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International Journal of Industrial Engineering Research and Development (IJIERD), ISSN 0976

6979(Print), ISSN 0976 6987(Online) Volume 2, Issue 1, May - October (2011), IAEME

69

A GENETIC PROGRAMMING APPROACH FOR THE

PREDICTION OF THERMAL CHARACTERISTICS OF

CERAMIC COATINGS

Prof. Mohammed Yunus1, Dr. J. Fazlur Rahman

2and S.Ferozkhan

3

1. Research scholar, Anna University of Technology CoimbatoreAssistant Professor, Department of Mechanical Engineering

H.K.B.K.C.E., Bangalore, India

[email protected]

2. Supervisor, Anna University of Technology CoimbatoreProfessor Emeritus, Department of MechanicalEngineering


[email protected]

3. Lecturer, Department of Mechanical Engineering,


[email protected]

ABSTRACT

In aerospace industry, the durability and efficiency of high temperature

components are improved by the usage of thermal barrier coatings (TBC). In

order to characterize the TBC, it requires a better understanding of mechanical

and tribological properties along with their failure mechanisms which are to be

thoroughly investigated to estimate their performance. At high temperature

applications, Thermal barrier (TB) and thermal cycling resistance (TCR)

parameters play a very important role. In this regard, Thermal tests were

carried out on three different types of commonly used industrial ceramic

coatings namely, Alumina (A), Alumina-Titania (AT)) and partially stabilizedzirconia (PSZ), in the present study.

Genetic programming (GP) has proved to be a highly versatile and useful

tool for identifying relationships in data for which a more precise theoretical

construct is unavailable. This technical paper highlights how we use GP

technique in the prediction of maximum thermal barrier (temperature) and

thermal cycling resistance (failure) of various ceramic coatings, for different

variables, which are used at high temperatures. Commercial Genetic

International Journal of Industrial Engineering Research

and Development (IJIERD), ISSN 0976 6979(Print)

ISSN 0976 6987(Online) Volume 2

Issue 1, May October (2011), pp. 69-79

IAEME, http://www.iaeme.com/ijierd.html

IJIERD

I A E M E


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Programming (GP) software-Discipulus is used to derive a mathematical

modelling of relations for various input and output parameters used in

characterisation. A special genetic approach for the modelling of thermal

properties in coated components is proposed on the basis of a training data set.

Various different genetic models for prediction of different thermal properties

with greater accuracy (less than 1%) were also proposed by simulatedevolution.

Keywords: TBC Thermal properties - Thermal tests Thermal Barrier

Thermal cycling resistance Genetic Programming Evolutionary Algorithm

GP software Discipulus.

1.1INTRODUCTIONThermal Barrier Coatings (TBC) which are ceramic coatings applied on

metal substrate have vast applications in aerospace, gas turbine engines, diesel

engines and power generators. A TBC protects a metal substrate from hightemperature as well as excessive wear and corrosion. TBC has very low

thermal conductivity, which insulates the underlying substrate material from

high temperature environment. In the case of aerospace and gas turbineapplication, the thickness of TBC generally varies 100 to 400 microns [1]. At

this thickness range, the temperature of insulated super alloy substrate can bereduced up to 200

0C enabling that gas turbine engines to function at higher

temperature. The characteristic of TBC originates from porosity, micro cracksand toughness of ceramic coatings.

Ceramic coatings have applications primarily as wear coatings and thermal

barrier coatings. TBCs are usually consisting of two layers; the first layer is a

metallic bond coat, whose function is to protect the substrate material againstoxidation, corrosion and to provide with a good adhesion to the thermal

insulating ceramic layer while the second layer is of ceramic material which

acts as TBC. The desirable properties of these include high thermal expansion,

low thermal conductivity and good thermal cycling resistance [1]-[8].

1.2 GENETIC PROGRAMMING (GP)

Genetic Programming is a form of machine learning that automatically

writes computer programs. It uses the principle of Darwinian Natural [12]

Selection to select and reproduce fitter programs. GP applies that principle to

a population of computer programs and evolves a program that predicts the

target output from a data file of inputs and outputs [9-12]. The programsevolved by GP software Discipulus [13], in this case Java, C/C++ and

assembly interpreter programs represents a mapping of input to output data.

