Gaurav Katendra - National Institute of Technology, Rourkelaethesis.nitrkl.ac.in/5386/1/211ME3172.pdf · National Institute of Technology, Rourkela by Gaurav Katendra, Roll No. 211ME3172

i

In partial fulfillment of the requirement for the degree of

Master of Technology

in

Department of Mechanical Engineering

by

Gaurav Katendra Roll No. 211ME3172

Under the guidance of

Dr. Suman Ghosh

Department of Mechanical Engineering

National Institute of Technology Rourkela -769 008 (India)

June, 2013

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NationalInstituteofTechnologyRourkela

CERTIFICATE

This is to certify that the report entitled “PREDICTION OF COATING

THICKNESS THROUGH THERMAL ANALYSIS” submitted to the

National Institute of Technology, Rourkela by Gaurav Katendra, Roll

No. 211ME3172 for the award of the Degree of Master of Technology in

Department of Mechanical Engineering with specialization in Thermal

Engineering is a record of bona fide work carried out by him under

my supervision and guidance.

Place:NITRourkela,Rourkela‐769008,Orissa.Date: June03,2013

Dr.SumanGhoshAssistantProfessorDepartmentofMechanicalEngineeringNITRourkela,Rourkela‐769008,India

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ACKNOWLEDGEMENT

First and foremost I offer my sincerest gratitude and respect to my project supervisor,

Dr. SUMAN GHOSH in the Department of Mechanical Engineering, for their

invaluable guidance and suggestions to me during my study. I consider myself

extremely fortunate to have had the opportunity of associating myself with them for

one year. This thesis was made possible by their patience and persistence.

After the completion of this Thesis, I experience the feeling of achievement

and satisfaction. Looking into the past I realize how impossible it was for me to

succeed on my own. I wish to express my deep gratitude to all those who extended

their helping hands towards me in various ways during my short tenure at NIT

Rourkela.

I express my sincere thanks to Professor K.P. MAITY, HOD, Department

of Mechanical Engineering, and also the other staff members of Department of

Mechanical Engineering, NIT Rourkela for providing me the necessary facilities that

is required to conduct the experiment and complete my thesis.

Last but not the least I am especially indebted to my parents and friends for

their love, sacrifice, and support. They are my first teachers after I came to this world

and have set great examples for me about how to live, study, and work

Date: GAURAV KATENDRA

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Contents

Description Page no

Title i

Certificate by Supervisor iii

Acknowledgement v

Contents vii

List of Figures ix

Abstract xi

Chapter1: Introduction and Literature Review 1

1.1Introduction 1

1.2 Literature Review 2

1.3 Gaps in the Literature 5

1.4 Aims and Objective 5

1.5 Organization of the Thesis 5

Chapter 2: Problem Statement 7

2.1 Problem descriptions 7 2.1.1 Forward problem 7

2.1.2 Prediction problem 8

Chapter 3: Methodology 9

3.1 Data Collection 9

3.1.1 Numerical calculation 11

3.1.1.1 Governing equation 12

3.1.1.2 Boundary condition 12

3.1.1.3 Grid pattern employed 12

3.1.1.4 Residual and convergence 13

3.2 Prediction Methodology 14

viii

Chapter 4: Results and Discussion 17

4.1 Grid Independence Test 17

4.2 Prediction of the Coating Thickness 22

4.2.1 Uniform thickness 24

4.2.1 Non-uniform thickness 27

Chapter 5: Concluding Remarks and Scope for Future

Work 37

5.1 Concluding Remarks 37

5.2 Scope of the Future Work 38

References 41

ix

LIST OF FIGURES

Figure No. Description Page No.

Figure 2.1

The schematic representation of square steel block with a

copper coating.

8

Figure 3.1 Schematic representation of data collection. 11

Figure 3.2 A schematic representation of the grids for a particular

coating thickness. 13

Figure 3.3 A schematic representation of NN 15

Figure 3.4 A schematic showing the proposed GA-NN methodology 16

Figure 4.1

Variation of temperature profile with start size of grid of

inner face. 18

Figure 4.2 Variation of maximum temperature at the bottom wall

with start size of the grid of inner face.

19

Figure 4.3 Variation of temperature profile with aspect ratio of inner

face.

20

Figure 4.4

Variation of maximum temperature at the bottom wall

with aspect ratio of inner face.

20

Figure 4.5 Variation of temperature profile with end size of grid. 21

Figure 4.6

Variation of maximum temperature at the bottom wall

with end size of grid for inner face

21

Figure 4.7 Variation of temperature profile at bottom with grid size

of outer face. 22

Figure 4.8 Variation of maximum temperature at the bottom wall

with the varying grid size of outer face.

