
Archive issue  vol.4 No.1
1.
A FOURTH ORDER EVOLUTION EQUATION FOR
CAPILLARYGRAVITY WAVES INCLUDING THE EFFECTS
OF WIND INPUT AND SHEAR IN THE WATER CURRENT
A.K. DHAR
Department of Mathematics,
B.E. College (Deemed University),
P.O. Botanic Garden, Howrah 711103, INDIA
K.P. DAS
Department of Applied Mathematics,
University of Calcutta,
92, Acharya Prafulla Chandra Road,
Calcutta  700009, INDIA
A fourth order nonlinear evolution equation is derived for capillary gravity waves in deep water including the effect of a surface drift current in the water and shear in the air flow. From this evolution equation instability conditions are derived for a uniform capillarygravity wave train. Graphs are plotted showing the maximum growth rate of instability and instability regions for weakly damped (linearly) and weakly growing (linearly) waves for some different values of friction velocity of the flow. From these graphs it is found that the effect of the wind input and shear in water current is to produce a decrease in the growth rate for weakly damped (linearly) waves and to produce an increase in growth rate for weakly growing (linearly) waves. The shear in the water current and the wind input are found to produce a shrinkage in the instability regions.

Key words: 
capillarygravity, evolutionequation, wave, instability. 
TOP OF PAGE 
2.
HEAT TRANSFER FROM A STRETCHING SURFACE
IN A MICROPOLAR FLUID
M.A EL.HAKIEM, A.A. MOHAMMADEIN
and S.M.M. ELKABEIR
Mathematics Department, Faculty of ScienceAswan,
South Valley University,
Aswan, EGYPT
M.A. MANSOUR
Mathematics Department, Faculty of ScienceAssuit,
Assuit University,
Assuit, EGYPT
R.S.R. GORLA
Department of Mechanical Engineering,
Cleveland State University,
Cleveland, Ohio 44115, USA
The theory of micropolar fluids due to Eringen is used to formulate a set of boundary layer equations for the heat transfer from an arbitrarily stretching surface with nonuniform surface temperature. A two dimensional similarity solution to the governing momentum, angular momentum and energy equations is presented. The effects of the boundary conditions used for the microrotation term are discussed. Numerical data for the friction factor and Nusselt number has been shown graphically for a range of values of the material properties.

Key words: 
heat transfer, stretching surface, micropolar fluid. 
TOP OF PAGE 
3.
TRANSPORT OF VORTICITY IN FLUID IN THE PRESENCE OF
SUSPENDED MAGNETIC PARTICLES IN POROUS MEDIUM
SUNIL
Department of Applied Sciences, Regional Engineering College
Hamirpur (H.P.)177 005, INDIA
Transport of vorticity in a magnetic fluid in a porous medium is considered in this note. Equations governing the transport of vorticity in magnetic fluid in a porous medium are obtained from the equations of magnetic fluid flow proposed by Wagh (1996) by replacing the usual viscous term in the equation of fluid motion by the resistance term __ to discuss the transport of vorticity in magnetic fluid in a porous medium. A twodimensional case is also studied.

Key words: 
magnetic fluid, magnetic particles, vorticity, porous medium. 
TOP OF PAGE 
4.
AN EFFICIENT STOCHASTIC FINITE ELEMENT
METHOD FOR RANDOM FIELD PROBLEMS
Subrata CHAKRABORTY
Department of Civil Engineering, Bengal Engineering College (D.U.),
Shibpur, Howrah 711103, INDIA
Santi SEKHAR DEY
Department of Civil Engineering, Indian Institute of Technology,
Kharagpur 721302, INDIA
The present paper primarily deals with the analysis of structures involving more than one parameter being stochastic in nature. The proposed method involves two stages. The first part hinges upon adequate representation of the stochastic process and a digital simulation of random parameters. This has been achieved by the local averaging technique followed by the Cholesky decomposition algorithm. Finally, the finite element solution has been obtained utilizing the Neumann expansion method within the framework of Monte Carlo simulation.The approach involves only single decomposition of the stiffnes matrix for the entire simulation and leads to a considerable saving of computing time. Another important flexibility of the approach is that more than one parameter can be handled simultaneously. Numerical examples are presented to elucidate the accuracy and efficiency of the method with respect to the direct simulation approach.

Key words: 
stochastic finite element, local averaging, Monte Carlo simulation, Neumann expansion technique. 
TOP OF PAGE 
5.
GENERATION OF WAVES AT AN INERTIAL INTERFACE
P. GHOSH and B.N. MANDAL
Physics & Applied Mathematics Unit,
Indian Statistical Institute,
203, B.T. Road, Calcutta  700 035, INDIA
This paper is concerned with the generation of threedimensional unsteady motion due to initial disturbances at the interface between two superposed fluids wherein the upper fluid extends infinitely upwards and the lower fluid is of uniform finite depth. The interface is composed of a thin but uniform distribution of a noninteracting material termed as an inertial surface. Assuming linear theory, the problem is formulated as a coupled initial value problem in the velocity potentials describing the motion in the two fluids. The Laplace transform in time and double Fourier transform in space have been utilised in the mathematical analysis to obtain the depression of the inertial interface in terms of a double integral, whose asymptotic form is obtained for large values of time and distance by the method of stationary phase. This is then depicted graphically for two types of initial disturbances in a number of figures to visualise the effect of the upper fluid and also the presence of the inertial surface at the interface on the wave motion. The time evolution of the interface depression is also shown graphically and the decaying phenomena are demonstrated by drawing the phase diagram.

