INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012

INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012

UK: Managing Editor International Journal of Innovative Technology and Creative Engineering 1a park lane, Cranford London TW59WA UK E-Mail: editor@ijitce.co.uk Phone: +44-773-043-0249 USA: Editor International Journal of Innovative Technology and Creative Engineering Dr. Arumugam Department of Chemistry University of Georgia GA-30602, USA. Phone: 001-706-206-0812 Fax:001-706-542-2626 India: Editor International Journal of Innovative Technology & Creative Engineering Dr. Arthanariee. A. M Finance Tracking Center India 17/14 Ganapathy Nagar 2nd Street Ekkattuthangal Chennai -600032 Mobile: 91-7598208700

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY & CREATIVE ENGINEERING Vol.2 No.11 November 2012

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From Editor's Desk Dear Researcher, Greetings! Research article in this issue discusses about Robust Scan Matching, Al6061/SiC Metal Matrix Composite by Taguchiâ€™s Technique. Let us review research around the world this month; Software revamp guard grid against cyberattack. Gas pipelines, factories and power stations aren't necessarily the first targets that spring to mind. But such facilities are often controlled by software that lacks the appropriate defences. Now the cyber security company Kaspersky Labs, based in Moscow, Russia, is developing an operating system that it claims will block hacker or malware attacks on critical infrastructure. Research has shown that different colours of light affect more than just our conscious vision system. A set of receptors in our eyes responds to blue light by suppressing production of sleep-inducing melatonin, so the naturally blue-rich light of daytime keeps us alert, while reddish evening light lets us ease into sleep. Fluorescent bulbs contain a lot of blue light, so being exposed to them late in the day or at night can contribute to sleep problems. Many LEDs bulbs perpetuate the problem, because they generate white light using blue LEDs coated in compounds that emit longer wavelengths when illuminated. The Hue bulb instead contains red, green and blue LEDs. That's a more expensive way to generate white light, but the level of each colour can be adjusted, meaning it's possible to produce a broad gamut of colours, including white mixtures that contain very little blue light. NASA is developing similar lights for the International Space Station because astronauts have trouble sleeping more than 6 hours a night. The lights will switch from blue-rich to keep the astronauts alert during their working day to red-rich light when they are relaxing before bed. Tiny engine runs on single hydrogen molecules. Power packs don't get much smaller than this. The random movements of single hydrogen molecules have powered a tiny, vibrating springboard, mimicking molecular machines in nature. Heat from their surroundings causes all molecules to move randomly, but engineers tend to regard such movements as noise to be avoided like the plague. Jose Ignacio Pascual at the Free University of Berlin in Germany and colleagues took inspiration from the natural world, where random motion powers structures such as proteins that move cargo around inside cells. They placed a quartz springboard, weighing a fraction of a milligram, next to a slab of copper coated with hydrogen molecules. When a molecule changed its orientation, the force between the molecule and the board changed, setting the board vibrating. The team could keep the board vibrating by injecting electrons that encouraged the molecules to move, one at a time.

It has been an absolute pleasure to present you articles that you wish to read. We look forward to many more new technology-related research articles from you and your friends. We are anxiously awaiting the rich and thorough research papers that have been prepared by our authors for the next issue. Thanks, Editorial Team IJITCE

Editorial Members Dr. Chee Kyun Ng Ph.D Department of Computer and Communication Systems, Faculty of Engineering, Universiti Putra Malaysia,UPM Serdang, 43400 Selangor,Malaysia. Dr. Simon SEE Ph.D Chief Technologist and Technical Director at Oracle Corporation, Associate Professor (Adjunct) at Nanyang Technological University Professor (Adjunct) at Shangai Jiaotong University, 27 West Coast Rise #08-12,Singapore 127470 Dr. sc.agr. Horst Juergen SCHWARTZ Ph.D, Humboldt-University of Berlin, Faculty of Agriculture and Horticulture, Asternplatz 2a, D-12203 Berlin, Germany Dr. Marco L. Bianchini Ph.D Italian National Research Council; IBAF-CNR, Via Salaria km 29.300, 00015 Monterotondo Scalo (RM), Italy Dr. Nijad Kabbara Ph.D Marine Research Centre / Remote Sensing Centre/ National Council for Scientific Research, P. O. Box: 189 Jounieh, Lebanon Dr. Aaron Solomon Ph.D Department of Computer Science, National Chi Nan University, No. 303, University Road, Puli Town, Nantou County 54561, Taiwan Dr. Arthanariee. A. M M.Sc.,M.Phil.,M.S.,Ph.D Director - Bharathidasan School of Computer Applications, Ellispettai, Erode, Tamil Nadu,India Dr. Takaharu KAMEOKA, Ph.D Professor, Laboratory of Food, Environmental & Cultural Informatics Division of Sustainable Resource Sciences, Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie, 514-8507, Japan Mr. M. Sivakumar M.C.A.,ITIL.,PRINCE2.,ISTQB.,OCP.,ICP Project Manager - Software, Applied Materials, 1a park lane, cranford, UK Dr. Bulent Acma Ph.D Anadolu University, Department of Economics, Unit of Southeastern Anatolia Project(GAP), 26470 Eskisehir, TURKEY Dr. Selvanathan Arumugam Ph.D Research Scientist, Department of Chemistry, University of Georgia, GA-30602, USA.

Review Board Members Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials,CSIRO Process Science & Engineering Private Bag 33, Clayton South MDC 3169,Gate 5 Normanby Rd., Clayton Vic. 3168, Australia Dr. Zhiming Yang MD., Ph. D. Department of Radiation Oncology and Molecular Radiation Science,1550 Orleans Street Rm 441, Baltimore MD, 21231,USA Dr. Jifeng Wang Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign Urbana, Illinois, 61801, USA Dr. Giuseppe Baldacchini ENEA - Frascati Research Center, Via Enrico Fermi 45 - P.O. Box 65,00044 Frascati, Roma, ITALY. Dr. Mutamed Turki Nayef Khatib Assistant Professor of Telecommunication Engineering,Head of Telecommunication Engineering Department,Palestine Technical University (Kadoorie), Tul Karm, PALESTINE.

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 Dr. Amala VijayaSelvi Rajan, B.sc,Ph.d, Faculty – Information Technology Dubai Women’s College – Higher Colleges of Technology,P.O. Box – 16062, Dubai, UAE

Naik Nitin Ashokrao B.sc,M.Sc Lecturer in Yeshwant Mahavidyalaya Nanded University Dr.A.Kathirvell, B.E, M.E, Ph.D,MISTE, MIACSIT, MENGG Professor - Department of Computer Science and Engineering,Tagore Engineering College, Chennai Dr. H. S. Fadewar B.sc,M.sc,M.Phil.,ph.d,PGDBM,B.Ed. Associate Professor - Sinhgad Institute of Management & Computer Application, Mumbai-Banglore Westernly Express Way Narhe, Pune - 41 Dr. David Batten Leader, Algal Pre-Feasibility Study,Transport Technologies and Sustainable Fuels,CSIRO Energy Transformed Flagship Private Bag 1,Aspendale, Vic. 3195,AUSTRALIA Dr R C Panda (MTech & PhD(IITM);Ex-Faculty (Curtin Univ Tech, Perth, Australia))Scientist CLRI (CSIR), Adyar, Chennai - 600 020,India Miss Jing He PH.D. Candidate of Georgia State University,1450 Willow Lake Dr. NE,Atlanta, GA, 30329 Jeremiah Neubert Assistant Professor,Mechanical Engineering,University of North Dakota Hui Shen Mechanical Engineering Dept,Ohio Northern Univ. Dr. Xiangfa Wu, Ph.D. Assistant Professor / Mechanical Engineering,NORTH DAKOTA STATE UNIVERSITY Seraphin Chally Abou Professor,Mechanical & Industrial Engineering Depart,MEHS Program, 235 Voss-Kovach Hall,1305 Ordean Court,Duluth, Minnesota 55812-3042 Dr. Qiang Cheng, Ph.D. Assistant Professor,Computer Science Department Southern Illinois University CarbondaleFaner Hall, Room 2140-Mail Code 45111000 Faner Drive, Carbondale, IL 62901 Dr. Carlos Barrios, PhD Assistant Professor of Architecture,School of Architecture and Planning,The Catholic University of America Y. Benal Yurtlu Assist. Prof. Ondokuz Mayis University Dr. Lucy M. Brown, Ph.D. Texas State University,601 University Drive,School of Journalism and Mass Communication,OM330B,San Marcos, TX 78666 Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials CSIRO Process Science & Engineering Dr.Sumeer Gul Assistant Professor,Department of Library and Information Science,University of Kashmir,India Dr. Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg., Rm 120,Hampton University,Hampton, VA 23688 Dr. Renato J. Orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business School,Rua Itapeva, 474 (8° andar) 01332-000, São Paulo (SP), Brazil