22

Figure 4.9 Plot between original thickness during simulation and

predicted thickness.(uniform) 25

x

Figure 4.10 Comparison between the thickness during simulation and

the predicted thickness through the developed

methodology.(uniform)

27


predicted thickness.(nonuniform bottom)

28



methodology.(nonuniform bottom)

29


predicted thickness.(nonuniform left)

30



methodology. (nonuniform left)

31


predicted thickness. (nonuniform top)

32



methodology. (nonuniform top)

33


predicted thickness. (nonuniform right)

34



methodology. (nonuniform right)

35

xi

Abstract

An attempt has been made to develop a methodology to predict the uniform or non-

uniform thickness of a coating material on a homogeneous solid material. At first the

effects of variation of (uniform and non-uniform) coating thickness, on the heat

transfer (by conduction) through the coated body have been rigorously investigated. A

solid square steel block coated with copper (of various coating thicknesses) has been

considered as the sample problem. A constant heat flux has been maintained at the

bottom side where, the other three sides kept at constant temperature. The temperature

profile built at the bottom side of the square block is different for different (uniform

or non-uniform) coating thickness. Depending on the statistical parameters (Mean,

Standard Deviation, Skew-ness and Kurtosis) extracted from the temperature profile

(which has been found through CFD analysis), it may possible to predict the thickness

of the coating. Two cases namely: uniform varying thickness and non-uniform

varying thickness have been considered in the present problem. The training and test

data have been collected using 2D conduction analysis with Finite Volume Method

(FVM) in a fully automated way. Feed-Forward Neural Network (NN) with Back-

Propagation Algorithm is used to predict the coating thickness. The NN has been

modelled using ‘C’ programming Language in LINUX operating system. A Genetic

Algorithm (GA) has also been coded (using ‘C’ programming language in Linux

operating system) to optimize the performance of the NN. The above described

methodology based on thermal analysis can also be used in thermography or in other

prediction problem.

Keywords: Heat Conduction, FVM, Neural Network, Genetic Algorithm, Mean,

Standard Deviation, Skew-ness and Kurtosis.

xii

1

Chapter 1: Introduction and Literature Review

1.1 Introduction

The steady-state heat conduction problems find several useful applications in the wide

era of developing technology. The multi-layered coated materials have numerous

industrial applications, such as transportation, aerospace, electronics and medical. In

such coated materials, the 2D or 3D analysis of heat conduction is one of the

furthermost significant corporeal phenomena which are needed to be considered.

Surface coating plays a very vital role in the manufacturing of a particular

product. The coatings provide surface protections against high temperature, wear,

corrosion, oxidation, and electrical conduction. The prediction of coating thickness is

very necessary for the safety of inner material (on which the coating has been done).

The study of thermal conduction across defective component (material with corroded

coating) plays a critical role in predicting the coating thickness for such material. By

knowing the temperature profile of any coated material it is possible to predict its

coating thickness.

The application of the above concept may be used in Thermography. In

medical science, Thermography is the technique that derives analytic suggestions

from vastly detailed and sensitive infrared images of the human body and it is

http://en.wikipedia.org/wiki/Infrared

http://en.wikipedia.org/wiki/Human_anatomy

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completely non-contact, involves no form of energy imparted onto or into the body.

Thermography has anticipatable applications in breast oncology, neurology,

orthopaedics, occupational medicine, pain management, vascular medicine/cardiology

and veterinary medicine. Thermography has a long history, although its use has

increased intensely with the commercial and industrial applications of the past fifty

years.

1.2 Literature Review

Several contributions of 2D heat conduction problem are available in scientific books

and journals. Firstly, a generalized fundamental solution with the estimation of

hardened layer dimensions in laser surface hardening processes with variations of

coating thickness has been proposed by Woo and Cho (1996). The heat conduction

across the interface between a thin isotropic thermal barrier coating and an anisotropic

substrate has been analysed by Shiah and Shi (2006) using the boundary element

method. Thin-film coating plays a prominent role on the manufacture of many

industrial devices. Coating can increase material performance due to the deposition

process. This paper proposes the estimation of hardness of titanium thin-film layers as

protective industrial tools by using multi-layer perceptron (MLP) neural network.

Based on the experimental data obtained during the process of chemical vapour

deposition (CVD) and physical vapour deposition (PVD), the optimization of the

coating variables for achieving the maximum hardness of titanium thin-film layers, is

performed. This optimization of coating variables for hardness of industrial tools by

using artificial neural networks has been demonstrated by Yazdi, Khorasani and Faraji

(2011). Prediction and control of surface roughness in CNC lathe is done by using

artificial neural network and this has been proposed by Karayal (2009). Effects of Ti-

and Zr-based interlayer coatings on hot-filament chemical vapour deposition of

http://en.wikipedia.org/wiki/Oncology

http://en.wikipedia.org/wiki/Neurology

http://en.wikipedia.org/wiki/Orthopedics

http://en.wikipedia.org/wiki/Occupational_safety_and_health

http://en.wikipedia.org/wiki/Pain_management

http://en.wikipedia.org/wiki/Cardiology

http://en.wikipedia.org/wiki/Veterinary_medicine

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diamond on high-speed steel has been analysed by Polini, Mantini, Braic, Amar,

Ahmed and Taylor (2006). Optimization of machinery variable by using micro

multivariable genetic algorithm has been proposed by Narimani and Rohani (2007).