This is done by Machine Learning that maps a set of input data to known

output data. The aims of using the machine learning technique on engineering

problems are to determine data mining and knowledge discovery. GP provides

a significant benefit in many areas of science and industry[14]. The Discipulus


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GP [13] system uses AIM Learning Technology. AIM stands for Automatic

Induction of Machine Code. AIM Learning and Discipulus deal with the

machine learning speed problem.

This speed allows the analyst to able to make many more runs to investigate

relationships between data and output, assess information content of data

streams, uncover bad data or outliers, assess time lag relationships betweeninputs and outputs, and the like. The evolved models have been or are being

used to develop process prediction or control algorithms. Hence GP technology

has been selected for the present work.

GP solutions are computer programs that can be easily inspected,

documented, evaluated, and tested. The GP solutions are easy to understand the

nature of the derived relationship between input and output data and to examine

the uncover relationships that were unknown before. Genetic Programmingevolves both the structure and the constants to the solution simultaneously.

Discipulus GP strongly discriminates between relevant input data and inputs

that have no bearing on a solution [13]. In other words, Discipulus performs

input variable selection as a by-product of its learning algorithm.The following step by step procedure will be implemented for a steady state

GP algorithm [9-13],[14]

1. Initialization of population: Generate an initial population of randomcompositions of the functions and terminals of the problem (computer

programs).2. Fitness evaluation: Execute each program in the population, randomly it

selects some programs and assign it a fitness value according to how well itsolves the problem by mapping input data to output data. Some programs are

selected as winners (best programs), and the others as losers.

3. Create a new population of computer programs by exchanging parts of the

best programs with each other (called crossover).4. Copy the best existing programs.

5. Create new computer programs by randomly changing each of the

tournament winners to create two new programs mutation.

6. Iterate Until Convergence. Repeat steps two through four until a program is

developed that predicts the behavior sufficiently.

GP has been successfully used to solve problems in a wide range of broad

categories [15-24]:

1. Systems Modelling, Curve Fitting, Data Modelling, and SymbolicRegression

2. Industrial Process Control3. Financial Trading, Time Series Prediction and Economic Modelling4. Optimisation and scheduling5. Medicine, Biology and Bioinformatics6. Design7. Image and Signal processing8. Entertainment and Computer games


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2. EXPERIMENTAL PROCEDURES

Three different commercially available ceramic coatings powders namely,

Alumina, Alumina-Titania, Partially Stabilized Zirconia of two different

thicknesses namely 100 to 250 microns were used for the preparation of

coatings. A 40 KW Sulzer,[1]and [8] Metco plasma spray system with 7MB

gun is used for this purpose. Mild steel plates of 50x50x6 mm were used assubstrate to spray the ceramic oxides. They were grit blasted, degreased and

spray coated with a 50 to 100 microns NiCrAl bond coat[. The ceramic TBC

were then plasma sprayed according to spray parameters mentioned in table1.

In this study, two response parameters such as thermal barrier and thermal

cycling tests were considered.

2.1 THERMAL BARRIER TEST

Thermal barrier tests were conducted by measuring the temperature of metal

substrate using thermocouples, after heating the coating surface with electric

heaters, between 7000

C and 10000

C for a period of half an hour to attain steadystate, to get temperature drop across the substrate and ceramic coating. The

heat transfer coefficient on the surface of coated plate is very important

parameter in the selection of TBC [2]-[6]. This parameter is studied fordifferent heat inputs under natural and forced convection. An electric heater

connected with ammeter, voltmeter and a dimmerstat to control the heat inputwas used in the experimental setup to heat the substrate with coated surface.

Two thermocouples of K-type namely chrome-alumel were used to measurethe temperature at the substrate surface and as well as on the top of the coating

for a given heat input. The temperature on the ceramic coated surface and metal

surface is measured for three different coatings namely, Alumina (A),

Alumina-Titania (AT) and Partially Stabilized zirconia (PSZ) and the heattransfer coefficients by natural and forced convection on the surface of the

coated plate were calculated. In the case of forced convection, a blower was

used to blow the air along the coated plate for different air velocities flowing

parallel to the surface of the coatings, on three different coatings, heat inputs

and the temperatures were measured using thermocouple.