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Dr. Messaoud Jake Bahoura Associate Professor-Engineering Department and Center for Materials Research Norfolk State University,700 Park avenue,Norfolk, VA 23504 Dr. V. P. Eswaramurthy M.C.A., M.Phil., Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India. Dr. P. Kamakkannan,M.C.A., Ph.D ., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India. Dr. V. Karthikeyani Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 008, India. Dr. K. Thangadurai Ph.D., Assistant Professor, Department of Computer Science, Government Arts College ( Autonomous ), Karur - 639 005,India. Dr. N. Maheswari Ph.D., Assistant Professor, Department of MCA, Faculty of Engineering and Technology, SRM University, Kattangulathur, Kanchipiram Dt - 603 203, India. Mr. Md. Musfique Anwar B.Sc(Engg.) Lecturer, Computer Science & Engineering Department, Jahangirnagar University, Savar, Dhaka, Bangladesh. Mrs. Smitha Ramachandran M.Sc(CS)., SAP Analyst, Akzonobel, Slough, United Kingdom. Dr. V. Vallimayil Ph.D., Director, Department of MCA, Vivekanandha Business School For Women, Elayampalayam, Tiruchengode - 637 205, India. Mr. M. Moorthi M.C.A., M.Phil., Assistant Professor, Department of computer Applications, Kongu Arts and Science College, India Prema Selvaraj Bsc,M.C.A,M.Phil Assistant Professor,Department of Computer Science,KSR College of Arts and Science, Tiruchengode Mr. G. Rajendran M.C.A., M.Phil., N.E.T., PGDBM., PGDBF., Assistant Professor, Department of Computer Science, Government Arts College, Salem, India. Dr. Pradeep H Pendse B.E.,M.M.S.,Ph.d Dean - IT,Welingkar Institute of Management Development and Research, Mumbai, India Muhammad Javed Centre for Next Generation Localisation, School of Computing, Dublin City University, Dublin 9, Ireland Dr. G. GOBI Assistant Professor-Department of Physics,Government Arts College,Salem - 636 007 Dr.S.Senthilkumar Post Doctoral Research Fellow, (Mathematics and Computer Science & Applications),Universiti Sains Malaysia,School of Mathematical Sciences, Pulau Pinang-11800,[PENANG],MALAYSIA. Manoj Sharma Associate Professor Deptt. of ECE, Prannath Parnami Institute of Management & Technology, Hissar, Haryana, India RAMKUMAR JAGANATHAN Asst-Professor,Dept of Computer Science, V.L.B Janakiammal college of Arts & Science, Coimbatore,Tamilnadu, India

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Contents Dirichlet series and approximate method for the solution of axisymmetric flow over a stretching sheet by Vishwanath B. Awati ……......…………...…………..………………………………………………………………………[1] Optimization of Tribological Parameters in Al6061/SiC Metal Matrix Composite by Taguchi’s Technique by Ashok Kr Mishra, Rakesh Sheokand, Gopal Pr Yadav, Dr. B. C. Sharma, Dr. R. K. Srivastava ………………[10]

Dirichlet series and approximate method for the solution of axisymmetric flow over a stretching sheet Vishwanath B. Awati Department of Mathematics,Rani Channamma University,Belagavi - 591156, India. e-mail: await_vb@yahoo.com is caused by stretching sheet in opposite directions with the velocity is proportional to the distance from the fixed axis studied by Crane [5], and also he has given an elegant solution of the problem . The more interesting fact is that the problem still admits an exact analytical solution. The other effects are taken into account, such as suction at the sheet was discussed by (Gupta and Gupta [6]), viscoelasticity of the fluid by Ariel [7,8], partial slip at the boundary by Wang [9]. The problem of flow due to the radial stretching of the sheet (i. e the velocity of the sheet is proportional to the distance from a vertical rather than a horizontal axis) does not have an exact solution. For this reason, this problem has received much less attention in the literature. Wang [10], discussed the numerical solution of the flow due to the radial stretching of the sheet. The effects of viscoelasticity were studied by Ariel for an elastico-viscous fluid [11] and the second grade fluid by [12]. Areal [13], discussed the axisymmetric flow due to stretching of a sheet in hydromagnetics as the prototype problem for the non-iterative algorithm and also develops an algorithm for solving the problems of the flow induced by the moving boundaries in hydromagnetics. Hayat et al.[14] has used modified decomposition method and Pade’ approximants, for the solution of equation third order nonlinear ODE with infinite interval arsing in MHD. Shahzad et al [15], investigated the exact solution for axisymmetric flow and heat transfer over nonlinearly radially stretching sheet by HAM. Recently, Khan and Shahzad [16] have analysed the axisymmetric flow of sisko fluid over a radially stretching sheet using HAM.

Abstract— We study the boundary layer flows induced by the axisymmetric stretching of a sheets are studied using more suggestive schemes. The equation of motion of a axisymmetric flow over a stretching sheet and the sheet is stretched with a velocity is proportional to the distance from the vertical axis. The governing nonlinear differential equations are reduced to nonlinear linear ordinary differential equations (ODEs) by using similarity transformations. The resulting nonlinear ODEs are solved by using fast convergent Dirichlet series method and an approximate analytical method by Method of stretching of variables. These methods have advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and these are valid in much larger domain as compared with the classical numerical schemes.

Keywords: Axisymmetric flow; boundary layer equations; Stretching sheet; Dirichlet series; Powell’s method; Least square approximation I.

INTRODUCTION

In this discussion, we consider boundary layer flow over axisymmetric stretching of a sheet which are of significant interest in the recent years due to their applications. The third order nonlinear ordinary differential equation over an infinite interval with parameter M, Hartman number (magnetic field) is of special interest and in very few specific cases they have analytical solutions. The flow of a viscoelastic fluid over a stretching sheet was investigated by Rajagopal et al. [1], Sarpkaya [2] who probably the first to consider the MHD flow of non-Newtonian fluids. Andersson [3] and Mamaloukas et al. [4] have obtained similarity solution of the boundary layer equation governing the flow of a viscoelastic and a second grade fluid past a stretching sheet in the presence of an external magnetic field. The fluid occupies the space above the sheet and the motion

The present investigation is to analyze the boundary layer flow induced by axisymmetric stretching of a sheet given by Mirgolbabaei et al [17]. The solution of the resulting third order nonlinear boundary value

1

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 problem with infinite interval is obtained by Dirichlet series method and approximation method. We seek solution of the general equation of the type

f ′′′ + A ff ′′ + B f ′2 + C f ′ = 0

II. MATHEMATICAL FORMULATION OF THE PROBLEM

(1)

Consider the equation of motion of electrically conducting, viscous incompressible fluid caused by radial stretching sheet at z=0 in the presence of transverse magnetic field. The stretching velocity of the sheet is proportional to the distance from the origin of the sheet. In the cylindrical polar coordinates (r ,θ , z )

(2)

and the flow takes place in the upper half plane z > 0 . In view of the rotational symmetry of the flow all physical

with the boundary conditions

f ( 0) = α1, f ′ ( 0) = β1, f ′ ( ∞ ) = 0 )

quantities are independent of

where A, B and C are constants and prime denotes derivative with respect to the independent variable η . This equation admits a Dirichlet series solution; necessary conditions for the existence and uniqueness of these solutions may also be found in [18, 19]. For a specific type of boundary condition i.e.

θ i.e ∂ ∂θ ≡ 0 . The

equation of motion for steady, laminar, axisymmetric flow and continuity are of the form (Mirgolbabaei et al [17])

f ′ ( ∞ ) = 0 , the

ρ u

Dirichlet series solution is particularly useful for obtaining the derived quantities. A general discussion of the convergence of the Dirichlet series may also be found in Riesz [20]. The accuracy as well as uniqueness of the solution can be confirmed using other powerful semi-numerical schemes. Sachdev et al. [21] have analyzed various problems from fluid dynamics of stretching sheet using this approach and found more accurate solution compared with earlier numerical findings. Recently, Awati et al [22, 23] and Kudenatii et al [24] have analysed the problems from MHD boundary layer flow with nonlinear stretching sheet using the above methods and found more accurate results compared with the classical numerical methods. Dirichlet series solution and MSV which we present here is more attractive than adapted variational iteration method (AVIM) discussed by Mirgolbabaei et al [17].

