
Archive issue  vol.6 No.1
No. 
Author(s)  Title 
Pages 
1. 
 75th Anniversary of Professor Edward KACKI 
79 
2. 
Dhar A.K. and Das K.P.  The effect of randomness on stability of surface gravity waves from fourth order nonlinear evolution equation 
1134 
3. 
Thangaraj R.P.  The effect of nonuniform basic temperature gradient on the convective instability of a fluid layer sandwiched between two porous layers with general velocity and thermal conditions 
3552 
4. 
Ataş C., Özcan R. and Aykul H.  Residual stress analysis and plastic zone behavior in antisymmetric metalmatrix laminated composite plates 
5370 
5. 
Mohapatra P., Padhy S. and Tripathy S.  Finite difference analysis of the flow of a second order liquid past an infinite vertical plate in the presence of a magnetic field 
7190 
6. 
Mazumder S.K. and Chattopadhyay A.K.  The stability of oil journal bearing including bearing surface deformation and variation of oil viscosity 
91106 
7. 
Yukhvid A.V., Stolin A.M., Yukhvid V.I. and Stelmakh L.S.  The melt spreading along the substrate surface in the course of SHS surfacing 
107116 
8. 
ElAmin M.F. and Mohammadien A.A.  MHD effects on a powerlaw fluid past a vertical plate embedded in a porous medium with variable surface heat flux 
117131 
9. 
Das S.  Three interfacial Griffith cracks between bonded dissimilar elastic media 
133149 
10. 
Gorla R.S.R. and Byrd L.W.  Effect of electrostatic field on rupture of thin liquid film on a cylinder 
151164 
11. 
Roy R. and Dutta S.C.  Differential settlement among isolated footings of building frames: the problem, its estimation and possible measures 
165186 
12. 
Bég O.A., Takhar H.S., Kumari M. and Nath G.  Computational fluid dynamics modelling of buoyancy induced viscoelastic flow in a porous medium with magnetic field effects 
187210 
13. 
Gac K., Jach K., Mroczkowski M. and Wolañski P.  Oneand twodimensional numerical modelling of shock inducend transition to detonation in the condensed explosives 
211226 
14. 
Brief note Perdikis C.  Local similarity transformations for the boundary layer flow through a homogeneous porous medium 
227230 

1.
THE EFFECT OF RANDOMNESS ON STABILITY OF SURFACE GRAVITY WAVES FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATION
A.K. DHAR
Department of Mathematics
Bengal Engineering College (D.U.), Howrah  711103, INDIA
email: math@becs.ernet.in
K.P. DAS
Department of Applied Mathematics, University of Calcutta
92, Acharya Prafulla Chandra Road, Calcutta  700009, INDIA
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves of wavesteepness up to 0.25, is used here to investigate the effect of randomness on stability of deepwater surface gravity waves in the presence of wind blowing over water. A spectral transport equation for narrow band Gaussian surface wave is derived. With the use of this transport equation stability analysis is made for an initial homogeneous wave spectrum having a very simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained, in which higher order contribution comes from only one of the fourth order terms in the evolution equation, which is responsible for waveinduced mean flow. This higher order contribution in this expression for growth rate of instability produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and ultimately the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order terms in the evolution equation.

Key words: 
surface gravity waves, randomness, evolution equation, instability. 
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2.



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3.
THE EFFECT OF NONUNIFORM BASIC TEMPERATURE GRADIENT ON THE CONVECTIVE INSTABILITY OF A FLUID LAYER SANDWICHED BETWEEN TWO POROUS LAYERS WITH GENERAL VELOCITY AND THERMAL CONDITIONS
R.P. THANGARAJ
V.L.B. Janakiammal College of Arts and Science
Coimbatore  641 042, INDIA
The stability of a horizontal fluid layer bounded on either side by porous layers with different permeabilities is examined for different nonuniform basic temperature gradients using general velocity and thermal conditions at the boundaries. In the case of sudden heating and cooling, analytical solutions are obtained using singleterm Galerkin expansion. Numerical solutions are obtained for all possible combinations of basic temperature gradients and boundary conditions in respect of velocity and temperature. General conclusion about the thermal depth and the destabilizing effects of the basic temperature gradients are presented. The classical results of freefree, rigidfree and rigidrigid boundaries with isothermal or adiabatic boundaries are recovered as limiting cases of the present study.