The use of design of experiments to improve a neural network model in order to

predict the thickness of the chromium layer in a hard chromium plating process has

been explained by Lasheras, Vilan, Neito and Diaz (2010). A ferrite-core probe design

has several parameters, which includes the selection of ferrite material and the design

of the probe structure and core and in this article a total of five variables, which are

most influential on probe performance, were considered. A three-layer back-

propagation neural network model is used to correlate these variables to probe

performance using the data generated based on experimental observations and it is

used for predicting the coating thickness and performance of ferrite-core probe using

neural network approach which has been analysed by Baseri and Damirchi (2009).

Prediction of the coating thickness of wire coating extrusion processes using artificial

neural network (ANN) has been demonstrated by Cirak and Kozan (2009). Here, a

three layer back propagation artificial neutral network (ANN) model was used for the

description of wire coating thickness and on comparing the experimental data with the

ANN model prediction; it is found that the ANN model is capable of predicting the

coating thickness. The neural network model shows how the significant parameters

influencing thickness can be found and in this study, a back propagation neural

network model is developed to map the complex non-linear wire coating thickness

between process conditions. Integrated ANN–GA for estimating the minimum value

for machining performance has been analysed by Zain, Haron and Sharif (2011).

Modelling of electrostatic fluidized bed (EFB) coating process using artificial neural

networks has been proposed by Barletta and Guarino (2006). Here, a verification

4

experimental plan was performed and a related analytical model was developed to

check the reliability of the neural network model with GA to predict the whole

coating thickness trends according to the operational parameters and a comparison

between the neural network model and an analytical model was also carried out.

Optimization of a photoresist coating process for photolithography in wafer

manufacture via a radial basis neural network has been explained by Shie and Yang

(2005). A grey-fuzzy Taguchi approach for optimizing multi-objective properties of

zirconium-containing diamond-like carbon coatings has been proposed by Yang and

Huang (2011). Regression and ANN models for estimating minimum value of

machining performance has been demonstrated by Zain, Haron, Qasem and Sharif

(2011). Two-dimensional optimization of material composition of functionally graded

materials using mesh less analyses and a genetic algorithm has been analysed by

Goupee and Vel (2004). A simulation technique for predicting the coating thickness

of thermal sprayed coatings has been proposed by Goedjen, Miller and Brindley

(1995). Here, a two dimensional finite difference simulation model has been

developed to predict the thickness of coatings deposited using thermal spray process

and the minimum coating thickness limit was predicted in order to determine the

application range of slot die coating. For this, a simulation technology is prepared to

predict the coating thickness limit in slot die coating by Yoshifumi and Makoto

(2010). Detection of defects in thermal barrier coatings by thermography analyses has

been done by Sakamoto, Kishi, Shobu, Tabaru, Tateyama and Akimune (2003).

Thermography is widely used medical. Thermography as a technique for

monitoring early age temperatures of hardening concrete has been analysed by

Azenha, Faria and Figueras (2011). The usage of IR thermography for the temperature

measurements inside an automobile cabin has been demonstrated by Korukcu and

5

Kilic. A review of thermography as promising non-invasive detection modality for

breast tumour has been proposed by Ng (2009).The study reveals the effect of heat

conduction on the thickness of coating material due to the change in temperature

profile.

1.3 Gaps in the Literature

As concluded from above, No theoretical models have employed GA-NN for

predicting the coating thickness according to the best of the author’s knowledge.

Hardly any few of the models are perfectly able to correlate the experimental results

with those of modelled ones.

1.4 Aims and Objective

The current work examines the effect of coating thickness of material on heat

conduction due to the change in temperature profile of solid material. The temperature

variation on surface of the solid bar has been used here to predict the thickness of the

coating material. Then a methodology is proposed using GA-tuned neural Network to

predict the thickness of coating by knowing the temperature distribution on the

surface. The basic goal is to correlate the statistical parameters of the temperature

distribution on the surface with the thickness of coating material.

1.5 Organization of the Thesis

The present thesis has been organized in five chapters. The present chapter (that is,

Chapter 1) introduces the problems studied in the present dissertation. To define the

aims and objective of the present dissertation, an exhaustive literature survey is

carried out related to the present problem. In Chapter 2, the detailed description about

the problem formulation is given. The developed methodology to solve the defined

problem is described in Chapter 3. Chapter 4 deals with the obtained results and

6

consequence discussions. Chapter 5 focus on the important findings concluded from

the present study. In this chapter, the scope for future work related to the problem is

also been described.

7

Chapter 2: Problem Statement

In the present chapter, the present problem is described in a detailed way endeavoured

in the current thesis.

2.1 Problem descriptions

Figure 1 shows the schematic representation of the problem consisting of a square

steel block with a copper coating on its surface. The dimensions of the square block

and its square coating are also shown in Figure 2.1. Each side of steel square block

represented by ‘a’ and has been kept equal to 1.0 m. The thickness of copper coating

is denoted by ‘b’ (b is varying case to case). All the locations or positions in the

present problem are considered with respect to a two-dimensional coordinate system

with its origin set at the centre of the block, where positive x and y axes are

considered along the right and upper directions, respectively.