2.2 THERMAL CYCLING TEST (TCT)

Thermal cycling test is performed to determine the resistance of coated part

for sudden changes in temperature [7] and to examine whether the sprayed

coating can withstand severity of thermal cycling. The three different ceramiccoatings with different thicknesses were subjected to thermal cycling by

exposing to oxyacetylene flame till the coated surface is maintained around

10000C for about 1minute and subsequently cooled down by air till the

temperature reaches down to around 1000C in the atmospheric conditions for 1

minute. The thermal cycling process is repeated until coating fails and peels off

from the substrate.


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3. GENETIC PROGRAMMING METHODOLOGY

In Genetic programming modelling, it is necessary to select suitable

terminal from set Fand available terminal genes from set f (0)[15-24]. From

these, the evolutionary process will try to build as fit an organism (i.e.

mathematical model) as possible for thermal characteristics prediction. The

organisms consist of both terminal and function genes and have the nature ofcomputer programs which differ in form and size.

In our case the set of terminal genesf (0) is: f (0) = {Process inputs}.

The selected set of function genes Fis: F= {+, -, *, /}, where +,-,*, / are

the mathematical operation of addition, subtraction, multiplication and

division. The quality of the individual organism (i.e. prediction) is found out

using fitness function. In our case, four different functions are used.

3.1 Process Inputs

Ambient Temperature (0C),

Temperature on coating side (0C),

Temperature on substrate side (0

C),Power (W),

Velocity of air (m/sec)

Toughness (MPa m)Thermal conductivity (W/m K)

Thermal Diffusivity (x 10-7

m2/sec)

3.2 Measured Process OutputsHeat transfer coefficient under Natural convection (W/m

2 0K)

Heat transfer coefficient under Forced convection (W/m2 0

K)

Thickness of coating against thermal Barrier (0C)

Thermal cycling Resistance (number of cycles withstood)

Table1. Experimental results of Thermal Cycling Resistance Test for different coatings

Sl.No. Thickness of

coating in m(V0)

Temperature of heating(V4)

Number of cyclesfor Alumina (A) (f0)

number of cycles forAlumina-Titania

(AT) (f0)

number of cyclesfor Partial

stabilised

zirconia(PSZ)(f0)

1 150 700 280 345 405

2 225 700 290 360 425

3 300 700 310 375 445

4 150 850 260 330 390

5 225 850 270 345 410

6 300 850 280 360 425

7 150 1000 250 320 360

8 225 1000 260 330 380

9 300 1000 270 340 400

Table 2. Experimental Results of evaluating thickness to withstand Thermal barrier for

different coatingsS.No.

Coating surface

Temperature in0C (V0)

Thickness of coatingin m(f0)

Temperature

difference in 0C forAlumina (V2)

Temperaturedifference in 0C for

Alumina- Titania(V2)

Temperaturedifference in 0C

for PSZ(V2)

1 700 150 120 160 190

2 800 150 125 165 180

3 900 150 125 160 190


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4 1000 150 120 160 180

5 700 300 135 170 210

6 800 300 145 175 215

7 900 300 140 170 210

8 1000 300 145 175 215

Table3. Experimental results of heat transfer coefficient of natural convection for

different coatingsSl.No.

Power in

W (V0)

Coating surfaceTemperature in0C (V1)

AmbientTemperature in0C (V2)

Thickness ofcoating in m

(V3)

H in W/m2Kfor Alumina

(f0)

H in W/m2Kfor Alumina-

Titania (f0)

H inW/m2K for

PSZ(f0)

1 5 69 35 150 3.9 3.48 3.29

2 5.5 75 40 150 4.14 3.65 3.31

3 6 85 45 150 3.95 3.65 3.39

4 6.5 94 55 150 4.26 3.75 3.23

5 5 106 85 300 3.44 3.25 3.03

6 5.5 115 100 300 3.44 3.2 3.05

7 6 174 130 300 3.8 3.2 3

8 6.5 183 164 300 3.66 3.4 3.15

Table 4. Experimental results of heat transfer coefficient of forced convection for

different coatings.S.N0.

