Archive issue - vol.3 No.2



   No.   Author(s) - Title
Pages

   1.
 

 Nsom B. -- Stability of Taylor-Dean flow of fiber suspensions
 

185-204
 

   2.
 

 Gorla R.S.R., Mansour M.A. and EL-Hawary H.M. -- Thermal radiation effects on boundary layer flow on a continuous porous flat surface
 

205-216
 

   3.
 

 Kohr M. -- An direct boundary integral equations method to Stokes flow past rigid bodies in ground effect
 

217-232
 

   4.
 

 Ghosh P. and Basu U. -- Waves due to initial disturbances at the interface between two superposed fluids
 

233-247
 

   5.
 

 Das S. and Patra B. -- Interaction between three line cracks in a sandwiched orthotropic layer
 

249-269
 

   6.
 

 Erdogan E. -- Effects of the side walls in generalized Couette flow
 

271-286
 

   7.
 

 EL-Hakiem M. -- Effects of a transverse magnetic field on natural convection with temperature dependent viscosity in micropolar fluids
 

287-304
 

   8.
 

 Slavova A. -- Stability analysis of nonlinear cellular neural networks with hysteresis in the output dynamics
 

305-322
 

   9.
 

 Shin S. and Kim B.-S. -- Numerical heat transfer in a rectangular duct for a non-Newtonian fluid with shear rate-dependent thermal conductivity and temperature dependent viscosity
 

323-337
 

   10.
 

 Walicki E. and Walicka A. -- Flow of a Vočadlo fluid in a slot between rotating surfaces of revolution
 

339-358
 

 



1.

STABILITY OF TAYLOR-DEAN FLOW OF FIBER SUSPENSIONS

Blaise NSOM

Laboratoire de Rhéologie (CNRS-UJF-INPG)
Domaine Universitaire-B.P. 53X 38041Grenoble, FRANCE

     We present a theoretical study of the stability of the Taylor-Dean flow of dilute and semi concentrated suspensions of stiff fibers. To this end, we consider a wide-gap Couette-Taylor configuration with pressure gradient acting in the transverse direction. The Ericksen anisotropic fluid equation of state is used to describe the suspension rheological behavior. The marginal stability states are computed with respect to three parameters: the gap-width, the ratio of representative pumping and rotation velocities and the rheological parameter h2 (h2 being an explicit function of the fiber aspect ratio (dilute suspension), concentration and number density (semi concentrated suspension)).

Key words:

fiber suspension, dilute, semi concentrated, rheological model, instabilities, Taylor-Dean flow.

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2.

THERMAL RADIATION EFFECTS ON BOUNDARY LAYER
FLOW ON A CONTINUOUS POROUS FLAT SURFACE

R.S.R. GORLA

Department of Mechanical Engineering
Cleveland State University
Cleveland, OH 44115, USA

M.A. MANSOUR and H.M. EL-HAWARY
Department of Mathematics Assiut University
Assiut, EGYPT

     An analysis is presented based upon the Chebyshev spectral method for the boundary-layer flow on a continuous porous flat surface. This technique reduces the problem to a system of nonlinear equations in the highest order derivatives which were solved by Newton's iterations.

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3.

AN DIRECT BOUNDARY INTEGRAL EQUATIONS METHOD TO
STOKES FLOW PAST RIGID BODIES IN GROUND EFFECT

Mirela KOHR

University Babes-Bolyai, Faculty of Mathematics
Cluj - Napoca, ROMANIA

     The aim of this paper is to give a direct boundary integral equations method for the slow motion of some rigid bodies of an arbitrary shape, near a plane wall in a viscous incompressible fluid. By using an integral representation of the velocity field as a sum between single-layer potentials and double-layer potentials, the problem is reduced to the study of a Fredholm integral system of the second kind. By following the properties of the single-layer and double-layer operators, the existence and uniqueness result of the corresponding solution is given. The numerical results are obtained by a standard boundary element method.

Key words:

Stokes flow, Green's function, double-layer and single-layer potentials, compact operators, Fredholm's results.

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4.

WAVES DUE TO INITIAL DISTURBANCES AT THE
INTERFACE BETWEEN TWO SUPERPOSED FLUIDS

Prity GHOSH

Physics and Applied Mathematics Unit,
Indian Statistical Institute
203 B. T. Road, Calcutta 700 035, INDIA

Uma BASU
Department of Applied Mathematics
92 A. P. C. Road, Calcutta 700 009, INDIA

     This paper is concerned with generation of interface waves due to an initial disturbance at the interface between two superposed homogeneous and inviscid fluids, the lower fluid being of finite depth and the upper fluid extending infinitely upwards. Assuming linear theory, the problem is formulated as a coupled boundary value problem in the velocity potentials describing the motion in the two fluids. The interface depression is obtained when the initial disturbance at the interface is in the form of a prescribed depression of the interface or an impulse concentrated at a point. In both the cases, the interface depression is obtained in terms of an infinite integral which is evaluated asymptotically for large time and distance. This is then displayed graphically in a number of figures to visualise the effect of the upper fluid and also the effect of the finite depth of the lower fluid on the wave motion at the interface.

Key words:

superposed fluids, inertial interface, lineariesd theory, initial disturbances, interface depression.

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5.