2.1.1 Forward Problem

Now, the left, top and right sides of square are kept at constant temperature with wall

boundary condition. The bottom side has been given wall boundary condition with

constant heat flux. Once the geometry, material with these boundary conditions are

specified, the temperature distribution at the bottom side (bottom wall) can be

determined by solving two dimensional heat conduction problems numerically using

Finite Volume method. This establishes the forward heat transfer problem.

8

2.1.2 Prediction problem

After solving the forward problem, the objective is decided to predict the coating

thickness of the solid block from some known temperature distribution at the bottom

side (bottom wall) of the block.

Figure 2.1: The schematic representation of square steel block with a copper coating.

Square steel block

Copper coating

9

Chapter 3: Methodology

Due to heat conduction by the constant heat flux used at the bottom wall, the heat

propagates towards the other three sides of the block. Now, the temperature

distribution within the block can be found by solving two-dimensional heat

conduction problem. For each coating thickness, there will be a distinct temperature

profile at the bottom wall. To solve the 2D heat transfer problem numerically, the two

commercial software (Gambit and Fluent) have been used. Gambit is used for

constructing geometry and meshing where Fluent is used for numerical calculation

(using Finite Volume method) purpose.

3.1 Data Collection

For a particular coating thickness (of copper) on the square steel block there will be a

particular temperature profile at the bottom wall. This particular coating thickness

with corresponding temperature profile (in terms of temperature values at some

positions along the bottom wall with a regular interval) constitutes one complete data.

The temperature profile is recorded in terms of temperatures at the different positions

across the bottom wall of square block. In the same way, a number of data have been

collected for the uniform and non-uniform varying thickness. This leads to the

forward problem. The data (temperature at different positions across the bottom wall

of square block) have been evaluated by using CFD software i.e. Gambit and Fluent.

10

In this way, a set of training and test data have been collected for both uniform and

non-uniform varying thickness. The network has been trained using the training data

and the test data is used to check the prediction capability of developed methodology.

For a specific coating thickness, Gambit is used to model the problem and then the

data has been kept in a mesh file. Now, Fluent has been used to solve the 2D heat

conduction problem taking that mesh file as input to achieve the temperature profile at

the bottom wall of the solid block. In this way, one complete set of data has been

collected. This process goes on until the complete data for all the different coating

thickness have been collected. For the whole data collection, Gambit and Fluent are to

be used simultaneously on the same task again and again, which is very problematic

to do manually. Here, for solution of this problem, Gambit and Fluent journal file are

used. The journal file of Gambit contains all the instructions required to create the

mesh file in a proper way and the Fluent journal file contains the instructions required

to solve the heat conduction problem. Now for a particular coating thickness, the

Gambit and Fluent operation occurred in a fully-automated way using the above

mentioned journal file respectively. At first, the coating thickness is calculated and

then, this information is given to the Gambit journal file which is then modified. Now,

Gambit is launched with this modified journal file and starts its operation to create the

mesh file. The mesh file has been exported after completion of its operation. Then,

Fluent starts its operation with Fluent journal file and this newly generated mesh file.

Figure 3.1 shows a schematic representation for data collection.

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Figure 3.1: Schematic representation of data collection.

3.1.1 Numerical calculation

The data have been numerically calculated by using software i.e., Gambit and Fluent.

Using Gambit the problem has been modeled and discretized for a particular coating

thickness as shown in Figure 3.2, and then this information has been stored in mesh

file. The two-dimensional heat conduction problem is solved by using Fluent, where

the mesh file has been taken as input and simultaneously, the temperature profile

across the bottom wall have been achieved. Statistical analyses have been made to

express the temperature profiles in term of four parameters i.e., mean, standard

deviation, skew-ness and kurtosis. The required statistical analysis to evaluate these

statistical parameters (mean, standard deviation, skew-ness and kurtosis), coding has

been made in MATLAB. A particular coating thickness with corresponding set of

statistical parameters (mean, standard deviation, skew-ness and kurtosis) constitutes

Calculation of coating thickness

(m)

Gambit journal file modified

Launch Fluent with Fluent

Journal file and mesh file

Launch Gambit with journal file

Solution of 2D heat conduction

problem

Gambit creates mesh file

Fluent exports the temperature

profile at bottom

Read the export temperatures

and write down in a file

Write down the coating thickness

in a file

Start

No Yes Written data ≥Maximum

numbers of data

End

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one data. This will be repeated till the data set for all the different coating thickness

with the square steel block have been collected.