Power

in W(V3)

Velocity

of air inm/sec (V1)

Coating

surface


Ambient


Thickness of

coating inm (V4)

H in

W/m2K for

Alumina(f0)

H in W/m2K

for Alumina-

Titania (f0)

H in

W/m2K

for PSZ(f0)

1 5.5 1.401 35 30 300 25 12.75 8.56

2 6.5 1.253 80 65 300 25 12.8 9.3

3 6 1.401 70 65 150 25 13.8 10.4

4 6.5 1.085 90 70 300 25 11.84 11.4

5 5 0.8858 78 65 150 25 8.8 8.05

6 6 1.085 85 80 150 25 11.43 8.8

7 6 1.085 105 60 300 25 11 10.05

8 6.5 1.253 69 48 150 25 13.2 11.05

9 5.5 1.253 40 35 300 25 12.05 8.89

10 6 1.253 75 70 150 25 12.84 9.56

11 5 1.085 75 60 150 25 9.5 10.85

12 5 1.253 56 50 300 25 10.75 11.8

13 5.5 1.253 56 50 150 25 12.6 8.4

14 6 1.401 88 40 300 25 13 9

15 5.5 1.401 46 40 150 25 13.1 10.5

16 6.5 1.085 72 52 150 25 12.64 11.517 6.5 0.8858 120 90 300 25 10.72 8.94

18 5.5 0.8858 65 60 150 25 10.6 10.42

19 5 1.253 60 55 150 25 11.21 11.9

20 5 1.401 50 45 300 25 11.64 12.6

21 6.5 0.8858 88 57 150 25 11.24 8.8

22 5 1.401 65 50 150 25 12.86 10

23 6 1.253 90 50 300 25 12.45 11.64

24 5.5 1.085 48 45 300 25 11.35 12

25 6.5 1.401 70 50 300 25 13.85 9

26 6 0.8858 115 70 300 25 10.25 10.56

27 5.5 0.8858 55 50 300 25 10 11.64

28 5 0.8858 65 60 300 25 8.4 12.89

29 6.5 1.401 65 42 150 25 14.64 9.6

30 6 0.8858 90 85 150 25 10.64 10

31 5.5 1.085 58 55 150 25 11.64 11.21

32 5 1.085 60 55 300 25 9 12.64

4. GENETIC MODELS RESULTS AND DISCUSSION

The best accuracy ( (i) = 0.175 %, and that of the testing data (i) = 0.

18%) of the GP model was obtained when the genes function set used and the

Output of the discipulus GP is in C program. The C program for the heat

transfer coefficient in natural convection as given below:


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{{ f[0]=f[1]=f[2]=f[3]=f[4]=f[5]=f[6]=f[7]=0; L0: f[0]-=v[7]; L1:

f[0]/=v[4]; L2:f[0]+=1.501374244689941f; L3:f[0]*=f[0]; L4:

f[0]*=f[0]; L5: f[0]-=1.987620830535889f; L6:f[0]*=v[0];

L7:f[0]*=v[2]; L8:f[0]*=v[5]; L9: f[0]/=v[7]; L10: f[0]/=v[1]; L11:

f[0]-=v[6]; L12:f[0]/=v[3]; L13: f[0]-=v[2]; L14: f[0]+=v[1];

L15: f[0]*=0.03275442123413086f; L16:f[0]/=-0.494312047958374f;L17:f[0]+=-1.549970149993897f; L18:f[0]/=v[5]; L19: f[0]+=v[1]; L20:

f[0]+=f[0];

L21: f[0]+=f[0]; L22: f[0]+=v[3]; L23:f[0]+=v[1]; L24: f[0]+=v[1];

L25: }}

Upon simplification, in case of natural convection, the heat transfer coefficient,

h is given by,

Where V4 = Thermal Conductivity, V5= thermal diffusivity and V6=Toughness

and

Using GP simulation, in case of forced convection, the heat transfer coefficient,

h is given by


and

Using GP simulation, in case of natural convection, the number of cycles

withstood (or thermal cycling resistance), TCR is given by

h


Using GP simulation, in case of natural convection, the thickness of coating

against the thermal barrier ,t is given by


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Where V1 = Thermal Conductivity

and

The results for thickness of coating against thermal barrier property

simulation are shown in figure 1 and heat transfer coefficient simulation for

natural and forced convection are shown in figure 2 and figure 3 and the

Thermal cycling resistance are presented in figure 4. The Discipulus GP

technique was able to simulate these output variables to within an average of

1.3% of their measured value, with no value exceeding a 0.01% deviation

except in case of thickness deviation which is up to 3%.

