
Archive issue  vol.3 No.1
1.
AN INTEGRAL METHOD FOR TWODIMENSIONAL STOKES
FLOWS PAST RIGID OBSTACLES IN THE HALFPLANE
Mirela KOHR
"BabeșBolyai" University of ClujNapoca
Faculty of Mathematics, 1
M. Kogălniceanu Str., 3400 ClujNapoca, ROMANIA
The problem of determining the slow viscous flow of a fluid past a cylinder
with an arbitrary cross section, in a domain with boundary limited by a plane
wall, is formulated as a system of Fredholm linear integral equations of the
second kind. We next complete the doublelayer potentials of the system with
some terms having singularities located inside the obstacle and which satisfy
the nonslip boundary condition on the wall. We next prove that this system of
integral equations has a unique continuous solution when the boundary of the
particle is a Lyapunov curve. Also, the numerical results are given for the case
of a fixed circular obstacle. For the numerical solution we use a standard
boundary element technique.

Key words: 
Stokes flow, Green tensor, doublelayer potentials, compact operators, Fredholm's alternatives. 
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2.
BOUNDARY LAYER HEAT TRANSFER IN A
MICROPOLAR FLUID OVER A FLAT PLATE
WITH VECTORED SURFACE MASS TRANSFER
I.A. HASSANIEN
Mathematics Department, Assuit University
Assuit, EGYPT
R.S.R. GORLA
Mechanical Engineering Department,
Cleveland State University
Cleveland, 44115 USA
A.A. MOHAMMADEIN
Mathematics Department, South Valley University
Aswan, EGYPT
An analysis is presented for the heat transfer in a micropolar fluid
boundary layer over a flat plate with uniformly distributed vectored surface
mass transfer. Numerical solutions for the governing nonsimilar boundary layer
equations are presented for a range of values of the material properties and
Prandtl number of the fluid. The results indicate that the micropolar fluids
display a reduction in drag as well as heat transfer rate when compared with
Newtonian fluids.

Key words: 
micropolar fluids, boundary layers, forced convection, nonsimilar flow. 
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3.
DISCRETIZATION SCHEMES OF ADVECTION TERM
IN THE FINITE ELEMENT METHOD FOR
INCOMPRESSIBLE NAVIERSTOKES EQUATION
Tomomi UCHIYAMA
School of Informatics and Sciences, Nagoya University
Furocho, Chikusaku, Nagoya 46401, JAPAN
In a finite element method for an incompressible NavierStokes equation, the
divergent, gradient, simplified, and mixed schemes are applicable to discretize
the advection term. The simplified scheme substitutes the average velocity in
each element for the advection velocity, and the mixed scheme is a combination
of the divergent and gradient schemes. This paper investigates the effects of
these schemes on the computational accuracy and CPU time of a finite element
method based on the SMAC method. The investigations are accomplished by solving
the flow in a square cavity for the cases in which the velocity field is
calculated by the masslumping and multipass algorithms. The computational
accuracy is higher in the order of divergent, mixed, gradient, and simplified
schemes, irrespective of the solution algorithms for the velocity. The divergent
scheme, allowing calculation with the shortest CPU time, is the most useful
among the four schemes. The improvement in computational accuracy produced by
the multipass algorithm is independent of the discretization scheme of the
advection term.

Key words: 
computational fluid dynamics, finite element method, masslumping algorithm, multipass algorithm, cavity flow. 
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4.
FINITE ELEMENT STATIC ANALYSIS OF STIFFENED SHELLS
Asokendu SAMANTA and Madhujit MUKHOPADHYAY
Department of Ocean Engineering and Naval Architecture
Indian Institute of Technology
Kharagpur 721 302, INDIA
Stiffened shell has been analyzed on the basis of a combination of Allman's
plane stress triangle and DKT plate bending element. As the same displacement
function is used for both the shell and the stiffener element, the compatibility
condition at the shell beam junction is ensured. The formulation of the
stiffener is done in such a manner that it can be placed anywhere within the
shell element. The applicability of this element is tested for different
structures, particularly for shallow and deep shells.

