Research and Applications of Thermal Engineering
Volume 2 Issue 3
Implementation of Generalized Regression Neural Network
Prediction Tool for Evaluating Thermal Performance in a Heat
Exchanger by using Triple Elliptical Leaf Angle Strips with Same
Orientation and Same Direction
J. Bala Bhaskara Rao1*, V. Ramachandra Raju2
1
Department of mechanical engineering, SSCE, India
2
Department of mechanical engineering, JNTUK, India
*Corresponding Author
E-mail Id:-raobasijarajapu@gmail.com
ABSTRACT
Heat exchangers have enormous power in changing the way we look around in this world.
Since we find its applications at almost every nook and corner of this world so enhancement
methods in heat exchangers leads to a great innovation. Here the augmentation technique of
passive method of leaf strip insert is utilized. Three elliptical shaped leaf strips with same
orientation and along same direction are inserted in the tube side for fluid flow. The strips are
placed at different angular orientation ranging from 0° to 180° with arrangements of 10° each
at 50 mm separated positions are placed. The obtained results are compared with a statistical
tool of GRNN (Generalized Regression Neural Network). An algorithm is created by using
the functions of dependent variables and independent variables and outputs are obtained. A
comparison between these values of experiment and GRNN are done to get the percentage of
error between them.
Keywords:-Heat transfer, heat exchanger, leaf strip, GRNN, Percentage of error.
INTRODUCTION
Heat transfer subject is a great path in the
field of research. An influential topic in the
heat transfer is the study of heat
exchangers. Heat exchangers are the
devices where the energy flow in the form
of heat is transferred from one part to
another utilizing which large energy
transformations is possible .These energy
transfers causes great outputs to industrial
applications actually applied in real life.
Hence heat exchanger output causes a
mighty difference to the society. Hence
with this approach various researchers
have done research with the motto of
increasing the output of heat exchangers
[1]. Various bended strips were used and
an experiment was performed on tube in
tube out heat exchanger. Using counter
flow configuration on a single phase water
to water heat transfer was performed by
varying the mass flow rates of annulus and
the inner tube [2]. Performed the task of
shot blasting to increase the heat transfer.
In this experiment analysis the roughness
of outer surface of inner pipe was changed
which gave the results of increased heat
transfer rate by 43% [3]. They used the
finite difference calculus to model the
temperature
profiles
across
heat
exchangers [4]. They found a method to
determine the pipe sizes, pipe lengths,
number of bends. The performance was
determined by using heat exchanger
effectiveness and the fouling factor [5].
Conducted experiment on Nano particle’s
concentration effect on Nusselt number
and heat transfer characteristics with
baffles and without baffles which resulted
in enhancement up to 12% for 0.2 %
concentration and enhancement up to 22%
for 0.1% concentration. All these results
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
were obtained when baffles were used in
the experimentation [6]. This paper
suggested inserting tapes in a twisted
pattern in double pipe heat exchangers
which gave positive results of coefficients
on both sides of the device. After finding
this they even further tested the
characteristics
of
heat
transfer
enhancement
with
pressure
drop
characteristics where there was a negative
result for pressure drop with enhancement
in heat transfer rates [7]. Proposed the use
of circular and square longitudinal strips to
find the effect on Nusselt number, Pressure
drop & overall heat transfer coefficient in
a double pipe heat exchangers. The results
ascertained the better flow in thermal
performance with development in mass
flow rate and size of the strips [8]. They
studied about the use of twisted tapes to
increase the rate of heat transfer. Results
gave better heat transfer rates by using
twisted tapes [9]. They found the effect of
condensation heat transfer rate by
introducing twisted tape. It created swirl
generation which increased the contact
area resulting in the increase of
condensation heat transfer coefficient for
steam [10]. Used the technique of baffle
spacing in finding better thermal
performances. They used the triangular
baffles of 100 and 50 mm pitches which
increased the values by 1.42 & 1.62 in
parallel flow and 1.338 & 1.62 times in
counter flow heat exchanger. [11] wrote a
review paper on the augmentation of
Active, passive and compound techniques.
In a plain tube the use of passive and
compound techniques produced better
results, by using helical tubes also better
heat transfer rates and pressure drops was
given [12] studied about the enhancement
techniques of double pipe heat exchangers
which indicated the enhancement of heat
transfer coefficient at 7.69 twist ratio for a
range of Reynolds’s number (2300-10000)
.It also stated that swirl flow also
improved the conductive characteristics of
the equipment [13]. They found the effect
of twisted tape, trapezoidal cut on double
pipe heat exchanger using al203water
based Nano fluids. From this experiment
they found the friction factor required for
performance analysis [14]. The passive
method technique is used to evaluate
thermal performance in concentric tube
heat exchanger for different fin profiles.