Figure 1. Percentage deviation curve between the best models regarding individual generation

and experimental results of thickness of coating against Thermal Barrier

Figure 2. Percentage deviation curve between the best models regarding individual generationand experimental results of Heat Transfer coefficient Data under Natural convection


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Figure3. Percentage deviation curve between the best models regarding individual generationand experimental results of Heat Transfer coefficient Data under Forced convection


and experimental results of Thermal Cycling Resistance Data.

5. CONCLUSIONS


tool for identifying relationships in data for which a more precise theoreticalconstruct is unavailable. The experimental data in this research were in fact the

environment to which the population of models had to be adapted as much as

possible. The models presented are a result of the self-organization and

stochastic processes taking place during simulated evolution. Only four

genetically developed models out of many successful solutions are presented

here. The accuracies of solutions obtained by GP depend on applied

evolutionary parameters and also on the number of measurements and the

accuracy of measurement. In general, more measurements supply more

information to evolution which improves the structures of models.

In this paper, the genetic programming was used for predicting the thermal

properties responsible for failure of ceramic coatings. In the proposed concept

the mathematical models for verifying the experimental results of thermal

characteristics are subject to adaptation. Its reliability is 99.26% in the first

three cases and whereas it is 97% in fourth case. In the testing phase, the

genetically produced model gives the same result as actually found out during

the experiment, thereby with the reliability of cent percent. It is inferred from

our research findings that the genetic programming approach could be well


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used for the prediction thermal characteristics of ceramic coatings without

conducting the experiments. This helps to establish efficient planning and

optimizing of process for the quality production of ceramic coatings depending

upon the functional requirements. Further work is on progress for the

prediction/optimization of mechanical and tribological characteristics of

ceramic coatings in addition to machinability of industrial ceramic coatings.

REFERENCES

[1] Dr. J. Fazlur Rahman et. al. and Mohammed Yunus et. al. (2009) ,

Benefits of TBC Coatings on Engine applications, Proceedings of

International conference, INCAM 2009 at Kalsalingam University, Tamil

Nadu, India.[2] Nusair Khan(2000), Behaviour of air plasma sprayed thermal barrier

coatings, Subjected to intense thermal cycling, LASMIS, BP 2060, 12 Rue de

Marie curie, Universite de Technologie de Troyes, France.

[3] W.F. Calosso and A.R. Nicoll, (1987), Process requirements for plasmasprayed coatings for internal combustion engine components, Energy Sources

Technology Conference and Exhibition, (Dallas, TX) 15-20 February, 87-ICE-

15, ASME, pp. 1-8.[4] Stragman T.E. (1985), Thermal barrier coatings for turbine airfoils the

Plasma Spray Process, J. Thin Solid Films, 127, pp. 93-105.[5] Dongming Zhu and Robert A. Miller (1998), Thermal-Barrier Coatings for

Advanced Gas Turbine Engines.[6] Nitin P. Padture, Maurice Gell, Eric H. Jordan (1998), Thermal Barrier

Coatings for gas Turbine Engine Applications, Department of Metallurgy and

Materials Engineering, Department of Mechanical Engineering, Institute of

Material Science, University of Connecticut, Storrs, CT06269-3136, USA.[7] P.Ramaswamy, S. Seetharamu, K. J. Rao, and K. B. R. Varma,(1998)

Thermal shock characteristics of plasma sprayed mullite coatings

Technology, J.Thermal spray Volume 7, Number 4, pp. 497-504(8).

[8] Dr.J.Fazlur Rahman and Mohammed Yunus (2008), Mechanical and

Tribological characteristics of Tungsten Carbide Cobalt HVOF coatings,

Proceedings of International conference on MEMS held at Anjuman college of

Engineering, Bhatkal, India.

[9] Nordin, J.P. and Banzhaf, W. (1996) Controlling an Autonomous Robot

with Genetic Programming.In: Proceedings of 1996 AAAI fall symposium on

Genetic Programming, Cambridge, USA.