∂u ∂u ∂p +w + =− ∂r ∂z ∂r (3) ∂ 2u 1 ∂u ∂ 2u u σB0 + + − − u , 2 r ∂r ρ ∂z 2 r 2 ∂r

µ

∂w

∂w

∂p

ρ u + w = − ∂z ∂r ∂r

∂ 2w 1 ∂w ∂ 2w + µ + + , 2 r ∂r ∂z 2 ∂r

∂u u ∂w + + ∂r r ∂z where

= 0,

(4)

(5)

is fluid density, µ is coefficient of viscosity,

σ is

the electrical conductivity of the fluid, p is the pressure

(u ,0, w ) are the velocity ( r ,θ , z ) directions. The boundary

and

The present work is structured as follows. In section 2 the mathematical formulation of the proposed problem with relevant boundary conditions is given. Section 3 is devoted to semi-numerical method for the solution of the problem using Dirichlet series. In section 4 the solution of the proposed problem by an approximate analytical method using the method of stretching of variables (MSV). In section 5 detailed results obtained by the novel method explained here are compared with the corresponding numerical schemes. Section 6 Conclusions.

components along conditions for the

above flow situations are

u = c r , w = 0 at z = 0 u → 0 as z → ∞

(6)

where c > 0 is the constant of proportionality relating to the stretching of the sheet. The boundary layer Eq. (3)-

2

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 .(6) admit the similarity solution (Wang [9]),

where p 0 is a constant. Substitution of g(r) from Eq.(13)

u =crf ′(η), w =−2 cυf (η), η= (c υ)z (7)

into Eq.(10) leads to

p = p0 +(1/2) ρc 2r 2A1−2cµf 2 −2cµf ′ (14)

υ = µ ρ is the kinematic viscosity of the fluid and prime denotes differentiation with respect to η , Since the entire motion of the fluid is caused due to where

stretching of the sheet, the pressure far away from the sheet must be given by the Bernoulli’s equation, i.e., Matching of the pressure from Eq. (14), gives A1=0. Hence from equation (11), we get the following DE for f (Mirgolbabaei et al [17])

eventually reduce the Navier-Stokes equation to an ODE. From Eq. (3), we get

∂p = ρc 2r f ′′′ + 2ff ′′ − f ′2 − M f ′ ∂r

(8)

f ′′′ + 2 ff ′′ − f ′2 − M f ′ = 0

M = σ B 0 ρ c is the magnetic parameter. On the where

Also the pressure p at any point in terms of the physical variables is

other hand Eq. (4), gives

∂p = −4c µ f f ′ − 2c µ f ′′ ∂η

1 ∂w p = p 0 − ρw 2 + µ 2 ∂z

(9)

which when integrated with respect to η yields,

p =−2cµf 2 −2c µf ′+g (r ),

ρc r 2

= f ′′′ + 2 f f ′′ − f ′2 − M f ′

f (0) = 0, f ′ (0) = 1, f ′ ( ∞ ) = 0

(10)

We seek a Dirichlet series solution of equation (1) satisfying the last boundary condition of Eq.(2)

(11)

automatically i.e f ′(∞ ) = 0 in the form of (Kravchenko and Yablonskii [18, 19])

6γ f = γ1 + A

order for it to be consistent, each side must be constant, say A1. Hence we have

2

(12)

where

∞

∑b a e i

i

i =1

− i γη (18)

γ and a are parameters. Substituting (18) into

(1), we get

Its integration with respect to r, gives

g ( r ) = p 0 + (1/2) ρ c 2r 2 A 1

(17)

III. DIRICHLET SERIES APPROACH TO THE BOUNDARY VALUE PROBLEMS OVER AN INFINITE INTERVAL

Since in Eq. (11), the left hand side is a function of r only, and the right hand side is a function of η only, in

g ′ (r ) = ρ c r A 1

(16)

The boundary conditions of the problem are

where g(r) is an arbitrary function of r. Substitute for p Eq. (10) into Eq. (8), we obtain

g ′(r )

(15)

(13)

3

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 ∞

∑{−γ i =1

helps in finding the unknown constants a and

i + A γγ 1i 2 − C i }b i a i e −iyη

2 3

uniquely for different values of the parameters A, B,

For i=1, we have

γ

γ

=

1

+ C A

C, α1 and β1. Alternatively, Newton’s method is also

(19)

6γ 2 ∞ i −1 + A k 2 + B k (i − k )}b k b i −k a i e −iyη = 0 { ∑∑ A i =2 k =1 2

γ

used to determine the unknown parameters a and γ

accurately. The shear stress at the surface of the problem is given by (20)

6γ A

f ′′ ( 0 ) =

Substituting (20) into (19) the recurrence relation for obtaining coefficients is given by

∞

∑

i =1

b ia

i

(i γ )

2

(25)

The velocity profiles of the problem is given by

bi =

i −1 6γ A k 2 + B k (i − k )}b k b i −k { ∑ 2 A i (i −1){γ i − C } k =1 2

(21)

f ′ (η

For i = 2, 3, ..... . If the series (18) converges absolutely when

γ >0

absolutely

η0 ,

for some

and

in

the

represents

half

an

analytic that series

These unknown parameters are determined from the remaining boundary conditions (2) at

and

γ2+C Aγ

+

6γ A

∞

∑b i =1

i

η =0

a i = α1

(22)

i =1

( − i )b i a i e

− iγη

(26)

R (ξ ,α ) which is called defect function. Using Least

6γ 2 ∞ ′ f ( 0) = ( −i ) b i a i = β1 ∑ A i =1

squares method, the residual of the defect function can be minimized. For details see (Ariel, [26]). Using the

(23)

transformation

The solution of these transcendental equations (22) and (23) yield, constants a and γ . The solution of these transcendental equations is equivalent unconstrained minimization of the functional 2

∞

∑

Many nonlinear ODE arising in MHD problems are not amenable for obtaining analytical solutions. In such situations, attempts have been made to develop approximate methods for the solution of these problems. The numerical approach is always based on the idea of stretching of variables of the flow problems. Method of stretching of variables is used here for the solution of such problems. In this method, we have to choose suitable derivative function H ′ such that the derivative boundary conditions are satisfied automatically and integration of H ′ will satisfy the remaining boundary condition. Substitution of this resulting function into the given equation gives the residual of the form

(18) contains two free parameters namely a and γ .

(0 ) =

2

IV. METHOD OF STRETCHING OF VARIABLES

plane

( 2π i γ ) periodic function f = f (η0 ) such f ′(∞ ) = 0 (Kravchenko & Yablonskii [19]). The

f

6γ A

this series converges

uniformly

Reη ≥ Reη0 and

)=

to

f = f w + F into Eq. (1), we get

F ′′′ + A ( f w + F ) F ′′ + B F ′2 + C F ′ = 0, 27)

the

and the boundary conditions (2) become 2

γ 2 +C 6γ 2 ∞ 6γ ∞ i + b a − α (−i ) bi a i −β1 ∑ ∑ i 1 + Aγ A i =1 A i =1

F ( 0) = 0, F ′ ( 0) = 1,

(24)

We introduce two variables

We use Powell’s method of conjugate directions (Press et al [25]) which is one of the most efficient techniques for solving unconstrained optimization problems. This

4

ξ

F ′ ( ∞ ) = 0 (28)

and Gin the form

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G (ξ ) = α F (η ) and ξ

= αη

f = fw +

(29)

where α >0, is an amplification factor. In view of Eq.(29), the system (27-28) are transformed to the form 2

(32)

which automatically satisfies the derivative conditions in Eq.(31). Integrating Eq. (32) with respect to ξ from 0 to using the first boundary conditions in (31) and then

substituting this into Eq. (30), we get the residual of the defect function

2 field Eq. (15) reduces to f ′′′ + 2 ff ′′ − f ′ = 0 and the

(33)

boundary conditions are same as of Eq.(17). We check the validity of our solution by comparing it with the exact solution. The measure of the physical quantity viz. shear

By using the least squares method as discussed in Ariel [26], the equation (33) can be minimized for which ∞

∂α

∫

R

2

(ξ , α )d ξ

= 0 .

stress at the sheet is − f ′′ ( 0) . The exact value

of − f ′′ ( 0) is 1.173721 and the value obtained by

(34)

Dirichlet series is 1.173721 and MSV is 1.15470.The error being very less as compared to AVIM.

0

Substituting (33) into equation (34) and solving cubic equation in α for a positive root, we get

α= and

(

1 3A f w ± 3 4A −8B −12C + 3A 2 f w2 6 α =

fw .