Key words: 
convection, stability, adiabatic, isothermal, free and rigid boundaries. 
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4.
RESIDUAL STRESS ANALYSIS AND PLASTIC ZONE BEHAVIOR IN ANTISYMMETRIC METALMATRIX LAMINATED COMPOSITE PLATES
C. ATAŞ
Department of Mechanical Engineering,
Dokuz Eylül University, Bornova, Izmir, TURKEY
cesim.atas@deu.edu.tr
R. ÖZCAN
Department of Mechanical Engineering,
Uludag University, Bursa, TURKEY
H. AYKUL
Department of Mechanical Engineering,
Celal Bayar University, Manisa, TURKEY
This paper presents a residual stress analysis and plastic zone behavior in antisymmetric aluminum metalmatrix laminated plates. Firstorder shear deformation theory and Finite Element Method are considered in the solution for small deformations. The plate is meshed into 64 elements and 289 nodes with both simply supported or clamped boundary conditions. Stainless steel fiber reinforced aluminum metalmatrix laminated plates of constant thickness are formed by stacking four layers bonded antisymmetrically. It is assumed that the laminated plates are subjected to transverse uniform loads. Loading is gradually increased from yield point of the plate as 0.0001 MPa at each load step. Load steps are chosen as 100, 150 and 200.

Key words: 
aluminum metalmatrix composite, antisymmetric laminated plates, uniform transverse load, small deformations, residual stresses, plastic zone behavior. 
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5.
FINITE DIFFERENCE ANALYSIS OF THE FLOW OF A SECOND ORDER LIQUID PAST AN INFINITE VERTICAL PLATE IN THE PRESENCE OF A MAGNETIC FIELD
P. MOHAPATRA and S. PADHY
Department of Mathematics
Utkal University, Bhubaneswar751004, INDIA
S. TRIPATHY
Department of Mathematics
Maharishi College of Natural Law
Bhubaneswar751004, INDIA
A free convection flow of a second order liquid past an impulsively started vertical plate in the presence of a transverse magnetic field has been studied in this paper. The solution has been obtained by finitedifference method. The effect of the parameters m (magnetic field strength), Pr (Prandtl number), Gr (Grashof number, Gr>0, cooling of the plate by free convection, Gr<0, heating of the plate by convection currents), E (the Eckert number) and 'alpha' (the elastic parameter) on the velocity, temperature and the skin friction has been shown through several graphs and tables.

Key words: 
second order liquid (Coleman and Noll, 1960), finite difference method, free convection, magnetohydrodynamic flow. 
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6.
THE STABILITY OF OIL JOURNAL BEARING INCLUDING BEARING SURFACE DEFORMATION AND VARIATION OF OIL VISCOSITY
S.K. MAZUMDER and A.K. CHATTOPADHYAY
Department of Mechanical Engineering
B. E. College (Deemed University), Howrah
West Bengal, INDIA
email: ajit@mech.becs.ac.in
This paper analyses the stability characteristics of oil journal bearings considering the effect of elastic distortion on the surface of bearing liner and variation of viscosity of oil due to pressure. The theoretical analysis is intended to show how the effects of elastic distortion on the journal bearing performance can be calculated for threedimensional bearing geometries. The deformation equations for bearing surface are solved simultaneously with hydrodynamic equations including variation of viscosity of oil, equation of motion to predict theoretically the fluid film pressure distribution and the journal orbit under dynamic condition. A nonlinear analysis determines the locus of the journal for the operating conditions. The stability of the system can be determined from the journal locus.

Key words: 
journal, bearing, deformation, viscosity, stability. 
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7.
THE MELT SPREADING ALONG THE SUBSTRATE SURFACE IN THE COURSE OF SHS SURFACING
A.V. YUKHVID, A.M. STOLIN and V.I. YUKHVID
Institute of Structural Macrokinetics and Materials Science
Russian Academy of Sciences
142432, Chernogolovka, Moscow region, RUSSIA
email: yukh@ism.ac.ru
L.S. STELMAKH
Institute of Problems of Chemical Physics
Russian Academy of Sciences
142432, Chernogolovka, Moscow region, RUSSIA
The role of spreading during SHS surfacing of the protective coatings has been investigated theoreticaly and experimentally. The case, when spreading of large drops is forced by the effect of gravity and the interface forces are low, is considered. Analytical and numeric solutions of the problem have shown that the ratio of the specific times of cooling and spreading is the main parameter, which determines the dynamics and the final characteristics of spreading. It has been shown that the process of spreading is most strongly affected by the initial melt mass and drop size, the activation energy of viscosity, and gravitation (microgravitation and overload) within these specific times. The experimental research into SHS surfacing has confirmed the theoretical data.