3.1.1.1 Governing equation

Here, 2D steady state heat conduction with no heat generation is considered in order

to calculate the coating thickness of solid block. In 2D steady state heat conduction

with no heat generation the governing equation is

0T T

k kx x x y

(3.1)

3.1.1.2 Boundary condition

The Wall boundary condition in Fluent has been used on the left, top, right and

bottom side of the square block (Figure 2.1). At the wall boundaries, the non-slip and

no penetration conditions have been applied, that is, at wall boundaries u = 0, v = 0.

Now, the left, top and right side of the square block are kept at a constant temperature.

But at the bottom side of the square a constant heat flux is maintained.

At left, top and right wall, Constant specified valueT (3.2)

At bottom wall Costant specified valueT

ky

(3.3)

3.1.1.3 Grid pattern employed

For the inner face (steel), the triangular grid has been taken with a start size of 0.0025

m, aspect ratio 1.5 and end size of 0.02 m. For the outer face (copper coating),

uniform triangular grid has been taken with a grid size of 0.0015 m.

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Figure 3.2: A schematic representation of the grids for a particular coating

thickness.

3.1.1.4 Residual and convergence

Residuals are used for checking the convergence of solution. For the discretization of

the governing equations, a first order upwind differencing scheme has been employed.

After discretization, the conservation equation for variable ∅ at a cell q can be

written as

q q nb nb

nb

a a b (3.4)

Here, ɑq is the centre coefficient, ɑnb are the influence coefficient for the neighbouring

cells, and b is the constant part of the source term Sc in S=Sc+Sq∅ and of boundary

conditions, in equation (3.4)

q nb q

nb

a a S (3.5)

In equation (3.4), the imbalance summed over all the computational cells q is denoted

by the residual R∅ which is computed by Fluent‟s pressure based solver as

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_

nb nb q q

cells q nb

R a b a (3.6)

The above equation represents the “unscaled” residual. Since no scaling is employed,

it is very difficult to judge the convergence by examining the residuals defined by

equation (3.6). To scale the residual, a scaling factor (representative of flow rate of ∅

through the domain) is used. The scaled residual is given as

_

_

nb nb q q

cells q nb

q q

cells q

a b a

Ra

(3.7)

For most of the problems the scaled residual is an appropriate indicator of

convergence. Fluent is used for computing the scaled residuals. Once the scaled

residuals falls below the given value, it is presumed that the convergence is reached.

In this study, the value of 1×10-6

was selected for the absolute criteria of continuity, x-

velocity and y-velocity. The absolute criterion of energy is 1×10-9

.

3.2 Prediction Methodology

To construct the training and test data an exhaustive statistical analysis has been done

using MATLAB software. After getting the temperature distribution through CFD

analysis, four statistical parameters have been extracted which are used as input to

Neural Network. The statistical parameters which have been extracted are mean,

standard deviation, skew-ness, and kurtosis which are used as input to the Neural

Network. The coating thickness has been used as the output the Neural Network.

Figure 3.3 shows the schematic representation of Neural Network.

15

Figure 3.3: a schematic representation of NN

Four neurons have been used as input. Only one neuron has been used as output. Only

one hidden layer has been used. A GA tuned feed-forward neural network with back-

propagation algorithm has been used. The parameters optimized through GA are

learning rate, momentum constant, constant slope in the input layer, transfer function

coefficient in hidden layer, transfer function coefficient in output layer and the

number of neuron in hidden layer. The NN has been modelled using „C‟ programming

Language in LINUX operating system. Figure 3.4 shows the schematic representation

of the combined GA-NN approach.

OUTPUT

INP

UT

S

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Figure 3.4: A schematic showing the proposed GA-tuned NN methodology

Yes

N

o Generation ≥ Maximum Generation?

String Number ≥ Population Size?

End

Evaluation of control variables

from GA-string

Formation of Neural network

N

o Yes

Mutation

Reproduction

Crossover

Generation = Generation + 1

Generation = 0

Star

t

Assignment of this RMS error as

the fitness value of the

corresponding string

String Number =

String Number + 1

Start back-propagation algorithm

Calculation of percentage error

No

No

17

Chapter 4: Results and Discussion

This chapter contains the obtained results and corresponding discussions for the

selected problem using the developed methodology. Firstly, the detail about the grid

independence test has been mentioned. Then the results obtained through developed

methodologies for the prediction of uniform and non-uniform coating thickness have

been presented and discussed.

4.1 Grid Independence Test

The temperature profiles at bottom wall of the solid block have been generated

numerically using Finite Volume Method. Before producing results, a brief discussion

on grid independent test has been given. A triangular pave type grid has been adopted

here. The grid size has been varied keeping other parameters (size of block, thickness

of coating) fixed. Corresponding to each value of the grid size a mesh file has been

generated and consequently the temperature profile at bottom wall has been evaluated.

For selecting the grid size of inner face a parametric study of three parameters (start

size, aspect ratio and end size) has been carried out. Firstly, the start size is varied

keeping the value of other two parameters (aspect ratio and end size) fixed. Figure 4.1

shows the temperature profiles with varying start size of grid (other two parameters

kept constant) for the inner face. The maximum temperature at the bottom wall has

18

been evaluated corresponding to each start size of grid (keeping other two parameters

fixed) and a plot has been made between maximum temperature at bottom wall and

grid size as shown in Figure 4.2, to capture the variation of maximum temperature

with start size of grid. There is a range of start size where there is no significant

change in temperature profile (in Figure 4.1) or maximum temperature (in Figure 4.2).

