=Paper=
{{Paper
|id=Vol-3314/PAPER_04
|storemode=property
|title=Artificial Neural Network with Multilayer Perceptron Model for the Prediction of Thermal Parameters of Nano Particle Coated Miniature Loop Heat Pipe Using Experimental Data
|pdfUrl=https://ceur-ws.org/Vol-3314/PAPER_04.pdf
|volume=Vol-3314
|authors=James Graham Steward,L. Godson Asirvatham,A. Hepzibah Christinal,S. Jebasingh,S. Manova
}}
==Artificial Neural Network with Multilayer Perceptron Model for the Prediction of Thermal Parameters of Nano Particle Coated Miniature Loop Heat Pipe Using Experimental Data==
https://ceur-ws.org/Vol-3314/PAPER_04.pdf
Artificial Neural Network with Multilayer Perceptron Model for
the Prediction of Thermal Parameters of Nano Particle Coated
Miniature Loop Heat Pipe Using Experimental Data
James Graham Steward a, L. Godson Asirvatham a, A. Hepzibah Christinal a, S. Jebasingh a,
S. Manova a
a
Karunya Institute of Technology and Sciences, Coimbatore, India
Abstract
The present study deals with the prediction of transfer parameters of a miniature loop heat
pipe using Artificial Neural Network (ANN). The outcome of various coating thicknesses on
heat transfer coefficient, thermal conductivity, and thermal resistance is predicted using
Multilayer Perceptron (MLP) approach. The experimental data for different coating
thicknesses are given as input to the ANN model and the heat transfer parameters are
predicted. 80% and 20% of the total experiment data are used as training and testing data
accordingly. High accuracy between experimental and the predicted values for the heat
transfer parameters (R2 =0.98) are observed. Based on the results, the root means square
error (RMSE) values of 1.77%, 17.9%, and 8.79% respectively are observed for thermal
resistance, thermal conductivity, and heat transfer coefficient. This study establishes the
ANN model with multilayer perceptron as an alternative method to estimate the heat transfer
parameters thereby reducing the cost and time in the thermal characteristic study of miniature
loop heat pipes.
Keywords 1
Miniature loop heat pipe, Thermal characteristic, Artificial neural network
1. Introduction
Loop heat pipes are special types of heat pipes used in the removal of heat stress generated in
electronic devices [1]. Thermal conductivity and heat capacity are the parameters that influence heat
transfer coefficient which also affects the dimension, flow pattern, and viscosity of the nanofluid. In
recent years LHP with different nanofluids are studied widely by many researchers [2] as it possesses
all the thermal properties of conventional heat pipes and more importantly due to its efficiency in heat
transfer. Several examinations have been undertaken by analysts on the effect of using nanofluids or by
the coating of nano particles on the boiling surface of heat pipes. The experimental study involves
meticulous preparation of nanoparticle-coated heat pipes and recording thermal characteristic of the
heat pipes under the various thickness of nanoparticle coating upon the boiling surface of the heat pipes
[3]. The conventional method of thermal behavior of loop heat pipes has limitations in the calculation
and predictions. As an alternative method, the ANN technique is found to be a promising technique
with significantly less error and validation of the parameters with MLFNN predictions [12]. In this
paper, we propose an ANN model with Multilayer Perceptron (MLP) to obtain the Heat Transfer
Coefficient, Thermal Conductivity, and Thermal Resistance of the Loop Heat Pipe where the working
fluid is water [5]. In [3] the authors employ the feed-forward ANN method to predict thermal resistances
of a closed vertical meandering pulsating heat pipe. In [Deshpande, Purva, et al ] the authors determine
the changes in heat rate and boiler efficiency in thermal plants using sensitivity coefficients. The study
WCES-2022: Workshop on Control and Embedded Systems, April 22 – 24, 2022, Chennai, India.
EMAIL: hepzia@yahoo.com (A. Hepzibah Christinal)
ORCID: 0000-0003-3965-3183 (A. Hepzibah Christinal)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
31
was also useful in improving the efficiency of the boiler.
In [Esfe, Mohammad Hemmat, et al] the authors evaluate dynamic viscosity and thermal
conductivity of ferromagnetic nanofluids including parameter temperature, particle diameter, and
solid volume fraction.