[10] Koza, J.R., (1992) Genetic Programming: On the Programming ofComputers by Natural Selection.MIT Press, Cambridge, MA.

[11] J. R. Koza, Genetic programming II, The MIT Press, Massachusetts, 1994.

[12] Koza, Bennett, Andre, & Keane, (1999) GENETIC PROGRAMMING III

Darwinian Invention and Problem Solving, Morgan Kaufmann Publishers, Inc.

pp. 1154.


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[13] Francone, F., (1998-2000) Discipulus Owners Manual and Discipulus

Tutorials, Register Machine Learning Technologies, Inc.

[14] Spector, L., Langdon, W., B., OReilly, U., Angeline, P.J. (1999)

Advances in Genetic Programming Volume 3, MIT Press, pp. 476

[15] Tanguy, B. Besson J., Piques R., Pineau A. (2005), Ductile to brittle

transition of an A508 steel characterized by Charpy impact test Part 1:experimental results, Engineering Fracture Mechanics 72, pp.49 - 72.

[16] M. Kovacic, J. Balic and M. Brezocnik, Evolutionary approach for cutting

forces prediction in milling, Journal of materials processing technology,

155/156, 2004, pp.1647-1652.

[17] H. Kurtaran, B. Ozcelik and T. Erzurumlu, Warpage optimization of a bus

ceiling lamp base using neural network model and genetic algorithm, Journal of

materials processing technology, 169(2), 2005, pp.314-319.[18] Sette S., Boullart L. Genetic programming: principles and applications,

Engineering Applications of Artificial Intelligence 14 (2001), pp.727 736.

[19] Pierreval H., Caux C., Paris J.L., Viguier F. Evolutionary approaches to

the design and organization of manufacturing system, Computers & IndustrialEngineering 44 (2003), pp.339-364.

[20] Gusel L., Brezocnik M. Modeling of impact toughness of cold formed

material by genetic programming, Comp. Mat. Sc. 37 (2006), pp.476 482.[21] Chang Y.S., Kwang S.P., Kim B.Y. Nonlinear model for ECG R-R

interval variation using genetic programming approach, Future GenerationComputer Systems 21, pp.1117-1123.

[22] Brezocnik M., Gusel L. (2004), Predicting stress distribution in cold-formed material with genetic programming,International Journal of Advanced

Manufacturing Technology, Vol 23, pp.467-474.

[23] M. Brezocnik, M. Kovacic and M. Ficko (2004), Prediction of surface

roughness with genetic programming, Journal of materials processingtechnology, 157/158, 28-36.

[24] M. Brezocnik and M. Kovacic (2003), Integrated genetic programming

and genetic algorithm approach to predict surface roughness, Materials and

manufacturing processes,18(4), pp.475491.


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categories [15-24]:




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C and 10000





















from the substrate.


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3.1 Process Inputs




C),Power (W),




m2/sec)


2 0K)


K)




Sl.No. Thickness of

coating in m(V0)




(AT) (f0)


stabilised

zirconia(PSZ)(f0)

1 150 700 280 345 405

2 225 700 290 360 425

3 300 700 310 375 445

4 150 850 260 330 390

5 225 850 270 345 410

6 300 850 280 360 425

7 150 1000 250 320 360

8 225 1000 260 330 380

9 300 1000 270 340 400



Coating surface



Temperature





for PSZ(V2)

1 700 150 120 160 190

2 800 150 125 165 180

3 900 150 125 160 190


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4 1000 150 120 160 180

5 700 300 135 170 210

6 800 300 145 175 215

7 900 300 140 170 210

8 1000 300 145 175 215



Power in

W (V0)




(V3)


(f0)


Titania (f0)

H inW/m2K for

PSZ(f0)

1 5 69 35 150 3.9 3.48 3.29

2 5.5 75 40 150 4.14 3.65 3.31

3 6 85 45 150 3.95 3.65 3.39

4 6.5 94 55 150 4.26 3.75 3.23

5 5 106 85 300 3.44 3.25 3.03

6 5.5 115 100 300 3.44 3.2 3.05

7 6 174 130 300 3.8 3.2 3

8 6.5 183 164 300 3.66 3.4 3.15



Power

in W(V3)

Velocity

of air inm/sec (V1)

