number equal
to Rec = 1530. However, the values obtained for
heat transfer rate through the model of Skočilas and

Figure 11. Heat transfer rate versus Reynolds num-
ber for cold fluid with the number of plates as a pa-
rameter [1].

Figure 12. Heat transfer rate versus the number of
plates for Reynolds number equal to 979 and with
inclination angle as a parameter.

Palaziuk [1] are relatively different from the maximum
possible for any number of plates within the range
under analysis.

Figures 12 and 13 show results for heat transfer rate
as a function of the number of plates, for Reynolds
numbers equal to Rec = 979 and Rec = 1530, with
slope angles as parameters. The heat transfer rate
increases with the number of plates and approaches
the maximum for the highest flow rates under anal-
ysis. For high plate numbers, the model developed
by Kumar is close to the model presented by Neagu
and Koncsag [2]. The inclination angle does not sig-
nificantly affect the heat transfer rate, regardless of
the model analysed.

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Élcio Nogueira Acta Polytechnica

Figure 13. Heat transfer rate versus the number of
plates for Reynolds number equal to 1530 and with
inclination angle as a parameter.

Figure 14. Outlet temperatures of fluids versus the
number of plates for Reynolds number equal to 979
and with inclination angle as a parameter [1, 2].

The graphical results presented in Figures 14 and 15
show the outlet temperatures for the cold and hot
fluids as a function of Reynolds numbers equal to
Rec = 979 and Rec = 1530, respectively, with slope
angles as parameters. The number of plate limit de-
pends on the model used in the analysis since the
second law of thermodynamics imposes a physical
limitation. It is observed that this limit depends on
the flow rates of the fluids and, again, is not much
influenced by the chevron tilt angle. As the model
presented by Neagu and Koncsag [2] significantly ap-
proaches 100 % of effectiveness (ε1) for both Reynolds
numbers under analysis, the maximum possible num-
ber of plates is the smallest among the models. In
this specific case, the maximum number of plates for

Figure 15. Outlet temperatures of fluids versus the
number of plates for Reynolds number equal to 1530
and with inclination angle as a parameter [1, 2].

Reynolds number equal to Rec = 979 is Nt = 78, and
for Reynolds number equal to Rec = 1530, Nt = 82.
When it comes to the Kumar model, you can see
that the limiting numbers are equal to Nt = 120 and
Nt = 122. As the effectiveness is very low in the case
of the model developed by Skočilas and Palaziuk [1],
the maximum numbers for both flows under analysis
are above Nt = 150.

5. Conclusion
The work analysed the influence of the chevron plate
inclination angle on the thermal performance of a
Gasket plate heat exchanger. Three models were used
to determine the Nusselt number through theoreti-
cal and experimental correlations. The models were
developed by Kumar, Skočilas and Palaziuk [1], and
Neagu and Koncsag [2].

Regarding the analysed models, there is a great
difference between them. It can be said that the
values obtained by the authors are very different from
each other. And in this sense, it is concluded that the
maximum flow rate and the limit number of plates to
be used in the heat exchanger strongly depend on the
used model.

Based on the results presented, the model developed
by Neagu and Koncsag [2] is the most efficient and
effective. It obtains final results for exit temperatures
very close to the other models, developed by Kumar
and Skočilas and Palaziuk [1], with a smaller number
of plates and a lower flow rate for the cold fluid. The
model developed by Kumar does not explicitly con-
sider the inclination angle, and the results obtained are
intermediate to the other two and slightly approach
the model developed by Neagu and Koncsag [2] for
high flow rates.

The flow rate variation is more significant as an
influence on the thermal performance of the heat ex-

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vol. 62 no. 6/2022 Theoretical analysis of the influence of the chevron . . .

changer than the angle of inclination, and the number
of plates to be used in the heat exchanger are the other
main factors responsible for the thermal performance.

The number of plates used in reference [2], Nt = 63,
is quite adequate, following the analyses performed.

Based on the results obtained, the need for new
theoretical and experimental works related to the
influence of chevron inclination angles is evident.

List of symbols
Ach channel cross-sectional free flow area [m2]
Ae heat transfer total area [m2]
Ach sin e channel cross-section transverse to the furrow

[m2]
b corrugation depth [m]
Cpc specific heat of the cold fluid [J/(kg K)]
Cph specific heat of the hot fluid [J/(kg K)]
Ch thermal capacity of the hot fluid [W/K]
Cmin minimum thermal capacity between the hot and

cold fluids [W/K]
C∗ = Cmin/Cmax

Dh hydraulic diameter [m]
Dh sin e hydraulic dynamic diameter of a sine duct [m]
DP port diameter [m]
fapp apparent friction coefficient
Gch mass velocity of the hot fluid [kg/(m2 s)]
Gcc mass velocity of the cold fluid [kg/(m2 s)]
hh coefficient of heat convection for hot fluid

[W/(m2 K)]
hc coefficient of heat convection for cold fluid

[W/(m2 K)]
hc sin e coefficient of heat convection for cold fluid

[W/(m2 K)]
hh sin e coefficient of heat convection for hot fluid

[W/(m2 K)]
kh thermal conductivity of the hot fluid [W/(m K)]
kc thermal conductivity of the cold fluid [W/(m K)]
kW thermal conductivity of the plate [W/(m K)]
l the corrugation wavelength
LC compressed plate pack length [m]
Lh horizontal length between centres of ports [m]
Lp plate length between ports [m]
LV vertical distance between centres of ports [m]
Lw plate width [m]
Lfurr furrow flow components [m]
Llong longitudinal flow components [m]
ṁch mass flow rate per channel [kg/s]
ṁc total mass flow rate of the cold fluid [kg/s]
ṁh total mass flow rate of the hot fluid [kg/s]
Ncp number of channels for one pass
Ne effective heat transfer number of plates
Np number of fluid passes
Nt number of plates
Nuc Nusselt number for cold fluid
Nuh Nusselt number for hot fluid
Nuc sin e Nusselt number for cold fluid for a sine duct
Nuh sin e Nusselt number for hot fluid for a sine duct

P rc is the Prandtl number of the cold fluid
P rh is the Prandtl number of the hot fluid
P it plate pitch [m]
Q̇ actual heat transfer rate [W]
Q̇max maximum heat transfer rate [W]
Q̇sin e actual heat transfer rate [W]
Rec Reynolds number for cold fluid
Reh Reynolds number for hot fluid
Resin ec Reynolds number for cold fluid in a sine duct
Resin eh Reynolds number for hot fluid in a sine duct
T ci inlet temperature of water [◦C]
T hi inlet temperature of vegetable oil [◦C]
T co outlet temperature for cold fluid [◦C]
T ho outlet temperature for hot fluid [◦C]
Uo global heat transfer coefficient [W/(m2 K)]
Uosin e global heat transfer coefficient of a duct sine

[W/(m2 K)]

Greek symbols
αc thermal diffusivity of the cold fluid [m2/s]
β corrugation angle of the plate
φ area enlargement factor
ρ density of the fluid [kg/m3]
µ dynamic viscosity of fluid [kg/(m s)]
νc the kinematic viscosity of the cold fluid [m2/s]
ε effectiveness

Acronyms
CFD computational fluid dynamics
GPHE gasket plate heat exchanger
NTU number of thermal units

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	Acta Polytechnica 62(6):627–638, 2022
	1 Introduction
	2 Methodology
	2.1 Equations for no explicit angle in the expressions of Nusselt number

	3 Equations for explicit angle in the expressions of Nusselt number
	4 Results and discussion
	5 Conclusion
	List of symbols
	References