2. Summary of the Experimental Work
In [18], the authors coated copper nanoparticles on the mLHP and studied the consequence of
coating of nanoparticle on the thermal characteristic of heat pipes. In the following, we briefly
summarize [18] the experimental details to calculate the three different parameters of miniature loop
heat pipe. In order to analyze the reaction of coating thickness on the parameters, the authors fabricated
mLHPs with six types of coating thicknesses (0 nm, 100nm, 200nm, 300nm, 400nm, and 500nm).
The evaporator with or without nanoparticles was compared using distilled water which was utilized
as a fluid working for finding out the performance of transfer of heat in the loop heat pipe. The filling
ratioof 30% on the total volume was engaged which is the optimum for this design in all heat pipes [9].
The testing of heat pipes in a vertical orientation to provide gravity-assisted operation. Water at 25
LPH is made to flow through the condenser at 25 c. Using the heater block and dimmest at the heat
load was pertained to the evaporator. After a few minutes, various points in mLHPs get to steady-
state temperature. For every 5 seconds, the temperature was calculated by a data logger and computer.
Only after 30 minutes, the heat load was changed to ensure 20 minutes of steady-state operation. The
input heat differs from 20 W to 380 W. For each step, there was a 40 W increase. The application of
heat loads was given the load was decreased to zero above all. The mLHPS were removed from the
experimental arrangement once it reaches room temperature. Each of the loop heat pipes was tested at
different temperatures at three different time instances to confirm the average value of temperatures.
These procedures were repeated for all five heat pipes. The variation was found to be 1.5%. A stability
test was conducted with a 400 mm coated pipe for evaluating the stability and strength four times.
2
Figure 1: (a) Miniature Loop Heat Pipe-Heater Assembly (b)Evaporator and CC, and (c) schematic of
the evaporator. (Reprinted with permission from Tharayil et al. [6]. Copyright 2016 by Elsevier).
32
The values of the experimentation were recorded for each pipe by the data logger. The various data
recorded due to the impact of nanoparticles coating and heat load were plotted in the table. The values
were recorded for the criterion such as thermal resistance, thermal conductivity, temperature, and heat
load by coating thickness for each evaporator surface. In this present study, the data collected from
the experimental study were utilized for modeling ANN and to evaluate the thermal parameters in
miniature loop heat pipes [18].
Figure 2: Experimental Setup
Figure 3: Condenser heat transfer coefficient versus heat load
Figure 4: Evaporator heat transfer coefficient versus heat load
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Figure 5: Thermal resistance versus heat load
Figure 6: Evaporator heat transfer coefficient versus heat load
The graph shown in Fig 3 represents the condenser heat transfer coefficient versus heat load taken while
experimenting. The graph shown in Fig 4 represents the Evaporator Coefficient Vs Heat load. Also, Fig
5 and Fig 6 represent the thermal resistance Vs Heat load and Evaporator Heat transfer Coefficient Vs
Heat Load respectively.
3. Artificial Neural Networks with Multilayer Perceptron (ANN-MLP)
ANN is a bio-inspired computational model abstracting the function of brain processing and
analyzing the huge amount of information received [10]. The model has been successfully applied in
solving computationally hard problems in the computer science field. ANN model consists of several
nodes (neurons) and links connecting the nodes for communication between the nodes. There are three
layer such as an input, hidden and an output layer (Fig 7), which are all determined through trial and
error. The input layer perceives which is then refined by the hidden layer and ahead dispatched to the
output layer. We use the Multilayer Perceptron (MLP) model to forecast the thermal characteristics of
the mhlp in this paper. [7].
Figure 7: ANN model with three layers
The input given to the ANN model is processed by the nodes, which is communicated to other
nodes of the model through the links and an output is produced [5]. The links between the nodes are
assignedweights which controls the flow of information between the nodes. If the output produced has
errors, then the weights associated with the links are altered and the model improves the output
produced by providing suitable feedback to the network of nodes. The ANN computational model has
the capacity of learning from the input data [6]. The MLP uses supervised learning which has
backpropagation method for training the data. For a detailed discussion on the functioning of model,
34
the reader may refer the article [15]. Figure 8 illustrate the step-by-step process of applying the model
in the evaluation of thermal parameters of the miniature loop heat pipes.