Case I. Consider the flow of a fluid with no magnetic

)

exp( − ξ ) + ( A + B ) exp( − 2ξ )

∂

defined in Eq. (35). Thus Eq. (36) gives the

In the present paper, the axisymmetric flow over a stretching of a sheet is discussed by using seminumerical method and approximate analytical method. The Eq. (15) and (17) are solved semi-numerically using one of the powerful techniques due to Dirichlet series method and the method of stretching of variables. We have given an exact analytical solution of the boundary value problem in more general form. In this seminumerical method and, it is important to note that the edge boundary condition automatically satisfied an also we have given analytical solution by approximate method.

(31)

We choose a trail velocity profile

R (ξ , α ) = (α 2 − A f w α − A + C

(36)

V. RESULT AND DISCUSSION

G (0) = 0, G′(0) = 1, G′(∞) = 0

ξ

(1− exp(−αη )) .

(30)

and the boundary conditions in Eq. (28) become

G ′ = exp(−ξ )

α

α

solution of Eq. (1) for all A , B , C and

α G ′′ + A ( f w α +G ) G ′ + BG ′ +CG ′ = 0, 2

with

1

Case II. In this case, consider the flow of an electrically conducting, viscous incompressible fluid over a radially stretching sheet in presence of a transverse magnetic filed. The governing equation is same as Eq. (15) and

)

M is the Hartmann number. As the value of M increased, Hartmann layers start in at η = 0 causing the

A fw . 2

great difficulties in obtaining the numerical solution. We have presented much better solution than AVIM by using Dirichlet series and MSV for arbitrary values of M which are comparable with exact numerical solutions by Ariel [26] which are listed in Table 1. The above said methods are capable for providing the solutions in the presence of Hartmann layers near the stretching sheet.

(35) Once the amplification factor is calculated, then using Eq.(27), original function f can be written as

5

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 Case III. The massive transfer of the fluid across the boundary, the type of the boundary layer is manifested near the boundary. The semi-numerical and approximation method are able to handle the suction boundary layer in an efficient manner with Hartmann layer. The suction takes place across the sheet, the boundary conditions (17) changes to

Case IV. In this case, we consider the flow of an electrically conducting viscous incompressible fluid due to radial stretching of a sheet in the presence of the transverse magnetic field and also the suction at the sheet. The governing equation is same as Eq. (15) and relevant

f w = ( w 0 2)

(ρ c µ )

conditions f (0) = f w , f ′(0) =1, f ′( ∞) =0.

Numerical computations are performed by using the above said methods for various values of the physical parameters involved in the equation viz., Hortmann

f (0) = f w , f ′(0) = 1, f ′( ∞) = 0, where f w is the suction

parameter given by

boundary

, where

number M, and mass suction parameter

w 0 is the suction velocity. The governing equation for f is

f w . The present

same as Eq. (15). The values of − f ′′ ( 0) are presented

solutions are then validated by comparing it with the previously published work of Migolbabaei et al [17] as

for various a vales of f w using Dirichlet series method

shown in the Tables 3.

and MSV are given in Table 2. and these values are comparable with numerical solution given by Ackroyd [27].

Table1. Comparison of Dirichlet series method, Method of stretching of variables (MSV) with exact solution and Adapted variational Iteration method (AVIM) for the flow in the presence of magnetic field. Dirichlet Series Method

Exact

MSV

AVIM

a

γ

− f ′′(0)

− f ′′(0)

− f ′′(0)

− f ′′(0)

0

-0.56719

1.50299

1.17372

1.17372

1.15470

1.182125

0.01

-0.18857

1.50659

1.17606

1.17783

1.15902

1.192910

0.04

-0.18627

1.51758

1.17902

1.17901

1.17189

1.209962

0.25

-0.16798

1.57558

1.25906

1.27303

1.25831

1.298851

1.0

-0.12258

1.77491

1.53417

1.53571

1.52752

1.556834

4.0

-0.05861

2.46267

2.31048

2.31172

2.30940

2.322880

25.0

-0.01249

5.19738

5.13178

5.13181

5.13160

5.151863

100

-0.00328

10.09967 10.06632 10.06647 10.06645 10.087672

500

-0.00066

22.40537 22.39211

---

22.39047

1000

-0.00033

31.65439 31.64398

---

31.64385

M

Table 2.Comparison of Dirichlet series method, Method of stretching of variables (MSV) with exact solution and Adapted variational Iteration method (AVIM) for the flow in the presence of magnetic field.

6

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Dirichlet Series Method A

Exact

MSV

− f ′′(0)

AVIM

a

γ

− f ′′(0)

− f ′′(0)

− f ′′(0)

0

-0.56719

1.50299

1.17372

1.17372 1.15470 1.182125

0.1

-0.16335

1.59707

1.27865

1.28242 1.25902 1.329105

0.2

-0.14159

1.69558

1.41216

1.40236 1.37189 1.488416

0.5

-0.09085

2.04339

1.79567

1.79867 1.75931 2.057265

Table 3. Comparison of Dirichlet series method, Method of stretching of variables(MSV) with exact solutionand Adapted variational Iteration method (AVIM) for MHD flow with sucion.

M

Dirichlet Series Method

Exact

γ

− f ′′(0)

A

a

− f ′′(0)

MSV

− f ′′(0)

AVIM

− f ′′(0)

0 -0.12258

1.77491

1.53417 1.53571 1.52753 1.556834

0.1 -0.10843

1.87345

1.64267 1.64312 1.63079 1.683059

0.2 -0.09608

1.97844

1.75491 1.75664 1.74056 1.821750

0.5 -0.06724

2.32755

2.13048 2.13194 2.10728 2.328433

0 -0.05861

2.46267

2.31049 2.31172 2.30940 2.322880

0.1 -0.05386

2.56390

2.41458 2.41586 2.41156 2.444133

0.2 -0.04948

2.66927

2.52468 2.52422 2.51804 2.576313

0.5 -0.03855

3.00932

2.87325 2.87403 2.86291 3.051377

0 -0.01249

5.19738

5.13178 5.13181 5.13160

0.1 -0.01202

5.29831

5.23308 5.23319 5.23258 5.289863

0.2 -0.01156

5.40116

5.33646 5.33653 5.33549 5.435615

0.5 -0.01029

5.72122

5.65798 5.65812 5.65590

1

4

5.15186

25

7

5.92565

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 withoutSuction. Journal of Computational and Applied Mathematics, vol. 59,pp. 9–24, 1995.

VI. CONCLUSIONS In this article, we describe the analysis of boundary value problem for third order nonlinear ODEs over an infinite interval arising in axisymmetric flow over a stretching sheet. The semi-numerical and an approximate analytical scheme described here offer some advantages over solutions by HAM, HPM, Adomain decomposition methods and AVIM etc. The convergence of the Dirichlet series methods is given. The results are presented in Tables.

[9] C. Wang , Flow due to a Stretching Boundary with Partial Slip-An Exact solution of the Navier-Stokes equations.Chemical Engineering Science, vol. 57, pp. 3745–3747 2002. [10] C.Wang, The three dimensional flow due to a stretching flat surface. Physics of Fluids, vol. 27,pp. 1915–1917, 1984. [11] P.D.Ariel, Computation of flow of viscoelastic fluids by parameter differentiation. International Journal for Numerical Methods in Fluids, vol. 15, pp.1295–1312, 1992. [12] P.D.Arie. Axisymmetric flow of a second grade fluid past a stretching sheet. International Journal of Engineering Science, vol. 39,pp. 529–553, 2001.

ACKNOWLEDGEMENTS The author is grateful to University Grant Commission, New Delhi for the financial support through Major Research Project (F. No. 41-781/2012 (SR)) for this work.

[13] P.D. Ariel, Computation of the MHD flow due to moving boundary. Trinity Western University. Dept. of Mathematical Sci. Tech. Report, 2004. MCS-2004-01. [14] T.Hayat, Q.Hussain and T. Javed , The modified decomposition method and Pade’ approximants for the MHD flow over nonlinear stretching sheet, Nonlinear Analysis: Real World Applications, vol. 10,pp. 966-973, 2009.

REFERENCES [1] K. R. Rajagopal, T.Y. Na and A.S. Gupta, AS., Flow of viscoelastic fluid over a stretching sheet, Rheology Acta.,vol. 23,pp. 213-215, 1984.

[15] A .Shahzad, R. Ali, M. Khan, On the exact solution for axisymmetric flow and heat transfer over nonlinear radially stretching sheet, Chin. Phys. Lett., Vol. 29(8), pp. 0847051-4, 2012.