Key words: 
initial disturbances, linearised theory, stationary phase,interface depression, phase diagram. 
TOP OF PAGE 
6.
A PAIR OF EQUAL COLLINEAR INTERFACIAL GRIFFITH CRACKS
S. DAS and B. PATRA
Department of Mathematics,
B. E. College (D.U.),
Howrah  711103, W.B., INDIA
The plane strain problem of determining stress intensity factors and crack energy for a pair of equal collinear moving Griffith cracks situated at the interface of two bonded dissimilar orthotropic half planes has been considered. The problem is reduced to solving a pair of simultaneous singular integral equations which have finally been solved by using Jacobi polynomials. Expressions for stress intensity factors and crack energy are obtained for some particular cases and the results are presented graphically.

Key words: 
interfacial crack, orthotropic, Mach number, stress intensity factor, crack energy, integral equation. 
TOP OF PAGE 
7.
LAMINAR FLOW DUE TO A ROTATING FRUSTUM OF A CONE
Ioan POP
Faculty of Mathematics
University of Cluj, R3400 Cluj, CP253, ROMANIA
TsungYen NA
Department of Mechanical Engineering
University of Michigan  Dearborn, Dearborn, MI, 48128, U.S.A.
A theoretical study is carried out to investigate the steady laminar boundary layer flow due to a rotating frustum of a cone. The effects of the streamwise coordinate and half cone angle on the velocity field and local skin friction coefficient are examined.

Key words: 
laminar, boundary layer, frustum of a cone. 
TOP OF PAGE 
8.
AUTOMATIC TECHNIQUE FOR SUPERFICIAL DEFECTS
IDENTIFICATION IN METAL PATCHES
An automatic system for the identification of superficial defects
Vincenzo NIOLA
Mechanic Department for Energetic, University of Naples,
Facoltá di Ingegneria DIME, Universitá di Napoli,
via Claudio 21 int.125, cap. 80125, Napoli, ITALIA
Aldo LONGOBARDO
B&W Electronics
Via Tasso 114, cap. 80121 Napoli, ITALIA
Marco LONGOBARDI
via G. Cosenza 153,
cap.80053 Castellammare di Stabia (Napoli), ITALIA
We have worked out an innovative system for the identification of superficial defects in low critical metallic patches. In a few seconds we reconstruct, using the fundamental principles of shape from shading, the third dimension of a digitized image, thanks to which we can identify the presence of a defect. Testing shows that the results achieved are more than satisfactory also in relation to the good rejection of the noises from the algorithm. Moreover we propose the advantages of using this system in an industrial field, and the conditions to be verified in industry in order to be able to test this technique.

Key words: 
shape from shading, superficial defects, automatic identification, depth map. 
TOP OF PAGE 
9.
THE INFLUENCE OF SURFACE MASS FLUX ON
MIXED CONVECTION IN NONNEWTONIAN FLUIDS
ALONG A VERTICAL PLATE IN A POROUS MEDIUM
M.A. MANSOUR
Department of Mathematics, Faculty of Science,
Assiut University, Assiut, EGYPT
The problem of mixed convection in powerlaw type nonNewtonian fluids along a nonisothermal vertical plate with surface mass transfer is investigated. The transformed conservation laws are solved numerically for the case of variable wall temperature conditions. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of suction and injection as well as the viscosity index on the surface heat transfer rate.

Key words: 
mixed convection, nonNewtonian fluids, porous medium, boundarylayer. 
TOP OF PAGE 
10.
FORMABILITY ANALYSIS OF TUBEHYDROFORMING PROCESS
FuhKuo CHEN
Department of Mechanical Engineering,
National Taiwan University,
Taipei, Taiwan, REPUBLIC OF CHINA
A formability analysis for the tubehydroforming process was investigated in the present study. The relationship between hydraulic pressure, outer corner radius of the deformed tube, the tube thickness and the tube yield stress was established based on a proposed theoretical model. Another theoretical model was also developed to calculate the die force generated in the tubehydroforming process under frictionless condition. In order to validate the theoretical models developed, the twodimensional finite element simulations were performed as well. The values predicted according to the proposed theoretical models are found to agree very well with those obtained from the finite element simulation results.

Key words: 
FE simulation, die force, tubehydroforming, yield stress. 
TOP OF PAGE 
11.
CALCULATION OF RESIDUAL STRESSES IN METALMATRIX
COMPOSITE LAMINATED PLATES UNDER TRANSVERSE LOADS
Halil AYKUL and Cevdet MERIÇ
Celal Bayar University, Faculty of Engineering,
Muradiye ManisaTURKEY
Hamit AKBULUT
Ataturk University, Faculty of Engineering,
Erzurum TURKEY
An isoparametric quadrilateral element with nine nodes is developed for the elastoplastic analysis of the laminated plates. A stainless steel fiber reinforced aluminum metal matrix laminated and simple supported plate is loaded transversely. Elastic, elastoplastic and residual stresses are calculated in the symmetric and/or antisymmetric crossply and angleply laminated plates for small deformations. Iteration numbers are chosen 50, 100 and 150. The spread of plastic zones is illustrated. A metalmatrix composite layer is manufactured by using moulds under the action of 30 MPa pressure and heating up to 600^{o}C. The firstorder shear deformation theory is used.

Key words: 
Residual stress, elastoplastic stress analysis, finite element method, metal matrix composite materials, transversely loaded laminated plate. 
TOP OF PAGE 