Selection of Input and Output Data
Dividing as Training and Testing Sets
Developing the Models of ANN
Selecting the parameters for training
Training models of ANN
No
Calculation Error
Yes
Selection of ANN models with Least RMSE
Figure 8: Flowchart
4. Prediction of Parameter by Applying ANN Techniques using MATLAB
The goal of this research is to use data from experimental results to estimate heat transfer
coefficient, thermal conductivity, and thermal resistance. [20]. The ANN-MLP is constructed using the
customized MATLAB code. The following input parameters are considered for modelling the ANN:
Temperature (Te), Heat load(W), Number of turns(N), Condenser length (Lc), Evaporator Length (Le),
Thermal Resistance (Rth). The observation of our dataset is given as input in the input layer. Randomly
the weights are initialized. Now in feed propagation the neurons are activated andthe activated neurons
are limited by the weights, which are propagated continuously until it attains the predicted value [17].
The predicted value is analyzed on the basis of original result and the flaw is measured. The error is
now back propagated in to the model for attaining better accuracy of the prediction of parameters.
According to the error the weights are updated by decision of learning [19]. After each observation of
enforcement learning the weights are updated. Finally, the whole training set is passed and epochs are
generated.
5. Results and Discussion
The table listed below are the predicted values using ANN and they are plotted in a table. The
Values which are predicted are MSE, PSNR, R, RMSE, NRMSE, Mape.
35
Table 4.1: Heat Transfer Coefficient_HC
Total Correlation Correlation Correlation
Total Total No.
neurons Coefficient Coefficient Coefficient Results MSE PSNR
Hidden of
in hidden of data for of data for for overall R RMSE NRMSE Mape
layers neurons
layers Training testing data
37.784049912735995,
32.357718545958080,
0.964950230940293,
1 1 3 7 0.98131 0.96338 0.97664
6.146873181767783,
0.092101785762178,
17.55157628
34.894155416014240,
32.703276698151925,
2 2 4(3,1) 8 0.97879 0.93169 0.97353 0.954749499686177,
5.907127509713519,
0.105371521757287, Inf
16.000176195166350,
36.089555957015385,
3 2 5(3,2) 9 0.9798 0.98325 0.98056 0.987181264904587,
4.000022024335160,
0.065746581596567, Inf
92.511135465475800,
28.468863494246450,
4 3 6(2,2,2) 10 0.9441 0.87687 0.92899 0.895277348876716,
9.618270918698215,
0.171816200762741, Inf
20.047827220982820,
35.110130500997740,
5 3 7(3,2,2) 11 0.97465 0.9928 0.97537 0.975498408176007,
4.477480007881980,
0.073594345954668, Inf
66.152825638083950,
29.925319615837100,
6 3 8(3,3,2) 12 0.96255 0.94846 0.95857 0.929043890653997,
8.133438733898716,
0.114297902387559, Inf
8.761551822771107,
38.704993268026930,
7 3 9(3,3,3) 13 0.98129 0.99104 0.98289 0.991211632318807,
2.959991861943392,
0.048652068736742, Inf
36
Table 4.2: Thermal Conductivity HE
Total Correlation Correlation Correlation
Total Total no.
neurons Coefficient Coefficient Coefficient Results MSE PSNR
Hidden of
in hidden of data for of data for for overall R RMSE NRMSE Mape
layers neurons
layers training testing data
1.348006631824366e+02,
26.833883320531480,
1 1 3 7 0.97287 0.90786 0.97287 0.966505259790726,
11.610368778916394,
0.116103687789164, Inf
44.382660546522274,
31.658670281354997,
2 2 4(3,1) 8 0.976 0.98258 0.97721 0.990363171898819,
6.662031262799828,
0.066620312627998, Inf
1.312368389942967e+02,
26.950245995612990,
3 2 5(3,2) 9 0.97419 0.99252 0.97679 0.964349419657705,
11.455864829610059,
0.097679611439376, Inf
1.159585597069651e+02,
27.487775484174620,
0.978932518739079,
4 3 6(2,2,2) 10 0.97282 0.89779 0.96792
10.768405625112988,
0.155883115592255,
16.20655434
1.326799558437884e+02,
26.902750425546998,
0.976706308650227,
5 3 7(3,2,2) 11 0.97294 0.92877 0.96836
11.518678563263600,
0.144326256900935,
18.80000751
2.044068143763205e+02,
25.025849909477840,
6 3 8(3,3,2) 12 0.9239 0.92533 0.92206 0.945538778485724,
14.297091115899082,
0.148695695433168, Inf
17.952095483159848,
35.589652113709896,
0.996860128752723,
7 3 9(3,3,3) 13 0.98361 0.98921 0.98121
4.236991324414041,
0.057716814118159,
5.207988507
37
Table 4.3: Thermal Resistance Rt
Total Correlation Correlation Correlation
Total Total no.