[2] T. Sarpkaya, Flow of non-Newtonian fluids in a magnetic field AIChE. J.,vol 7,pp. 324-328, 1961.

[16] M.Khan, A. Shahzad, On axisymmetric flow of sisko fluid over a radially stretching sheet, Int. Jl.Nonlin. Mech.,vol. 47, pp. 999-1007, 2012.

[3] H.I. Andersson, MHD Flow of a Viscoelastic Fluid past a Stretching Surface. Acta Mechanica, , vol 95, pp. 227– 230, 1992.

[17] H.Mirgolbabaei, D.D.Ganji, M.M. Etghani and A. Sobati, Adapted variational iteration method and axisymmetric flow over a stretching sheet, World Jl. Modelling and Simulation, vol.5(4), pp. 307-314, 2009.

[4] Ch. Mamaloukas, S.Spartalis, Z. Manussaridus, Similarity approach to the problem of second grade fluid flows over a stretching sheet, ICNAAM, Wiley-VCH, ESCMSE, pp. 239-245, 2004. [5] L.Crane, Flow past a stretching sheet. ZAMP, vol. 21, pp. 645-647, 1970.

[18] T.K.Kravchenko, A.I.Yablonskii, Solution of an infinite boundary value problem for third order equation, Differential’nye Uraneniya, vol. 1,pp. 327, 1965.

[6] P. Gupta, A. Gupta , Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing. Can. J. Chem Eng., vol. 55, pp. 744-746,1977.

[19] T.K. Kravchenko, A.I.Yablonskii, A boundary value problem on a semi-infinite interval, Differential’nye Uraneniya, vol. 8(12), pp. 2180-2186, 1972.

[7] P.D. Ariel, A Hybrid Method for Computing the Flow of Viscoelastic Fluids. Int. Jl. Numerical Methods in Fluids, vol. 14, pp. 757–774, 1992.

[20] S.Riesz , Introduction to Dirichler series, Camb. Univ. Press, 1957.

[8] P.D.Ariel, A Numerical Algorithm for Computing the Stagnation Point Flow of a Second Grade Fluid with or

[21] P.L.Sachdev, N. M.Bujurke and V. B. Awati, Boundary value problems for third order nonlinear ordinary differential equations, Stud. Appl. Math., vol. 115, pp. 303-318, 2005.

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 [22] V.B.Awati , N.M.Bujurke and R.B.Kudenatti, An exponential series method for the solution of the free convection boundary layer flow in a saturated porous medium. AJCM, vol. 1 , pp. 104-110, 2011.

[25] W.H.H.Press, B.P.Flannery, S.A.Teulosky and W.T.Vetterling, Numerical Recipes in C, Camb. Univ. Press, UK, 1987. [26] P.D.Ariel, Stagnation point flow with suction ; an approximate solution. Journal of Applied Mechanics, vol. 61(4), pp. 976-978, 1994.

[23] V.B.Awati ,N.M. Bujurke and R.B. Kudenat, Dirichlet series method for the solution of MHD flow over a nonlinear stretching sheet. IJAMES, vol. 5(1), pp.07-12, 2011.

[27] J. A. D. Ackroyd, A series method for the solution of laminar boundary layers on moving surface, ZAMP, vol. 29, pp.729-741, 1978.

[24] R.B.Kudenatti, V.B.Awati and N.M.Bujurke, Exact analytical solutions of class of boundary layer equations for a stretching surface, Appl Math Comp, vol. 218, pp. 29522959, 2011.

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Optimization of Tribological Parameters in Al6061/SiC Metal Matrix Composite by Taguchi’s Technique 1

2

3

4

5

Ashok Kr Mishra , Rakesh Sheokand , Gopal Pr Yadav , Dr. B. C. Sharma , Dr. R. K. Srivastava 1. Astt. Prof. in BRCM College of Engineering & Technology, Bahal 2. Astt. Prof. in Jind Institute of Engineering & Technology, Jind 3. Prof. & Head Deptt. of Mechanical, BRCM CET, Bahal 4. Principal & Prof. in BRCM CET, Bahal 5. Prof. & Head Deptt. of Production, B. I. T. Sindri, Jharkhand 1 Corresponding Author : email: ashokaero04@gmail.com

enhance their uses in automotive and tribiological application in the field of automobile,MMCs are used for piston, Brake Drum and Cylinder block because of better corrosion and wear resistance [7,8].

Abstract Tribological behavior of aluminium alloy Al 6061 reinforced with silicon carbide (10%) fabricated by stir casting process was investigated. Dry sliding wear test was conducted to understand the tribological behavior of samples. This study is carried out to optimize the tribological properties: wear rate & frictional force of Al / SiC metal matrix composite. The experiments were conducted as the Taguchi design of experiment. A L9 orthogonal array was selected for analysis of the data. The wear parameters chosen for the experiment were: sliding speed, applied load & sliding distance. Each parameter was assigned three levels. Signal to Noise ratio analysis has been carried out to determine optimal parametric condition, which yields minimum wear rate & frictional force. Investigation to find the influence of applied load, sliding speed and sliding distance on wear rate, as well as the frictional force during wearing process was carried out using ANOVA and regression equations for each response were developed. Objective of the model was chosen as “smaller the better” characteristics to analyze the dry sliding wear resistance. Result show that sliding distance and load have the highest influence on minimum wear rate and frictional force respectively. Finally, confirmation tests were carried out to verify the experimental results and Scanning Electron Microscopic (SEM) studies were done on the wear surfaces.

The principle tribiological parameter effects the friction and wear performance of dis-continously reinforced aluminium composite are surface interaction, Mechanical characteristic (Extrinsic to materials), Material characteristic (Intrinsic to material) and tribocontact condition. Most frequently encountered factors which are associated with four tribological parameter such as mechanical parameter, surface interaction, material parameter and tribo contact which yields wear and friction mechanism. The mechanical parameter depends upon the different factor such as loading condition, contact geometry and duration of interaction. Surface interaction parameter depends upon the various operations such as rolling, sliding, impact, erosion, fretting and reciprocating. Material parameter associated with types of chemical bonding, thermal properties, fracture toughness, hardness and yield strength. Tribo contact parameter concern with chemical reaction during dry or lubricated sliding. Dry sliding wear behavior of Al Metal Matrix Composite has been reported (and abrasive wear of Al Composites has extensively reviewed by Deuis et al [13]. Uyyuru et al [14] studied the effect of reinforcement volume fraction and size distribution of reinforced the tribological behavior of AlComposites and Martin investigated the temperature effect on the wear behavior of particulate reinforced Al based composite[15] and influence of heat treatment on the wear behavior of Al Composites by M. A. Chowhury et al[12]. Effect of aging on behavior of MMCs was carried out by Guo et al [16] The result shows that SiC particles are effective agents in increasing dry sliding wear resistance of Al6061/SiC Composite.

Keywords: Metal matrix composites; Silicon Carbide; Taguchi Technique; Signal to Noise I. INTRODUCTION In the last two decades, Researcher has shifted from monolithic materials to composite materials to meet the global demand for light weight, high performance, environmental friendly, wear & corrosion resistant materials. Particulate reinforced metal matrixes Composites have combination of low density, improved stiffness and strength, high wear resistance and isotropic properties [5]. These properties of MMCs

10

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 Much research carried out to understand wear behavior of composite material. Meager information is available regarding the optimization of tribological parameters: Sliding wear rate and Frictional force of the metal matrix composite. In this light, this study is carried out to optimize tribological parameters of Silicon Carbide (10%) reinforced Al Metal Matrix Composite using Taguchi’s Parameter design methodology.

2.2 Composite Preparation In order to achieve high level of mechanical properties in the composite, a good interfacial bonding (wetting) between the dispersed phase and the liquid matrix has to be obtained. Stir-casting technique is one such simplest and cost effective method to fabricate metal matrix composites which has been adopted by many researchers. This method is most economical to fabricate composites with discontinuous fibres and particulates and was used in this work to obtain as the cast specimens. Care was taken to maintain an optimum casting parameter of pouring temperature (650°C) an d stirring time (15 min). The reinforcements were preheated prior to their addition in the aluminium alloy melt. Degassing agent (hexachloro ethane) was used to reduce gas porosities. The molten metal was then poured into a permanent cast iron mould of diameter 26mm and length 300mm. The die was released after 6 hours and the cast specimens were taken out.