Key words: 
selfpropagating hightemperature synthesis, combustion, spreading, surfacing, protective inorganic coatings. 
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8.
MHD EFFECTS ON A POWERLAW FLUID PAST A VERTICAL
PLATE EMBEDDED IN A POROUS MEDIUM WITH
VARIABLE SURFACE HEAT FLUX
M.F. ElAMIN and A.A. MOHAMMADIEN
Department of Mathematic
Faculty of Science, South Valley University
Aswan, EGYPT
The present study is devoted to investigating the influences of magnetic field on buoyancy induced flow over vertical flat plate embedded in a nonNewtonian fluid saturated porous medium. The Ostwaldde Waele powerlaw model is used to characterize the nonNewtonian fluid behavior. A similarity solution for the transformed governing equations is obtained with a prescribed variable surface heat flux. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Excess surface temperature has been presented for different values of the powerlaw index n, magnetic parameter Mn^{*} and the exponent 'lambda'.

Key words: 
nonNewtonian powerlaw fluid, porous medium, buoyancy induced flow, magnetic field. 
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9.
THREE INTERFACIAL GRIFFITH CRACKS BETWEEN BONDED DISSIMILAR ELASTIC MEDIA
S. DAS
Department of Mathematics
B.P. Poddar Institute of Management & Technology
Poddar Vihar, 137, V.I.P. Road, Calcutta  700 052, INDIA
email: sananda_das@hotmail.com
The paper deals with three collinear Griffith cracks propagating with constant velocity under antiplane shear stress at the interface of an elastic layer of finite thickness h and a semiinfinite half plane of different elastic properties. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips and crack opening displacements are obtained for large h. The graphical plots of these results are also presented for some particular cases.

Key words: 
Griffith crack, Fourier transform, integral equation, Hilbert transform, stress intensity factor, crack opening displacement. 
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10.
EFFECT OF ELECTROSTATIC FIELD ON RUPTURE OF THIN LIQUID FILM ON A CYLINDER
R.S.R. GORLA
Department of Mechanical Engineering, Cleveland State University
Cleveland, Ohio 44115, USA
Email: gorla@csaxp.erg.csuohio.edu
L.W. BYRD
Thermal Structures Branch, Air Vehicles Directorate
Air Force Research Laboratory
Wright Patterson Air Force Base, Ohio 45433, USA
The dynamic rupture process of a thin liquid film on a cylinder has been analyzed by investigating the stability under the influence of a nonuniform electrostatic field to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The effect of the electric field is included in the analysis only in the boundary condition at the liquid vapor interface. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. The electric field stabilizes the film and increases the time to rupture when a long wavelength perturbation is introduced.

Key words: 
film rupture, thin film, microfilm, electrostatic effects. 
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11.
DIFFERENTIAL SETTLEMENT AMONG ISOLATED FOOTINGS OF BUILDING FRAMES: THE PROBLEM, ITS ESTIMATION AND POSSIBLE MEASURES
R. ROY
Department of Civil Engineering
Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
S.C. DUTTA
Department of Applied Mechanics
Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
email: scdutta@lycos.com
The conventional design of building frames is based on the assumption that the settlement of footings has no effect on the load of the corresponding columns. In reality, the differential settlements among various footings result in a redistribution of the column loads, the amount of which depends on the rigidity of the structure and the loadsettlement characteristics of the soil. The present paper attempts to study the effect of the same on design force quantities for frame members of building frames with isolated footings. The nonlinear settlement versus stress relationship arising in case of building frames with isolated footings on clayey soils is attempted to be dealt with two alternative iterative approaches. Results of a few simple threedimensional frames obtained by the simpler approach are compared with the results of the more rigorous approach and found to be satisfactory. Frames resting on sandy soil are also studied by idealising the soil medium below the footing as linear elastic springs. Various representative case studies are presented for frames resting on sandy and clayey soil. These case studies may help in arriving at design provisions to account for such effects. The simpler iterative approach may be exercised with the help of available commercial frame analysis software and may prove useful in improved design of buildings accounting for the effect of soilstructure interaction. Adequacy of providing tie beams, continuous lintels, and diagonal braces in minimising the redistribution of force quantities are also studied and presented in the paper in limited form. The addition of diagonal braces are found to be effective in substantially minimising the change in force quantities due to the soilstructure interaction.