neurons Coefficient Coefficient Coefficient Results MSE PSNR R RMSE
Hidden of
in hidden of data for of data for for overall NRMSE Mape
layers neurons
layers training testing data
43.137837421745600,
31.782219915279946,
0.970340707187143,
1 1 3 7 0.96655 0.97448 0.9671
6.567940120140073,
0.088302502287444,
2.551676661021013
12.758283476160496,
37.072881133619400,
0.991637846251108,
2 2 4(3,1) 8 0.97673 0.98729 0.97797
3.571873944606738,
0.046545138710017,
6.970743991709018
57.611320578981630,
30.525725305365160,
0.962941817466203,
3 2 5(3,2) 9 0.97145 0.94119 0.96647
7.590212156388096,
0.114482837954572,
7.290600765185099
16.001471637375610,
36.089204347994276,
0.990137282784463,
4 3 6(2,2,2) 10 0.97538 0.9821 0.9746
4.000183950442231,
0.056788528541201,
6.786050844727903
65.739101281370920,
29.952565983174573,
0.953861391604532,
5 3 7(3,2,2) 11 0.98471 0.9781 0.98093
8.107965298480927,
0.104457166947706,
16. 728962865294204
36.929866162412935,
32.457026271414065,
0.976228971663768,
6 3 8(3,3,2) 12 0.9742 0.97584 0.97406
6.076994829882031,
0.078636061463277,
5.673455509985892
1.777331966742656,
45.633118087746816,
0.998844059334908,
7 3 9(3,3,3) 13 0.99454 0.99808 0.99501
1.333166143713024,
0.017472688646304,
2.164644920109018
38
The correlations available in the literature for the performance of looped heat pipes are similarly the
same from the data predicted and the input parameters are within the range. Thus, ANN method has
more advantages than obtaining the values through experimental methods. Artificial Neural Networks
are used to estimate the performance of tiny Loop Heat Pipes in order to make the prediction accurate
and reliable [19]. The iterative constructive error method is integrated with the statistical error method
by comparing ANN models. The optimum ANN type is found to be the multilayer perceptron with back
propagation structure.
6. Best Performance in heat transfer coefficient Hc Graph
Figure 9 (a): Heat Transfer coefficient anticipated by ANN model with the test data
Figure 9 (b): Regression Graph of the overall data
Figure 9 (c): Training data sets predicted by ANN
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7. Best performance thermal conductivity He graph
The heat transfer coefficient anticipated by ANN model with the test data is indicated in Fig 9 (a).
The inputs given to evaluate the heat transfer coefficient were heat load, number of coating and
temperature. From the graph we infer that the values predicted by ANN is identical with the data. The
blue line gives the values obtained using ANN and the red line illustrates the data for
experimentation. The test data are indicated along the X -axis then heat transfer coefficients are plotted
along the Y-axis.Graph shown in Fig 9 (b) is the regression graph of the overall data. The relationship
between the experimental data and training data set is represented graphically. The ratio of training set
data and testing data was 70% and 30% respectively. The dotted lines passing through the data set is
given as Y=T and the blue line denotes the fit. The red dots represent the experimental data.
The graph in fig 9(c) shows the training data sets predicted by ANN. The training results has
showed regression coefficient (R) up to 0.98129. The experimental data was trained with 70% of the
data for the training set. Minor deviation was observed from the experimental data.
The graph in fig (d) shows the result of the testing done. These testing was done with 30% of the
input parameters. The regression value of the testing data was 0.99104. The data obtained were
observed to be accurate with the experimental values. The tested data was fitted with linear equation
which shows the accuracy of the prediction and the dotted lines are represented by Y=T.