1.1 Design of Experiment Quality characteristic of a product under investigation in response to a factor introduced in the experimental design is the ‘signal’ of the desired effect. The effect of external factors (uncontrollable factor) on the outcome of quality characteristics under test is termed as ‘noise’. The S/N Ratio measures the sensitivity of the quality characteristic being investigated in a controlled manner to those of external influencing factors (noise factor) not under control. The S/N Ratio is transformed figure of merit, created from the loss function. S/N Ratio combines both the parameters (the mean level of the quality and the variation around this mean) in a signal metric. The aim in any experiment is always to determine the highest possible ratio for the result (wear rate and frictional force) a high value of S/N Ratio implies the signal is much higher then the random effect of noise factor.

2.3 Wear Behaviour The aim of the experimental plan is to find the important factors and combination of factors influencing the wear process to achieve the minimum wear rate and frictional force. The experiments were developed based on an orthogonal array, with the aim of relating the influence of sliding speed, applied load and sliding distance. These design parameters are distinct and intrinsic feature of the process that influence and determine the composite performance [17]. Taguchi recommends analysing the S/N ratio using conceptual approach that involves graphing the effects and visually identifying the significant factors.

II. EXPERIMENTAL DETAILS

2.1 Test Materials In the present investigation, Al 6061 was chosen as the base matrix since its properties can be tailored through heat treatment process. The reinforcement of SiC was, average size of 150 to 160 microns, and there are sufficient literatures including the improvement in wear properties through the addition of SiC. Due to the property of high hardness and high thermal conductivity, SiC after accommodation in soft ductile aluminium base matrix, enhance the wear resisting behaviour of the Al / SiC metal matrix composite.

2.4 Plan of experiment using orthogonal array Dry sliding wear test was performed with three parameters: applied load, sliding speed, and sliding distance and varying them for three levels. According to the rule that degree of freedom for an orthogonal array should be greater than or equal to sum of those wear parameters, a L9 Orthogonal array which has 9 rows and 3 columns was selected.

Table 1 Chemical composition of matrix alloy Al – 6061 C he m i c a l c o m p o s i ti o n

Si

Fe

Cu

Mn

Mg

Cr

Zn

Ti

Al

%

0 .4 -0 .8

0 .7

0 .1 5 -0 .4 0

0 .1 5

0 .8 -1 .2

0 .0 4 - 0 .3 5

0 .2 5

0 .2

B a l a nc e

Table 2 Process parameters and levels L evel 1 2 3

11

L o a d (N ) 10 20 30

S lid i n g S p e e d ( m /s ) 2 3 4

S lid i n g D is ta n c e (m ) 1000 1750 2500

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 2.5 Experimental Procedure

Where n = no. of tests in a trial

To evaluate the tribological performance of the composites under dry sliding condition, wear tests were carried out on a pin on disc type friction and wear monitoring test rig. Specimens of size 10 mm diameter and 25 mm length were cut from the cast samples, and then machined. The contact surface of the cast sample (pin) was made flat so that it should be in contact with the rotating disk. During the test, the pin was held pressed against a rotating EN31 carbon steel disc (hardness of 65HRC) by applying load that acts as counterweight and balances the pin. The track diameter was varied for each batch of experiments in the range of 50 mm to 100 mm and the parameters such as the load, sliding speed and sliding distance were varied in the range given in Table 2. A LVDT (load cell) on the lever arm helps determine the wear at any point of time by monitoring the movement of the arm. Once the surface in contact wears out, the load pushes the arm to remain in contact with the disc. This movement of the arm generates a signal which is used to determine the maximum wear and the coefficient of friction is monitored continuously as wear occurs and graphs between co-efficient of friction and time was monitored for the specimens i.e., 10 % SiC/ Al-6061 MMCs.

For the present study n = 2 The aim of this experiment is to determine the highest possible Signal to Noise ratio for the parameters under study. A high value of S/N ratio implies that signal is much higher than the random effects of noise factors. The S/N ratio was computed using above formula for each response of the Table 3. 3.2 Results of Statistical Analysis of Experiments The results for various combinations of parameters were obtained by conducting the experiment as per the orthogonal array. The measured results were analysed using the commercial software MINITAB 15 specifically used for design of experiment applications [23]. Table 3 shows the experimental results average of two repetitions for wear rate and frictional force. To measure the quality characteristics, the experimental values are transformed into signal to noise ratio. The influence of control parameters such as load, sliding speed, and sliding distance on wear rate and frictional force has been analysed using signal to noise response table. The ranking of process parameters using signal to noise ratios obtained for different parameter levels for wear rate & frictional force are given in Table 3 and Table 4 for 10% reinforced SiC MMCs. The control factors are statistically significant in the signal to noise ratio and it could be observed that the sliding distance is a dominant parameter on the wear rate and frictional force followed by applied load significantly. Figure 1 to Figure 4 shows for 10% influence of process parameters on wear rate and coefficient of friction graphically. The analysis of these experimental results using S/N ratios gives the optimum conditions resulting in minimum wear rate and coefficient of friction. The optimum condition for wear rate and frictional force as shown in Table 8.

Table 3 Results of L9 Orthogonal array for Al – 6061 / 10% SiC MMC S. No.

L (N )

S (m /s )

D (m )

1 2 3 4 5 6 7 8 9

10 10 10 20 20 20 30 30 30

2 3 4 2 3 4 2 3 4

1 00 0 1 75 0 2 50 0 1 75 0 2 50 0 1 00 0 2 50 0 1 00 0 1 75 0

F ric tio na l F o rc e (F F ) N 3 .1 1 2 .9 0 2 .7 7 7 6 .8 6 7 .4 4 1 0 .8 1 2 .3 1 1 .7

W e a r r a te (m m 3 /m )

S /N ra tio (F F ) db

S /N ra tio (w e a r ra te ) d b

0 .0 0 4 8 1 0 .0 0 3 6 0 .0 0 1 7 8 0 .0 0 4 2 2 0 .0 0 2 2 2 0 .0 0 3 7 0 .0 0 2 9 6 0 .0 0 3 7 0 .0 0 2 5 4

- 9 .8 5 5 2 - 9 .2 7 7 9 - 8 .8 4 9 6 - 1 6 .9 0 2 - 1 6 .7 2 6 5 - 1 7 .4 3 1 5 - 2 0 .6 6 8 5 - 2 1 .7 9 8 1 - 2 1 .3 6 3 7

4 6 .3 5 7 1 4 8 .8 7 3 9 5 4 .9 9 1 6 4 7 .4 9 3 8 5 3 .0 7 2 9 4 8 .6 3 6 0 5 0 .5 7 4 2 4 8 .6 3 6 0 5 1 .9 0 3 3

III. RESULT DISCUSSION 3.1 Signal to Noise Ratio

3.3 Analysis of Variance Results for Wear Test

The experimental observations are transformed into Signal to Noise ratio. There are several S/N ratios available depending on the type of characteristics under study. The wear rate & frictional force are coming ‘smaller is better’ type of quality characteristic and the respective S/N ratio is calculated using formula given below.

The experimental results were analysed with Analysis of Variance (ANOVA) which is used to investigate the influence of the considered wear parameters namely, applied load, sliding speed, and sliding distance that significantly affect the performance measures. By performing analysis of variance, it can be decided which independent factor dominates over the other and the percentage contribution of that particular independent variable. Table 6 and Table 7 shows 10% SiC MMCs of the ANOVA results for wear rate and coefficient of

S/N

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 friction for three factors varied at three levels and interactions of those factors. This analysis is carried out for a significance level of •=0.05, i.e. for a confidence level of 95%. Sources with a P-value less than 0.05 were considered to have a statistically significant contribution to the performance measures.