Coating

surface


Ambient


Thickness of

coating inm (V4)

H in

W/m2K for

Alumina(f0)

H in W/m2K

for Alumina-

Titania (f0)

H in

W/m2K

for PSZ(f0)

1 5.5 1.401 35 30 300 25 12.75 8.56

2 6.5 1.253 80 65 300 25 12.8 9.3

3 6 1.401 70 65 150 25 13.8 10.4

4 6.5 1.085 90 70 300 25 11.84 11.4

5 5 0.8858 78 65 150 25 8.8 8.05

6 6 1.085 85 80 150 25 11.43 8.8

7 6 1.085 105 60 300 25 11 10.05

8 6.5 1.253 69 48 150 25 13.2 11.05

9 5.5 1.253 40 35 300 25 12.05 8.89

10 6 1.253 75 70 150 25 12.84 9.56

11 5 1.085 75 60 150 25 9.5 10.85

12 5 1.253 56 50 300 25 10.75 11.8

13 5.5 1.253 56 50 150 25 12.6 8.4

14 6 1.401 88 40 300 25 13 9

15 5.5 1.401 46 40 150 25 13.1 10.5

16 6.5 1.085 72 52 150 25 12.64 11.517 6.5 0.8858 120 90 300 25 10.72 8.94

18 5.5 0.8858 65 60 150 25 10.6 10.42

19 5 1.253 60 55 150 25 11.21 11.9

20 5 1.401 50 45 300 25 11.64 12.6

21 6.5 0.8858 88 57 150 25 11.24 8.8

22 5 1.401 65 50 150 25 12.86 10

23 6 1.253 90 50 300 25 12.45 11.64

24 5.5 1.085 48 45 300 25 11.35 12

25 6.5 1.401 70 50 300 25 13.85 9

26 6 0.8858 115 70 300 25 10.25 10.56

27 5.5 0.8858 55 50 300 25 10 11.64

28 5 0.8858 65 60 300 25 8.4 12.89

29 6.5 1.401 65 42 150 25 14.64 9.6

30 6 0.8858 90 85 150 25 10.64 10

31 5.5 1.085 58 55 150 25 11.64 11.21

32 5 1.085 60 55 300 25 9 12.64







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{{ f[0]=f[1]=f[2]=f[3]=f[4]=f[5]=f[6]=f[7]=0; L0: f[0]-=v[7]; L1:

f[0]/=v[4]; L2:f[0]+=1.501374244689941f; L3:f[0]*=f[0]; L4:

f[0]*=f[0]; L5: f[0]-=1.987620830535889f; L6:f[0]*=v[0];

L7:f[0]*=v[2]; L8:f[0]*=v[5]; L9: f[0]/=v[7]; L10: f[0]/=v[1]; L11:

f[0]-=v[6]; L12:f[0]/=v[3]; L13: f[0]-=v[2]; L14: f[0]+=v[1];


f[0]+=f[0];

L21: f[0]+=f[0]; L22: f[0]+=v[3]; L23:f[0]+=v[1]; L24: f[0]+=v[1];

L25: }}


h is given by,


and


h is given by


and



h





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and












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5. CONCLUSIONS




















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78







REFERENCES




























pp. 1154.


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155/156, 2004, pp.1647-1652.


















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69



CERAMIC COATINGS


2and S.Ferozkhan

3



[email protected]



[email protected]



[email protected]

ABSTRACT





















IJIERD

I A E M E


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categories [15-24]:




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C and 10000





















from the substrate.


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3.1 Process Inputs




C),Power (W),




m2/sec)


2 0K)


K)




Sl.No. Thickness of

coating in m(V0)




(AT) (f0)


stabilised

zirconia(PSZ)(f0)

1 150 700 280 345 405

2 225 700 290 360 425

3 300 700 310 375 445

4 150 850 260 330 390

5 225 850 270 345 410

6 300 850 280 360 425

7 150 1000 250 320 360

8 225 1000 260 330 380

9 300 1000 270 340 400



Coating surface



Temperature





for PSZ(V2)

1 700 150 120 160 190

2 800 150 125 165 180

3 900 150 125 160 190


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74

4 1000 150 120 160 180

5 700 300 135 170 210

6 800 300 145 175 215

7 900 300 140 170 210

8 1000 300 145 175 215



Power in

W (V0)