8. Best performance in thermal conductivity He graph
11
Figure 10: Graphs of Thermal Conductivity He – ANN - 3 Hidden Layers 13 Neurons
(a) Prediction He Graph (b) Regression Graph Overall data
40
Figure 10: Graphs of Thermal Conductivity He – ANN - 3 Hidden Layers 13 Neurons
(c) Regression Graph ofTraining Data (d) Regression Graph of Data for testing
The thermal conductivity parameter evaluated by ANN with the test data is indicated in Fig 10
(a). From the graph we infer that the predicted data is approximately same as that of the test data. The
linear relationship of entire data shown is given in the graph (Fig 10 (b)) for the thermal conductivity.
Also, we find that the straight line fits the data linearly. The blue line is the best fit of the data which
shows the accuracy when comparing with the experimental data.
The fig 11 (c), fig 11 (d) shows the graph of training data and testing data respectively using ANN
model for thermal conductivity. Both graphs are almost accurate and the regression coefficient is
0.98.These graphs were generated using customized MATLAB coding.
9. Best performance in thermal resistance rt graph
41
Figure 11: Graphs of Thermal Resistance Rt – ANN – Hidden Layers – 3, Neurons – 13
(a) Prediction RtGraph (b) Regression Graph of Overall Data
The first Graph shows the prediction of the Thermal Resistance. This Graph has proved its
accuracy with the Experimental Data. The inputs given to predict are heat load, no of coating and
temperature. There shows a decline at the last which shows the accuracy of the thermal resistance.
The Blue line shows the ANN and the red line shows the data for experimenatation. The X - Axis
shows the test data and the Y-axis shows the heat transfer coefficient. These both are predicted and
the Graph already proves its approximately accurate to the experimental data given. The Next graph
shows Regression Graph the overall data. This Graph is the output after testing and training data set.
The training set is taken 70% and testing as 30%. The dotted lines passing through is given as Y=T
and the blue straight line denotes the Fit. The red dots represent the experimental data. The graph
shown in fig 10 and 11 represents the best performance of the prediction of heat Transfer coefficient
Hc, thermal conductivity He, thermal resistance Rt. We observe that both the experimental and ANN
values coincide
42
Fig. 11: Graphs of Thermal Resistance Rt – ANN – Hidden Layers – 3, Neurons – 13
(c) Regression Graph of Training data (d) Regression Graph of Testing data
The number of neurons and layers in the ANN model are critical factors in forecasting loop heat
pipe performance. We have considered multiple sets of predictions with several number of neurons
and hidden layers to obtain the best result. Initially we set the ANN system with a total of seven
neurons in single layer mode and three hidden layer neurons. Subsequently the training of data was
processed with two hidden layers and a total of eight neurons 5(3,2) in the hidden layer. Finally,
training data was processed with nine neurons 5(3,2) having three hidden layers with different set of
neurons as plotted in the table. The accuracy of the predicted data was high with the three hidden layers
having 13 neuronsin total which was split as 9(3,3,3). Also, the mean square error of the predicted and
experimental datais low when compared with other results.
10. Conclusion
The prediction of thermal conductivity, coefficient of heat transfer and thermal resistance of
miniature loop heat pipes has been studied using the novel method ANN with Multilayer perceptron
technique. The results obtained shows that the predicted data is approximately same as the experimental
results. The below tables show the prediction accuracy from the experimental results and the
predicted results of heat transfer coefficient, thermal resistance and thermal conductivity. The results
acquired by the MLP network developed are MSE(Hc)=8.76155 MSE(He)=17.95209,
MSE(Rt)=1.77733. The prediction accuracy for heat transfer coefficient, thermal conductivity and
thermal resistance are 98.02%, 98.01% and 98.04% respectively. Thus, the average divergence
between the data for experimentation and values which are predicted is1.5%. The accuracy was high
with the three hidden layers having 13 neurons in total which was split as 9(3, 3, 3). The mean square
error for thermal resistance, thermal conductivity, heat transfer coefficient was given by 1.77%, 17.9%
and 8.76 % respectively. Approximation is high when the neurons and the hidden layers are increased
43
in the ANN model. It was discovered that in hidden layers maximising the total neurons improves the
anticipated data outputs.
11. Acronyms
• MSE – Mean Square Error
• PSNR- Peak to Signal Noise Ratio
• R – Regression Coefficient
• RMSE- Root Mean Square Error
• NRMSE-Normalized Root Mean Square Error
• Mape-Mean Absolute Percentage Error
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