M a in E ff e c t s P l o t f o r M e a n s D a ta M e a n s LO AD

V E L O C ITY

0 .0 0 4 0

M ea n o f M ea n s

0 .0 0 3 5

Table 4 Response Table for Signal to Noise Ratios Smaller is better (Wear Rate)

0 .0 0 3 0 0 .0 0 2 5 10

20 D IS T A N C E

30

1 00 0

1750

250 0

2

4

3

0 .0 0 4 0 0 .0 0 3 5 0 .0 0 3 0 0 .0 0 2 5

L evel 1 2 3 D e lta R ank

L oad 5 0 .0 7 4 9 .7 3 5 0 .3 7 0 .6 4 3

S pe e d 4 8 .1 4 5 0 .1 9 5 1 .8 4 3 .7 0 2

D is t a n c e 4 7 .8 8 4 9 .4 2 5 2 .8 8 5 .0 0 1

S ig n a l - to - n o is e : S m a lle r to b e tte r

Fig.3 Main effects plot for Means –Wear Rate M a i n E ff e c t s P l o t f o r S N ra ti o s D a ta M e a n s

Table 5 Response Table for Signal to Noise Ratios Smaller is better (friction force)

LOAD

V E L O C IT Y

5 2 .8

L oad - 9 .3 2 8 -1 7 .0 2 0 -2 1 .2 7 7 11 .9 4 9 1

S peed -1 5 . 8 0 9 -1 5 . 9 3 4 -1 5 . 8 8 2 0 .1 2 6 3

M e a n o f S N ra tio s

5 1 .6

L evel 1 2 3 D e lta R ank

D i s ta n c e -1 6 .3 6 2 -1 5 .8 4 8 -1 5 .4 1 5 0 .9 4 7 2

5 0 .4 4 9 .2 4 8 .0 10

20 D IS T A N C E

30

1000

1750

2500

2

4

3

5 2 .8 5 1 .6 5 0 .4 4 9 .2

M a i n E ff e c t s P l o t f o r S N ra ti o s

4 8 .0

D a ta M e a n s LOAD

V E L O C IT Y

- 1 0 .0

S ig n a l - to - n o is e : S m a lle r to b e tte r - 1 2 .5

M e a n o f S N ra tio s

- 1 5 .0

Fig.4 Main effects plot for S/N ratios –Wear Rate

- 1 7 .5 - 2 0 .0 20 D IS T A N C E

10

30

2

4

3

Table 6 Analysis of Variance for Means (Wear Rate)

- 1 0 .0 - 1 2 .5

S o u rc e L o ad S peed D istan ce E rro r T o ta l

- 1 5 .0 - 1 7 .5 - 2 0 .0 1000

1 75 0

2 50 0

S ig n a l - to - n o is e : S m a lle r to b e tte r

Fig.1 Main effects plot for S/N ratios –Frictional force

S o u rc e L oad S peed D is ta n c e R e s id u a l E r ro r T o ta l

D a ta M e a n s V E L O C ITY

12 10 8

M ea n of M eans

Seq S S 0 .6 0 9 5 2 0 .6 3 8 1 3 9 .3 6 9 7 2 .2 0 3 1 6 2 .8 2 0 3

A dj S S 0 .6 0 9 5 2 0 .6 3 8 1 3 9 .3 6 9 7 2 .2 0 3 1

A dj M S 0 .3 0 4 7 1 0 .3 1 9 0 1 9 .6 8 4 9 1 .1 0 1 5

F 0 .2 8 9 .3 7 1 7 .8 7

P 0 .7 8 3 0 .0 9 6 0 .0 5 3

Pr (% ) 0 .9 7 0 2 2 8 3 2 .8 5 2 6 6 2 .6 7 0 3 5 3 .5 0 6 9 8 7 100

Table 7 Analysis of Variance for Means (Frictional force)

M a in E ff e c t s P l o t f o r M e a n s L O AD

DF 2 2 2 2 8

DF 2 2 2 2 8

S eq S S 2 2 0 .0 7 7 0 .0 2 4 1 .3 4 8 0 .0 5 6 2 2 1 .5 0 5

A dj S S 2 2 0 .0 7 7 0 .0 2 4 1 .3 4 8 0 .0 5 6

A dj M S 1 1 0 .0 3 9 0 .0 1 2 0.6 7 4 0 .0 2 8

F 3 8 9 6 .4 0 0 .4 2 2 3.8 6

P 0 .0 0 0 0 .7 0 3 0 .0 4 0

P r(% ) 9 9 .3 5 5 3 2 0 .0 1 0 8 3 5 0 .6 0 8 5 6 4 0 .0 2 5 2 8 2 100

6

It can be observed that for aluminium 10% SiC Metal Matrix Composites, from the Table 6,that the sliding distance has the highest influence (Pr =62.5%) on wear rate. Hence sliding distance is an important control factor to be taken into consideration during wear process followed by applied loads (P=0.99%) & sliding speed (Pr=32.85%) respectively. The pooled error is very low accounting for only 3.5%. In the same way from the Table 7 for frictional force, it can observe that the load has the highest contribution of about 99.35%,

4 10

20 D IS T A N C E

30

1 000

1 750

250 0

2

3

4

12 10 8 6 4

S ig n a l - to - n o is e : S m a lle r to b e tte r

Fig.2 Main effects plot for Means –Frictional force

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 MMCs. This can be attributed to the oxidation of aluminium alloy Al – 6061 which forms an oxide layer at higher interfacial temperature thus preventing the sliding, thereby decreases the wear rate & frictional force which is represented in Eq (2) and a similar behaviour has been observed [17].

followed by sliding distance (0.6%) & sliding speed (0.01%) for Al-6061 with 10% SiC metal matrix composites means that negligible effect of rest both parameters. The interaction terms have little or no effect on wear rate & frictional force & the pooled errors accounts only 3.5% & 0.025%. From the analysis of variance & S/N ratio, it is inferred that the sliding distance and applied load have the highest contribution on wear rate & frictional force respectively.

From Eq (2), it is observed that the positive value of coefficient of applied load & sliding speed reveals that increase in applied load & sliding speed increases the wear rate and frictional force of 10% reinforced SiC metal matrix composites. This can be related to the reinforcement of weight percentage of silicon carbide in Al – 6061 MMCs from 10% resulted the hard & tough property of the material. Wear rate & Frictional force are largely governed by the interaction of two sliding surfaces.

IV. MULTIPLE LINEAR REGRESSION MODEL A multiple linear regression model is developed using statistical software “MINITAB 15”. This model gives the relationship between an independent / predicted variable & a response variable by fitting a linear equation to observe data. Regression equation thus generated establishes correlation between the significant terms obtained from ANOVA analysis namely applied load, sliding speed & sliding distance.

To understand the wear mechanism of composites for 10% SiC, the worn surfaces were examined by Scanning Electron Microscope. During sliding, the entire surface of the pin has contact with the surface of the steel disc & machine marks can also be observed. Fig: 5 shows the microstructure of the worn surfaces of composites (for 10% SiC) at an applied load 30 N, sliding distance of 1000 m for sliding speed of 2 m/s, 3 m/s and 4 m/s respectively. Grooves were mainly formed by the reinforcing particles of SiC. As the sliding speed increases, the number of grooves also increases & the reinforcements are projecting out from the surface due to ploughing action counterface & pin and formation of wear debris was also observed in 10% SiC reinforced Al-6061 MMCs.

The regression equation developed for Al-6061 / (10%) SiC MMCs wear rate (Wr) and frictional force (FF) are as follows Wr = 0.00764 - 0.000016 L - 0.000662 S - 0.000001 D Eq (1) FF = - 1.02 + 0.433 L + 0.167S - 0.000538 D (2)

Eq

From Eq (1), it is observed that the applied load, sliding speed & sliding distance increases or decreases at any parametric value, it will be decrease the wear rate of the value of 0.00764mm3/m. But in case of frictional force Eq (2), applied load plays a major role as well as followed by sliding speed and sliding distance. Overall for the 10% reinforced SiC in Al-6061 MMCs regression equation gives the clear indication about frictional force is highly influenced by applied load. Following are the observation of optimum level process parameter for wear rate and frictional force.

The negative value of distance is indicative that increase in sliding distance decreases the wear rate as well as frictional force for both MMCs, the presence of hard SiC particle which provides abrasion resistance, resulting in enhanced dry sliding wear performance.

Table 8 Optimum level Process Parameters for Wear Rate and Frictional Force

30

S liding S p e e d (m /s ) 3

S l id ing D is ta nc e (m ) 1000

10

2

1750

S r. N o .

L o a d (N )

1 2

W e a r R a te (m m 3 /m ) 0 .0 0 3 7

F ric tio na l f o rc e (N )

S /N R a tio (d b) 4 8 .6 3 6 0

3 .1 1

4 9 .9 7 8 8

V. CONFIRMATION TEST A confirmation experiment is the final step in the Design process. A dry sliding wear test was conducted using a specific combination of the parameters & levels to validate the statistical analysis.

From Eq (1), observed that the negative value of coefficient of speed reveals that increase in sliding speed decreases the wear rate of 10% reinforced SiC

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 •

After the optimal level of testing parameters have been found, it is necessary that verification tests are carried out in order to evaluate the accuracy of the analysis & to validate the experimental results. Table 11 Confirmation Experiment for Wear Rate and Coefficient of Friction MMCs

Exp. No.