The results showed that concave parabolic
fins had minimum pressure when
compared with other two [15]. Found the
design criteria required for hot fluid
flowing in a double pipe heat exchanger. It
showed that with more pressure drop more
temperature difference occurred between
the fluids [16]. Tried to find the
enhancement of heat transfer rate by using
triangular fins which gave the results as
increase in effectiveness of heat transfer
rate by inserting fins to the outer surface of
the copper tube [17]. Found a numerical
simulation of Nano fluids flow in a heat
exchanger using porous baffles. The
solution was found in a finite volume
method [18]. They analyzed the heat
exchanger analysis in an equipment where
the heat transfer coefficient was found to
be higher for a laminar flow [19] used a
rotor inserted tube to get high turbulent
flow in a counter flow heat exchanger and
found the numerical and experimental
values [20]. They analyzed a horizontal
triple tube heat exchanger having internal
threaded pipes. The heat transfer analysis
was found on a triple tube heat exchanger.
Based on this survey from various sources
passive
method
was
used
for
experimentation. In this investigation
novelty stands for the utilization of an
elliptical leaf in the pipe for heat transfer
rate. Since the elliptical shape is preferred
for better flow in ducts so keeping this as
reference an elliptical shaped leaf is used
for allowing better flow of fluids in the
pipe. So in this passive method an
elliptical leaf strip insertion placed at
various orientations provides the rate of
heat transfer and pressure drop. After the
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
experimentation a prediction tool is used
known as GRNN (Generalized Regression
Neural Network) for finding the
formulation between inputs and outputs.
The inputs such as different elliptical leaf
angles, different masses of hot and cold
fluids and inlet temperatures are taken to
give outputs such as outlet temperatures of
hot and cold fluid and pressure drops in
tube and annular side. The values from
GRNN & experiment are compared to find
the percentage of error between both the
obtained values.
EXPERIMENTAL SETUP
The experimentation started with the
utilization of double pipe heat exchanger
with inner and outer pipe made up of
copper and steel respectively as shown in
Figure 1. The fluid flow is incompressible
and turbulent in the pipes.
Here the experimentation is conducted
based on 19 scenarios where three
elliptical leaf strips are placed at different
angles from 0° to 180° at 10° intervals as
shown in Figure 2. The elliptical leafs are
designed as major to minor axes as 2:1 and
the thickness is 1mm. These elliptical leafs
are located at 50mm distance at 90°
rotation
towards
the
shaft.
Fig.1:-Experimental equipment of double pipe heat exchanger
Since the fluid taken is water which is
arriving from the sump where it is made to
flow in two streams comprising of cold
fluid going through the annular side and
hot fluid passing through the tube side
which is heated by an electrical heater and
sent in to it. All the values are taken after a
steady state is attained. The specifications
for the experiment are taken as following
for hot water inner pipe temperature is 348
K for fluids flowing at 0.15785, 0.3827,
0.55763 & 0.71782 kg/s & cold water
inner pipe is at 298 K with mass flow rates
of 0.34589, 0.8403, 1.2245 & 1.5762 Kg/s.
Certain accessories are used for
measurement during these fluid flows such
as thermo couples for temperature
measurements at inlet and outlet of the
pipes, flow meters to measure the volume
flow rates at the stream division. Both
thermo couples and Rota meters where
calibrated before experimentation to obtain
accurate results. The atmospheric pressure
is defined as the pressure boundary at the
outlets. While analysis is done constant
temperatures of working fluids are
considered for the design modifications of
double pipe heat exchanger.
For the analysis of the experiment, flow
consideration is made either on Laminar or
turbulent flow which is determined by
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
Reynold’s number. In this analysis,
turbulent flow is considered for both the
pipes and accordingly calculations are
performed. After obtaining the results from
experiment they are compared with a
prediction tool known as GRNN
(Generalized
Regression
Neural
Network).The values between this
experiment and GRNN are compared &
percentage
of
error
is
found.
Fig.2:-Three elliptical leaf strips positioning at various angles
RESULTS AND DISCUSSION
Heat Transfer Analysis
In this paper the heat transfer rate is one of
the outputs so in this regard the heat
transfer rate is studied with different
orientation of the three elliptical leaf
angles with same orientation and direction
which was increased for 0 to 180 degrees
and the effects were plotted by using CFD
as shown in Figure3.