INTERACTION BETWEEN THREE LINE CRACKS
IN A SANDWICHED ORTHOTROPIC LAYER

S. DAS and B. PATRA

Department of Mathematics
B.E.College (D.U.)
Howrah - 711103, W.B. INDIA

     The paper deals with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic elastic layer of finite thickness 2h sandwiched between two identical orthotropic half planes. The Fourier Transform Technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cook's result. The analytical expressions for the stress intensity factors and stress magnification factors at the crack tips are obtained for large h. Numerical results for stress intensity factors and stress magnification factors have been illustrated graphically.

Key words:

interaction, crack, orthotropic, stress intensity factor, stress magnification factor, integral equation, Hilbert transform.

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6.

EFFECTS OF THE SIDE WALLS IN GENERALIZED COUETTE FLOW

M.Emin ERDOGAN

Instanbul Teknik Üniversitesi
Makina Fakültesi 80191, Gümüssuyu
Istanbul, TURKEY

     The effects of the side walls on the flow of an incompressible viscous fluid in a conduit of rectangular cross-section by the combined effect of the velocity of the top wall and a constant pressure gradient along the conduit are considered. For this purpose, four different flow conditions are used. In the first case, a separation occurs at the bottom wall. In the second case, the volume flux is zero. In the third case, a separation occurs at the top wall. In the fourth case, the flow is set up by the motion of the top wall in the absence of the pressure gradient. Furthermore, the effect of the side walls in a channel of rectangular cross-section is discussed.

Key words:

effects of the side walls, viscous fluid, Couette flow.

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7.

EFFECTS OF A TRANSVERSE MAGNETIC FIELD ON
NATURAL CONVECTION WITH TEMPERATURE DEPENDENT
VISCOSITY IN MICROPOLAR FLUIDS

M. EL-HAKIEM

Mathematics Department
Faculty of Science, South Valley University
ASWAN, EGYPT

     A regular parameter perturbation analysis is presented to study the effect of uniform transverse magnetic field with temperature dependent viscosity in micropolar fluids. Four different vertical flows have been analyzed: these adjacent to an isothermal surface, uniform heat flux surface, a plane plume and wall plume. Viscous dissipation, motion pressure and volumetric energy source effects are neglected. The absolute viscosity 'mi' is taken to be variable in the force momentum balance while the fluid volumetric coefficient of thermal expansion, 'beta', specific heat, Cp and thermal conductivity, k, are assumed to be constant. Numerical solutions are obtained for different values of the magnetic field, material parameters and micropolar parameters.

Key words:

natural convection, micropolar fluids, magnetic field.

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8.

STABILITY ANALYSIS OF NONLINEAR CELLULAR
NEURAL NETWORKS WITH HYSTERESIS
IN THE OUTPUT DYNAMICS

Angela SLAVOVA

Department of Mathematics,
University of Mining and Geology
Sofia 1100, BULGARIA

     In this work, hysteresis of cellular neural network is investigated. The general state equation with linear and nonlinear templates is introduced. Moreover, the output equation is own dynamics where the nonlinearity in the feedback is allowed to exibit hysteresis. Stability analysis of this cellular neural network is made. New approach for studying such dynamical systems is introduced using Lyapunov's majorizing equations.

Key words:

cellular neural networks, hysteresis, periodic solutions, bifurcations.

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9.

NUMERICAL HEAT TRANSFER IN A RECTANGULAR DUCT FOR A NON-NEWTONIAN FLUID WITH SHEAR RATE-DEPENDENT THERMAL CONDUCTIVITY AND TEMPERATURE DEPENDENT VISCOSITY

Sehyun SHIN and Byung-Suk KIM

School of Mechanical Engineering
Kyungpook National University,
Taegu, 702-701 KOREA

     The present numerical study investigates the effect of the shear rate-dependent thermal conductivity (SRDC) fluids on the heat transfer enhancement in a 2:1 rectangular duct flow. An axially and peripherally constant heat flux boundary conditions (H2) was adopted for a top-wall-heated configuration. The present numerical results of Nusselt numbers for SRDC fluid show the heat transfer enhancement over those of a shear rate-independent thermal conductivity fluid. The heat transfer enhancement is due to the effect of the increased thermal conductivity near the wall, which is attributed to the thigh wall shear rates. The present study proposes a correlation between the Nusselt number and variable thermal conductivity as follows; ___ . Both the temperature and shear rate-dependencies of the properties play important roles on the heat transfer enhancement.

Key words:

shear-rate dependent thermal conductivity, temperature-dependent viscosity, heat transfer enhancement.

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10.

FLOW OF A VOČADLO FLUID IN A SLOT
BETWEEN ROTATING SURFACES OF REVOLUTION

Edward WALICKI and Anna WALICKA

Department of Mechanics, Technical University,
Zielona Góra, POLAND

     This paper contains formulae which define such parameters of the steady laminar flow of a Vočadlo fluid between rotating surfaces of revolution as the velocity components 'TETA'x, 'TETA'teta, 'TETA'y and pressure p. The quasi-linearized equations of motion of the Vočadlo fluid flow for axial symmetry in the intrinsic curvilinear coordinate system x, 'teta', y are used. The obtained solutions to the equations of motion have been illustrated by an example of flow through the slot of constant thickness between rotating disks and between rotating spherical surfaces.

Key words:

Vočadlo fluid, surfaces of revolution, rotational inertia effects.

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