Load(N)

Sliding Speed(m/s)

Sliding Distance(m)

1

13

2.4

1200

2

19

2.8

1800

3

28

3.5

2200

Al6061+10% SiC

REFERENCES [1]. Boq-Kong Hwu, ‘Effects of process parameters on the properties of squeeze-cast SiC,-606 1 Al metal-matrix composite, Materials Science and Engineering’, A 207 (1996). [2]. Mingzhao Tan, Qibin Xin, Zhenghua Li, B. Zong, Y. ‘Influence of SiC & Al2O3 particulate reinforcements & heat treatments on mechanical properties & damage evolution of Al-2618 Metal Matrix Composites’, Journal of Materials Science 36(2001), 2045-2053. [3]. D.K. Dwivedi, ‘Adhesive wear behaviour of cast aluminium–silicon alloys: Overview, Materials and Design’, 31 (2010) 2517–2531. [4]. Dinesh. A, S. Basavarajappa, ‘Dry sliding wear studies on hybrid mmc’s - a Taguchi technique’, International Symposium of Research Students on Materials Science and Engineering, 2004. [5]. E. Candan , H. Ahlatci , H. C. Imenoglu (2001) ‘Abrasive wear behaviour of Al–SiC composites produced by pressure infiltration technique’. Wear 247 133–138. [6]. G. B. Veeresh Kumar, C. S. P. Rao (2011) ‘Mechanical and Tribological Behavior of Particulate Reinforced Aluminum Metal Matrix Composites – a review’, Journal of Minerals & Materials Characterization & Engineering, Vol. 10, No.1, pp.59-91. [7]. Hemanth Kumar. T.R., ‘Taguchi Technique for the Simultaneous Optimization of tribological Parameters in Metal Matrix Composite’ Journal of Minerals & Materials Characterization & Engineering, Vol. 10, No.12, pp.11791188, 2011. [8]. Hsiao Yeh Chu, Jen Fin Lin, ‘Experimental analysis of the tribological behavior of lectroless nickel-coated graphite particles in aluminum matrix composites under reciprocating motion Wear’ 2000, 126–142. [9]. Hui-Hui Fu, Wear properties of Saffil/Al, Saffil/Al2O3/Al and Saffil/SiC/Al Hybrid metal matrix composites, Wear 256 (2004) 705–713. [10]. J.S.S. Babu , C.G. Kang ,H.H. Kim, Dry sliding wear behavior of aluminum based hybrid composites with graphite nano fiber–alumina fiber, Materials and Design 32 (2011) 3920–3925 [11]. K.C. Chan, A theoretical and experimental investigation of surface generation in diamond turning of an Al6061/SiCp metal matrix composite, International Journal of Mechanical Sciences 43 (2001) 2047–2068.

Table 12 Result of Confirmation Experiment and their comparison with Regression MMCs A l6 0 6 1 + 1 0 % S iC

E xp. W ear R a te (m m 3 /m ) 0 .0 0 5

R e g . M o d e l E q (1 ), W e a r R a te (m m 3 /m ) 0 .0 0 4 6 4

7 .8 9

E x p . F ric tio na l F o rc e (N ) 4 .1 4 1 5

R e g . M o d e l E q (2 ), F ric tio na l F o rc e (N ) 4 .3 6 4 2

0 .0 0 3 8 9

0 .0 0 3 6 8

5 .7

6 .1 4 1 3

6 .7 0 6 2

8 .1 2 5

0 .0 0 3 0 8

0 .0 0 2 7 7

1 1 .2 3

1 0 .1 5 9 3

1 0 .5 0 4 9

3 .2 9

% E rro r

Confirmation experiment was carried out & made a comparison between experimental values showing an error associated with dry sliding wear rate & frictional force in composites varying from 5.7% to 11.23%, and 3.29% to 8.125% respectively. Thus design of experiments by Taguchi method was successfully used to optimize the parameter for tribological behavior of composites.

% E rro r 5 .1 1

The experimental value of wear rate is found to be varying from wear rate calculated in regression equation by error percentage between 5.7% to 11.23%, while for frictional force it is between 3.29% to 8.125% for 10% weight percentage of SiC reinforced with Al-6061 MMCs. 6. Conclusions Following are the conclusions drawn from the study on dry sliding wear test using Taguchi’s technique. •

Sliding distance (62.67%) has the highest influence on wear rate followed by sliding speed(32.85%) and applied load (0.97%) and for frictional force, the contribution of applied load is 99.36%, sliding distance is 0.608% for Al – 6061/ 10% SiC metal matrix composites.

•

From the above conclusion we predict that sliding distance & applied load have the highest influence on wear rate & frictional force in composites.

•

Regression equation generated for the (10% SiC MMCs) present model was used to predict the wear rate & frictional force of Al – 6061/(10%) SiC MMCs for intermediate conditions with reasonable accuracy.

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INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.11 NOVEMBER 2012 [12]. M. A. Chowdhury The Effect of Sliding Speed and Normal Load on Friction and Wear Property of Aluminum , International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol: 11 No: 01. [13]. R. L. Deuis, C. Subrananian & J. M. Yellup, ‘Abrasive wear of Aluminium composites- A review’, Wear, 201. (1996) 132-144. [14]. R. K. Uyyuru, M. K. Surappa, S. Brusethaug, Effect of reinforcement of volume fraction & size distribution on the tribological behavior of Al- Composite’, Wear, 260 (2006) 1248-1255. [15]. Miroslav Babic - Mitrovic Slobodan, Tribological Behavior of Composites Based on ZA-27 Alloy Reinforced with Graphite Particles, Tribol Lett (2010) 37:401–410. [16]. M.L.Ted Guo,C.-Y.A.Tsao, Tribological behavior of self-lubricating aluminium / SiC / graphitehybrid composites synthesized by the semi-solid powder-densification method Composites Science and Technology 60 (2000) 65-74. [17]. N.Radhika,R.Subramanian, Tribological Behaviour of aluminium / Alumina / Graphite Hybrid Metal Matrix Composite Using Taguchi’s Techniques, Journal of Minerals & materials Characterization & Engineering, Vol. 10, No.5, pp.427-443, 2011. [18]. Ramachandra M, Radhakrishna, ‘Sliding wear, slurry errosive wear & corrosive wear of Al/SiC Composites’, Material Science, Vol. 24, [19]. G. Taguchi, introduction to quality engineering, Asian productivity orgnization, 1990. [20]. P. J. Ross, Taguchi Technique for Quality nd Engineering, McGraw Hill, NewYork, Ny, USA, 2 edition1996. [21]. R. A. Fisher, Design of Experiments, Oliver & Boyd, Edinburgh, UK, 1951. [22]. S. Basavarajappa, G. Chandramohan , Application of Taguchi techniques to study dry sliding wear behaviour of metal matrix composites, Materials and Design 28 (2007) 1393–1398. [23]. Mintab User Manual (Release 13.2), Making Data Analysis Easier, MINITAB, State College, Pa, USA, 2001.

[24]. S.Basavarajappa and G.Chandramohan , Wear Studies on Metal Matrix Composites: a Taguchi Approach , J. Mater. Sci. Technol., Vol.21 No.6, 2005. [25]. S. Dharmalingam, R. Subramanian, Optimization of Tribological Properties in Aluminum Hybrid Metal Matrix Composites Using Gray-Taguchi Method, JMEPEG (2011) 20:1457–1466. [26]. Slobodan Mitrovi, Miroslav Babi, Tribological potencial of hybrid composites based on zinc and aluminium alloys reinforced with sic and graphite particles, 12th International Conference onTribology. [27]. S. Suresha, B.K. Sridhara, Friction characteristics of aluminium silicon carbide graphite hybrid composites Materials and Design 34 (2012) 576–583. [28]. S.V.S. Narayana Murty, On the hot working characteristics of 6061Al–SiC and 6061Al–Al2O3 particulate reinforced metal matrix composites, Composites Science and Technology 63 (2003) 119–135. [29]. T. Sritharan, L.S. Chan, A feature of the reaction between Al and SiC particles in an MMC, Materials Characterization 47 (2001) 75– 77. [30]. Ashok Kr. Mishra, Rakesh Sheokand, Dr. R K Srivastava AlTribological Behaviour of Al-6061 / SiC Metal Matrix 6061 Composite by Taguchi’s Techniques, International Journal of Scientific and Research Publications, Volume 2, Issue 10, October 2012

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IJITCE November 2012

International Journal of Innovative Technology and Creative Engineering (ISSN:2045-8711). Vol.2 Issue.11

IJITCE November 2012

Published on Dec 26, 2012

International Journal of Innovative Technology and Creative Engineering (ISSN:2045-8711). Vol.2 Issue.11

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