Fig.3:-Temperature contours for three elliptical leaf angle strips of heat exchanger
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
A passive technique of improving the
convective heat transfer rate is the use of
strips with elliptical leafs in a tube. The
graphs obtained showed us the variation of
heat transfer with Reynolds number where
it was found that at 60 degrees the
maximum heat transfer rate is found from
Figure 4. Hence after getting the heat
transfer rates for all angular dimensions
ranging from 0 to 180 a final graph plotted
showed us the variation of heat transfer
rate for the best values obtained in the
above three graphs . From this it is
concluded that the final value of maximum
heat transfer rate corresponding to
Reynolds number is obtained at 60° as per
the analysis reports.
Fig.4:-Heat transfer variation at different elliptical leaf angles for different Reynolds
numbers
Pressure Drop Analysis
The pressure drop analysis is done at
various three elliptical leaf angles with
same direction and orientation and the
results obtained were plotted as shown in
Figure 6 .The parameters required to find
fluid flow are Pressure ,velocity &
temperature.
Fig.5:-Pressure contours for three elliptical leaf angle strips of heat exchanger.
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
As a novice in heat transfer also knows
that the heat transfer rate increases with
increased temperature difference in the
heat exchangers which ultimately causes
the pressure to drop exceedingly which is
not recommendable in heat exchanger
devices as it affects the performance and
life of the equipment. Focus being made
on obtaining uniform heat transfer rate in
the heat exchanger so an analysis of
pressure drop is made in the results section
to obtain an optimum rate of pressure drop
at various angles. The vector contours in
mathematical model shown in Figure 5 for
heat exchanger with strip indicates
pressure drop variation in tube side with
different elliptical leaf inclinations.
Fig.6:-Annular and Tube side pressure drop variation at different elliptical leaf angles
say “Y” from a measured reading of “X”
of a random variable “x” where mean is
utilized in the equation and this is known
as
regression
“y”
on
“x”
GRNN Methodology
GRNN is a statistical tool used to measure
certain outputs by giving some known
inputs. Here to find an unplanned value
given as ( ⁄ )
( )
∑
∑
(
(
∫
∫
)
)
(
(
(
(
)
)
) ∫
)
∫
[
[
(
(
HBRP Publication Page 1-11 2019. All Rights Reserved
)
)
]
]
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
Table.1:-Input and output for GRNN analysis
The above two equations are used for a
continuous
function
of
f(x,
y).
Investigation shows us that the above
inputs and outputs are nonlinear and we
cannot find a specific relation for input and
output Hence they are converted into
another statistical equation and combined
with artificial neural network
⁄
(
)
∑
∑
(
⁄
Hence to get a relation for the nonlinear
results clustering operations is chosen to
measure the output values .By performing
the clustering operation through various
processes the system yields us desired
outputs. This clustering technique is done
by ANN (Artificial neural network) in this
experiment.
)
(
∑
∑
)
(
(
⁄
⁄
)
)
Fig.7:-Comparison between Experimental values & GRNN values for 68 trainee data
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Research and Applications of Thermal Engineering
Volume 2 Issue 3
As this experiment deals with finding the
heat transfer rate and pressure drop rates
so in this regression method taking the
values of temperatures and mass flow rates
outputs of pressure drop is found out
.Hence in this model we used “68”
experimental data sets “trainee data” sets
are chosen & “8” “test data “sets are
chosen randomly to find the results and to
match them and get the results more
accurately. Based on the equation used the
pressure drops at both the pipes and
temperatures at cold and hot fluid are
represented
as
outputs.
Fig.8:-Comparison between Experimental values & GRNN values for 8 tested data
Fig.9:-Error percentage between GRNN & experimental values
Once the values are calculated they are
checked with the experimental results to
find the accuracy of this regression
analysis. From the graphs the value
obtained between the experimental sets
and regression analysis gave us enormous
accuracy.
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Research and Applications of Thermal Engineering
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CONCLUSION
In the present era cut throat competition is
prevailing were all the devices are updated
on a daily basis. From the apps in our
smart phones to the facilities offered by
the aviation industry or rocket science
everything is updated. So, in this modern
world getting updated is very important for
growth. Hence we came up with the idea
of designing a formulation for finding the
heat transfer rates and pressure outputs
using regression analysis. By utilizing this
it becomes lucid for the researcher to find
the angle orientation for maximum heat
flow and temperature difference. Although
we found only the angles orientation one
can find other such outputs like different
mass flow rates or multi leaf strips
orientation etc. as a future work. So to
conclude with the GRNN is a modern,
innovative and user friendly tool which
can be used to enhance the working of a
heat exchanger devices when it is used in
an optimal way.
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