Key words: 
finite element, static analysis, shell, stiffener. 
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5.
EFFECTS OF DESIGN PARAMETERS ON AIRWATER
TWOPHASE FLOW PERFORMANCE OF A RADIALFLOW PUMP
Kiyoshi MINEMURA and Katsuhiko KINOSHITA
School of Informatics and Sciences, Nagoya University
Nagoya 46401, JAPAN
Masaru IHARA, Kazuyuki EGASHIRA
Technology Research Center
Japan National Oil Corporation
Chiba 261, JAPAN
In offshore oil field development, we foresee an increase in the demand for
oil  well pumps having improved gas handling capacity. To meet the demand by
improving the performance of a radialflow centrifugal pump of low specific
speed, many kinds of impellers, fabricated by changing systematically the design
parameters, such as discharge angle, location and shape of leading edge, number
of blades, location of the split for dividing the blade length into two parts
and so on, were experimentally investigated under airwater twophase flow
conditions to clarify the parameters on pump performance. The optimum blade is
found to be one that has a split in the latter half of the impeller and is
installed with discharge angle of approximately 90^{o}.

Key words: 
pump, multiphase flow, oilwell pump, airwater twophase flow. 
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6.
A CONTRAVARIANT VELOCITY BASED IMPLICIT MULTILEVEL METHOD FOR SIMULATING THE WHOLE PROCESS OF INCOMPRESSIBLE FLOW TRANSITION ARROUND
JOUKOWSKY AIRFOILS
Zhining LIU, Chaoqun LIU, Guohua XIONG
Department of Mathematics and Statistic
Louisiana Tech University
Ruston, Louisiana, USA
A contravanant velocity based incompressible NavierStokes governing system is derived to generate an implicit multilevel method so that we can simulate the receptivity and flow transition in cases with complex geometnes. The two and three dimensional development of leadingedge receptivity and flow transition in a 2D Joukowsky airfoil boundary layer are investigated by direct numencal simulation (DNS) using this system. The numencal investigation is based on the socalled spatial approach. The numencal results agree very well with linear stability theory (LST) and the experimental results for the flat plate case. They also agree well with the result obtained by other researchers for the 2D elliptic leadingedge receptivity case. Some new phenomena for the transition around Joukowsky airfoils are abserved. The details of this approach are described.

Key words: 
contravanant, incompressible, implicit, multilevel, transition. 
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7.
THERMOSOLUTAL CONVECTION IN RIVLINERICKSEN
FLUID IN POROUS MEDIUM IN HYDROMAGNETICS
R.C. SHARMA
Department of Mathematics, Himachal Pradesh University,
Summer Hill, Shimla  171 005, INDIA
SUNIL
Department of Applied Sciences,
Regional Engineering College,
Hamirpur (H.P.)  177 005, INDIA
Suresh CHAND
Department of Mathematics,
Government Post Graduate College,
Hamirpur (H.P.)  177 005, INDIA
The thermosolutal convection in RivlinEricksen fluid in porous medium is
considered in the presence of uniform vertical magnetic field. For the case of
stationary convection, the stable solute gradient and magnetic field have
stabilizing effects on the system, whereas, the medium permeability has
destabilizing effect on the system. The kinematic viscoelasticity has no effect
on stationary convection. The stable solute gradient and magnetic field
introduce oscillatory modes in the system, which were nonexistent in their
absence. The sufficient conditions for the nonexistence of overstability are
also obtained.

Key words: 
thermosolutal convection, RivlinEricksen fluid, porous medium. 
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8.
Brief note
MASS TRANSFER EFFECTS ON UNSTEADY FREE CONVECTION COUETTE FLOW
H.S. TAKHAR
School of Engineering, University of Manchester
Manchester, M13 9PL, UK
B.K. JHA
Department of Mathematics, Banaras Hindu University
Varanasi.221 005, INDIA
In the present paper, mass transfer effect on the unsteady freeconvective flow of an incompressible viscous fluid between two vertical parallel plates is discussed for impulsive start of one of the plate. Expressions for velocity, temperature and concentration are obtained by the Laplace transform technique. The influence of the Prandtl number (Pr), Schmidt number (Sc) and time parameter (t) on velocity field and skinfriction are discussed extensively.

Key words: 
unsteady flow, heat and mass transfer, free convection. 
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