Key words: 
building frames, isolated footings, differential settlement, soilstructure interaction, tie beams, lintels, diagonal braces. 
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12.
COMPUTATIONAL FLUID DYNAMICS MODELLING OF BUOYANCY INDUCED VISCOELASTIC FLOW IN A POROUS MEDIUM WITH MAGNETIC FIELD EFFECTS
O.A. BÉG
BNFL Engineering, ANSYS Group
Civil, Structural & Architectural Division
Level 3, Hinton House, Risley, WA3 6AS, UK
H.S. TAKHAR
Manchester School of Engineering
University of Manchester, Simon Building
Oxford Road, Manchester, M13 9PL, UK
M. KUMARI and G. NATH
Mathematics Department, Indian Institute of Science
Bangalore, INDIA
A 2dimensional computational fluid dynamics analysis of steady state thermal boundary layer flow of a second order nonNewtonian fluid past a horizontal wedge in a BrinkmanDarcy porous medium, in the presence of a transverse magnetic field, is presented. The governing equations are transformed from Cartesian coordinates (x,y) into a sixth order system of partial differential equations in a 'ksi'n coordinate system. These complex equations are then reduced to a set of six first order equations which are solved using the robust Keller finite difference method, and a block tridiagonal iterative solver, SOLV6. It is shown that heat transfer magnitude is depressed by magnetic field parameter (Hartmann number, Ha) and also considerably reduced with increasing viscoelasticity parameter (K). Surface shear stresses are also reported to fall considerably with increase in viscoelasticity of the fluid. Effects of other hydrodynamic and thermal parameters on the flow are discussed in detail.

Key words: 
computational, boundary layer theory, viscoelastic material, magnetic body forte, Brinkman vorticity diffusion, Darcy law, Keller implicit difference method, surface heat transfer, shear stress, natural convection heat transfer. 
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13.
ONEAND TWODIMENSIONAL NUMERICAL MODELLING OF SHOCK INDUCEND TRANSITION TO DETONATION IN THE CONDENSED EXPLOSIVES
K. GAC, K. JACH and M. MROCZKOWSKI
Institute of Optoelectronic, Military University of Technology
ul. Kaliskiego 2, 01489 Warszawa, POLAND
P. WOLAÑSKI
Institute of Heat Engineering, Warsaw University of Technology
ul. Nowowiejska 25, 00665 Warszawa, POLAND
In this paper, the basic processes accompanying a shock initiation of a detonation have been analyzed theoretically using numerical methods. The detailed discussion of initiation of a detonation by nonstationary shock waves generated by a solid body impact or explosively driven inertial partition is presented. The physicalmathematical model applied here comprises the set of equations of gasdynamics, the elasticplastic, and elastic/viscousplastic theory. The additional elements of the model are constitutive relations rendering properties of materials and semiempirical model of chemical reactions. In order to study these problems, the time dependent one and twodimensional fluiddynamic equations have been numerically integrated for specific initial conditions. Onedimensional code is based on finite difference method. The twodimensional numerical code is based on so called free particle method (HEFP  model). One of the fundamental questions answered is whether or not a stationary detonation wave will result from the given initial parameters. The better understanding of the nonstationary phenomena has been achieved, particularly at the transient processes preceding formation of a detonation wave. A phenomenon of generation of retonation wave was explained.

Key words: 
shock waves, initiation of detonation, retonation. 
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14. Brief note
LOCAL SIMILARITY TRANSFORMATIONS FOR THE BOUNDARY LAYER FLOW THROUGH A HOMOGENEOUS POROUS MEDIUM
C. PERDIKIS
University of Ioannina, Department of Mathematics
Ioannina 451 10, GREECE
In this paper, we point out local similarity transformations for the flow through a medium with high porosity bounded by a semiinfinite horizontal plate when the free stream velocity is of exponential form.

Key words: 
porous media. 
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