Then, a value of grid size lying in this range has been chosen as start size of grid for

the inner face in Gambit for data (training and test) generation. Through this study,

the optimum start size has been selected and it’s equal to 0.0025 m.

Figure 4.1: Variation of temperature profile with start size of grid of inner face

(varying star size).

-0.51 -0.40 -0.30 -0.20 -0.10 0 0.10 0.20 0.30 0.40 0.51400

500

600

700

800

900

1000

1100

Dimension along the bottom of solid bar (m)

Tem

pera

ture

(K

)

0.0005 m

0.0010 m

0.0015 m

0.0020 m

0.0025 m

0.0030 m

0.0035 m

0.0040 m

0.0045 m

0.0050 m

0.0055 m

0.0060 m

0.0065 m

0.0070 m

0.0075 m

0.0080 m

0.0085 m

0.0090 m

0.0095 m

0.0100 m

19

Figure 4.2: Variation of maximum temperature at the bottom wall with start size of

the grid of inner face.

Now, the aspect ratio is varied keeping the other parameters (start size and end size)

fixed. The optimum value of aspect ratio has been selected in the same way as before

and it is equal to 1.5. Figure 4.3 shows the variation of temperature profile with the

varying aspect ratio (keeping other two parameters constant) for the inner face. Figure

4.4 shows the variation of maximum temperature at the bottom wall with aspect ratio.

At last, the end size is varied keeping the other parameters (start size and ratio) fixed.

Through this study, the optimum value of end size has been selected and it’s equal to

0.02 m. Figure 4.5 shows the variation of temperature profile with variation in end

size (other two parameters kept constant) for the inner face. Variation of maximum

temperature at bottom wall with the varying end size is shown in Figure 4.6. Variation

of temperature profile of bottom wall with uniform grid size of outer face is shown in

Figure 4.7. Figure 4.8 shows the variation of maximum temperature at bottom wall

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

x 10-3

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

Start size (m)

Max

imu

m t

em

pera

ture

at

the b

ott

om

wall

(K

)

20

with uniform grid size of outer face. Through this test, the uniform grid size for the

outer face has been decided as 0.0015 m.

Figure 4.3: Variation of temperature profile with aspect ratio of inner face.

Figure 4.4: Variation of maximum temperature at the bottom wall with aspect ratio of

inner face.

-0.51 -0.40 -0.30 -0.20 -0.10 0 0.10 0.20 0.30 0.40 0.51400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

Ratio

Max

imu

mT

em

pera

ture

(K

)

21

Figure 4.5: Variation of temperature profile with end size of grid.

Figure 4.6: Variation of maximum temperature at the bottom wall with end size of

grid for inner face

-0.51 -0.40 -0.30 -0.20 -0.10 0 0.10 0.20 0.30 0.40 0.51400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.0025 m

0.0050 m

0.0075 m

0.0100 m

0.0125 m

0.0150 m

0.0175 m

0.0200 m

0.0225 m

0.0250 m

0.0275 m

0.0300 m

0.0325 m

0.0350 m

0.0375 m

0.0400 m

0.0025 0.005 0.0075 0.01 0.0125 0.015 0.0175 0.02 0.0225 0.025 0.0275 0.03 0.0325 0.035 0.0375 0.04400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

End size (m)

Max

imu

m T

em

pera

ture

(K

)

22

Figure 4.7: Variation of temperature profile at bottom with grid size of outer face.

Figure 4.8: Variation of maximum temperature at the bottom wall with the varying

grid size of outer face.

4.2 Prediction of Coating Thickness

Firstly the training data has been used to train the Neural-Network (NN) and then, the

test data has been used to predict the coating thickness of solid block. Here, a Genetic

-0.51 -0.40 -0.30 -0.20 -0.10 0 0.10 0.20 0.30 0.40 0.51400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.00025 m

0.00050 m

0.00075 m

0.00100 m

0.00125 m

0.00150 m

0.00175 m

0.00200 m

0.00225 m

0.00250 m

0.00275 m

0.00300 m

0.00025 0.0005 0.00075 0.001 0.00125 0.0015 0.00175 0.002 0.00225 0.0025 0.00275 0.003400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

Grid size (m)

Max

imu

m T

em

pera

ture

(K

)

23

Algorithm (GA) has also been coded to optimize the performance of Neural Network.

Then, a comparison has been made between the predicted thickness and the original

thickness.