(V3)


(f0)


Titania (f0)

H inW/m2K for

PSZ(f0)

1 5 69 35 150 3.9 3.48 3.29

2 5.5 75 40 150 4.14 3.65 3.31

3 6 85 45 150 3.95 3.65 3.39

4 6.5 94 55 150 4.26 3.75 3.23

5 5 106 85 300 3.44 3.25 3.03

6 5.5 115 100 300 3.44 3.2 3.05

7 6 174 130 300 3.8 3.2 3

8 6.5 183 164 300 3.66 3.4 3.15



Power

in W(V3)

Velocity

of air inm/sec (V1)

Coating

surface


Ambient


Thickness of

coating inm (V4)

H in

W/m2K for

Alumina(f0)

H in W/m2K

for Alumina-

Titania (f0)

H in

W/m2K

for PSZ(f0)

1 5.5 1.401 35 30 300 25 12.75 8.56

2 6.5 1.253 80 65 300 25 12.8 9.3

3 6 1.401 70 65 150 25 13.8 10.4

4 6.5 1.085 90 70 300 25 11.84 11.4

5 5 0.8858 78 65 150 25 8.8 8.05

6 6 1.085 85 80 150 25 11.43 8.8

7 6 1.085 105 60 300 25 11 10.05

8 6.5 1.253 69 48 150 25 13.2 11.05

9 5.5 1.253 40 35 300 25 12.05 8.89

10 6 1.253 75 70 150 25 12.84 9.56

11 5 1.085 75 60 150 25 9.5 10.85

12 5 1.253 56 50 300 25 10.75 11.8

13 5.5 1.253 56 50 150 25 12.6 8.4

14 6 1.401 88 40 300 25 13 9

15 5.5 1.401 46 40 150 25 13.1 10.5

16 6.5 1.085 72 52 150 25 12.64 11.517 6.5 0.8858 120 90 300 25 10.72 8.94

18 5.5 0.8858 65 60 150 25 10.6 10.42

19 5 1.253 60 55 150 25 11.21 11.9

20 5 1.401 50 45 300 25 11.64 12.6

21 6.5 0.8858 88 57 150 25 11.24 8.8

22 5 1.401 65 50 150 25 12.86 10

23 6 1.253 90 50 300 25 12.45 11.64

24 5.5 1.085 48 45 300 25 11.35 12

25 6.5 1.401 70 50 300 25 13.85 9

26 6 0.8858 115 70 300 25 10.25 10.56

27 5.5 0.8858 55 50 300 25 10 11.64

28 5 0.8858 65 60 300 25 8.4 12.89

29 6.5 1.401 65 42 150 25 14.64 9.6

30 6 0.8858 90 85 150 25 10.64 10

31 5.5 1.085 58 55 150 25 11.64 11.21

32 5 1.085 60 55 300 25 9 12.64







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{{ f[0]=f[1]=f[2]=f[3]=f[4]=f[5]=f[6]=f[7]=0; L0: f[0]-=v[7]; L1:

f[0]/=v[4]; L2:f[0]+=1.501374244689941f; L3:f[0]*=f[0]; L4:

f[0]*=f[0]; L5: f[0]-=1.987620830535889f; L6:f[0]*=v[0];

L7:f[0]*=v[2]; L8:f[0]*=v[5]; L9: f[0]/=v[7]; L10: f[0]/=v[1]; L11:

f[0]-=v[6]; L12:f[0]/=v[3]; L13: f[0]-=v[2]; L14: f[0]+=v[1];


f[0]+=f[0];

L21: f[0]+=f[0]; L22: f[0]+=v[3]; L23:f[0]+=v[1]; L24: f[0]+=v[1];

L25: }}


h is given by,


and


h is given by


and



h





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and












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5. CONCLUSIONS




















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78







REFERENCES




























pp. 1154.


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155/156, 2004, pp.1647-1652.


















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69



CERAMIC COATINGS


2and S.Ferozkhan

3



[email protected]



[email protected]



[email protected]

ABSTRACT





















IJIERD

I A E M E


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70




































36/110



71






streams, uncover bad data or outliers, assess time lag relationships bet

genetic programming 2

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