In NN here, there are six parameters; i.e. learning rate (η), momentum factor

(α), slope of linear transfer function of input layer (ɑI), transfer function coefficient of

hidden layer (ɑH) and output layer (ɑO) and lastly the number of neurons in the hidden

layer (NH). The neurons are assumed to have linear transfer function in the input

layer, whereas neurons of hidden and output layer are assumed to have log-sigmoid

transfer function. A GA is used to optimize these NN parameters. The value of

particular parameter for which the average training percentage error is minimum, has

been treated as optimum one. The average percentage error is defined as follows

1 1

1 1100

z Z KOzk Ozk

z k Ozk

T O

Z K T

(4.1)

where Z is the number training/test situations and K is the number of outputs, TOzk

indicates target output of k-th neuron corresponding to the z-th situation, OOzk denotes

the network predicted value for the same. The performance of optimized NN has been

tested with the help of test data set.

Here, a brief out-line is presented about the working principle of GA. The GA

starts with the different set of NN parameters in the present case, which are generated

at random. The field size has been chosen as 12 for each of the variable. As there are

six variable, the chromosome becomes 72. Hence, a specific GA-string will look as

follows:

ɑI ɑH ɑO α η NH

000010000100 000000000100 111001001000 010011001100 111110000001 100101110001

24

The first 12 bits, that is 000010000100 yields the decoded value (DV) as 0×211

+

0×210

+ 0×29 + 0×2

8 + 1×2

7 + 0×2

6 + 0×2

5 + 0×2

4 + 0×2

3 + 1×2

2 + 0×2

1 + 0×2

0 =

132. The real value of ɑ can be determined following the linear mapping rule as given

below.

,max ,min

,min2 1

I I

I I fieldsize

a aa a DV

(4.2)

Similarly, the real value of the other variables can also be calculated. After finding the

real values from the GA string the network is formed. Now, a BP algorithm is used to

optimize the weights of the network, so that it can predict the output with minimum

error. After this, the fitness values of all the members of population are calculated. In

the present problem, the fitness value is the sum of the percentage training and test

error in prediction. Two cases namely: uniform thickness and non-uniform thickness

have been considered in the present problem. To find an optimal set of GA parameter

(like population size, number of generation, crossover probability, mutation

probability, tournament size), a parametric study has been made. In this study, a

particular parameter has been varied from its minimum value to its allowable

maximum value keeping the other parameters fixed to find its optimal value. Once an

optimum value for a particular parameter has been found, it is keep fixed for

remaining part of study. A similar process is carried out, to find the optimal values of

other parameters.

4.2.1 Uniform thickness

Here, thickness of coating across each of the side of the solid block is equal. The

optimized fitness value (optimized through GA) got in this case is equal to 0.084285

and the corresponding optimized NN parameter values (optimized through GA) are

as follows: learning rate (η) = 0.033211, momentum factor (α) = 0.000977, slope of

25

linear transfer function of input layer (ɑI) = 2.678388, transfer function coefficient of

hidden layer (ɑH) = 1.499389, transfer function coefficient of output layer (ɑO) =

4.846154 and lastly the number of neurons in the hidden layer (NH) = 19. Using this

optimum set of NN parameters, the predicted thickness corresponding to each

individual input set of the test cases has been calculated. Now, a comparison has been

made between the predicted and original thickness of coating. The Figure 4.9 shows

this comparison between original thickness during simulation and predicted thickness

for each individual test case. In the Figure, a line passing through all the points has

been drawn. A line making an angle 450 with x or y axis is also been drawn. The

deflection between these two lines showing the gap between the original and

predicted thickness.

Figure 4.9: Plot between original thickness during simulation and predicted thickness.

26

Using optimum set of NN parameters, comparison between temperature

profile with original and predicted thickness has also been made. Figure 4.10a, 4.10b

and 4.10c shows this type of 2 comparisons.

-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100

1200

1300

1400


Tem

pera

ture

(K

)

0.0020m(Original)

0.001587m(Predicted)

-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000


Tem

pera

ture

(K

)

0.0120m(Original)


a

b

27

Figure 4.10(a, b and c): Comparison between the thickness during simulation and the

predicted thickness through the developed methodology.

4.2.2 Non-Uniform thickness

In this case, thicknesses of coating for the sides of the homogeneous solid block are

not equal to each other. Thickness of coating on one particular side is varying where

on the other sides the coating thickness remain unchanged. The optimized fitness

value (optimized through GA) got in this case is equal to 0.24874 and the

corresponding optimized NN parameter values (optimized through GA) are as

follows: learning rate (η) = 0.362637, momentum factor (α) = 0.037851, slope of

linear transfer function of input layer (ɑI) = 1.310623, transfer function coefficient of

hidden layer (ɑH) = 3.300366, transfer function coefficient of output layer (ɑO) =

4.144078 and lastly the number of neurons in the hidden layer (NH) = 23. Using this

optimum set of NN parameters, the predicted thickness corresponding to each

individual input set of the test cases has been calculated. Now, a comparison has been

-0.4 -0.2 0 0.2 0.4 0.6400

450

500

550

600

650

700

750


Tem

pera

ture

(K

)

0.0320m(Original)


c

28

made between the predicted and original thickness of coating. Here, there are four

cases for the four sides (bottom, left, top and right) respectively.

4.2.2.1 Thickness varying on bottom side (keeping fixed on the other sides)

With present condition, the Figure 4.11 shows the comparison between original

thickness during simulation and predicted thickness for each individual test case. In

the Figure, a line passing through all the points has been drawn. A line making an

angle 450 with x or y axis is also been drawn. The deflection between these two lines

showing the gap between the original and predicted thickness.

Figure 4.11: Plot between original thickness during simulation and predicted

thickness.

29


profile with original and predicted thickness has also been made. Figure 4.12a and

4.12b shows this type of 2 comparisons.

Figure 4.12 (a, b): Comparison between the thickness during simulation and the


-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100

1200

1300

1400

Dimension along bottom of solid bar (m)

Tem

pera

ture

(K

)

0.002m(Original)


-0.4 -0.2 0 0.2 0.4 0.6400

450

500

550

600

650

700

750


Tem

pera

ture

(K

)

0.032m(Original)


b

a

b

a

30

4.2.2.2 Thickness varying on left side (keeping fixed on the other sides)

With the present condition, the Figure 4.13 shows the comparison between original

thickness during simulation and predicted thickness for each individual test case with

the present condition.


thickness.




31

Figure 4.14(a, b): Comparison between the thickness during simulation and the


-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.002m(Original)


-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.032m(Original)


a

b

32

4.2.2.3 Thickness varying on top side (keeping fixed on the other sides)

In the same way, for the present condition, the Figure 4.15 shows the comparison

between original thickness during simulation and predicted thickness for each

individual test case.


thickness.




33



-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

0.002m(Original)


-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.032m(Original)


a

b

34

4.2.2.4 Thickness varying on right side (keeping fixed on the other sides)

With this condition, Figure 4.17 shows this comparison between original thickness

during simulation and predicted thickness for each individual test case.


thickness.




35



-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.002m(Original)


-0.4 -0.2 0 0.2 0.4 0.6400

500

600

700

800

900

1000

1100


Tem

pera

ture

(K

)

0.032m(Original)


b

a

36

37

Chapter 5: Concluding Remarks and Scope for Future Work

5.1 Concluding Remarks

Attempt has been made to develop a methodology for the prediction of coating

thickness by conduction analysis using ‘C’ programming language and commercial

CFD software: Gambit and Fluent. The performance of the developed methodology

has been tested to predict the uniform or non-uniform thickness of a coating material

on a homogeneous solid body (solid square block) from some known temperature

values elsewhere at the bottom side (bottom wall) of block. The known temperature

values at several positions along the bottom wall has been used in terms of some

statistical parameter (for example: mean, standard deviation, skew-ness and kurtosis)

in the developed methodology. The temperature profiles at the bottom wall for

different coating thickness have been numerically evaluated by the forward

calculation using commercial CFD software: Gambit and Fluent in a fully automated

way by an indigenously developed journal file. Statistical parameters of the

temperature profile have been extracted using MATLAB to build the training and test

data. Here, Feed-Forward neural network (NN) with back-Propagation algorithm is

38

used to predict the coating thickness. The NN has been modelled using ‘C’

programming Language in LINUX operating system. A Genetic Algorithm (GA) has

also been designed (using ‘C’ programming language in Linux operating system) to

optimize the performance of the NN by optimizing the values of NN parameters.

By seeing the temperature profile at bottom wall for the different coating

thickness, it can be concluded that the temperature profile at bottom wall is very much

effected by thickness of the coating. The thickness of coating can be predicted by

knowing the statistical parameters for temperature profile at the bottom wall.

The NN parameters have been optimized simultaneously using a local

optimizer namely BP-algorithm and a global optimizer like GA in the developed

methodology. That menas, local search power of BP-algorithm has been coupled with

the global search capability of GA and a hybrid optimization scheme has been

implemented and consequently, it has performed very well. The developed scheme is

seen to be an practically effective tool for prediction in heat transfer problems.

Morever, it can be said that one may apply the developed methodology for

other kinds of prediction problems in heat conduction or heat convection.

5.2 Scope for Future Work

The boundary conditions used to develop the methodlogy can change to get a more

robust methodology. For example one may use the constant heat flux boundary at two

different wall (where as, in the present study, constant heat flux boundary is used only

at a single wall) and constant temperature boundary conditions at the remaining two

wall (where as, in the present study, constant temperature boundary is used at three

sides) or so on. The boundary conditions may be changed in other ways also. Attemt

may be made in future to develop the methodology using experimental data through

an experimental investigation. The similar concept (as used here) may be used to

39

predict inportant parameters related to other conduction or convection heat transfer

problem. The proposed GA-NN approach used here can be modified and extended to

solve other different kind of problems in heat conduction or other prediction problem

related to another mode of heat transfer.

40

41

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Gaurav Katendra - National Institute of Technology, Rourkelaethesis.nitrkl.ac.in/5386/1/211ME3172.pdf · National Institute of Technology, Rourkela by Gaurav Katendra, Roll No. 211ME3172