
Archive issue  vol.5 No.3
No. 
Author(s)  Title 
Pages 
1. 
 70th Anniversary of Professor Stanis³aw Jerzy PYTKO 
503506 
2. 
Shivakumara I.S. and Suma S.P.  RayleighBénard convection with throughflow  a comparative study between the singleterm and higher order Galerkin methods 
507520 
3. 
Li Q.S.  Exact solutions for free longitudinal vibration of bars with nonuniform Crosssections 
521541 
4. 
Özcan R. and Aykul H.  Calculation of residual stresses in thermoplastic matrix composite laminated plates under inplane loading 
543555 
5. 
Kohr M.  A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number 
557577 
6. 
Gorla R.S.R.  Transient conjugate forced convection and conduction in a circular pin under radiative effect 
579591 
7. 
Dumitrescu H. and Cardoş V.  Two computation methods for oscillatory airfoils 
593611 
8. 
Aykul H. and Özcan R.  Calculation of residual stresses in thermoplastic matrix composite laminated plates under inplane loading 
613628 
9. 
Nedelcu S. and Postelnicu A.  Solving the nolinear problem of gaslubricated hybrid circular bearings. Part I: Steady case 
629653 
10. 
Sunil and Kumar P.  Hall effect on thermal instability of Walters' (model B?) fluid in a porous medium 
655671 
11. 
Vighnesam N.V., Soundalgekar V.M. and Ray S.N.  Combined mixed convection flow past a semiinfinite vertical porous plate with oscillating plate temperature 
673683 
12. 
Heim A., Kuncewicz Cz., Rzyski E. and Stelmach J.  Gas holdup for selfaspirating impellers 
685693 
13. 
Conforto F.  Weakly nonlinear high frequency waves for a first order quasilinear system involving sourcelike terms: a covariant formulation 
695713 
14. 
Elliott J.W.  The axisymmetric compressible boundary layer flow along a circular cylinder 
715751 

2.
RAYLEIGHBÉNARD CONVECTION WITH THROUGHFLOW 
A COMPARATIVE STUDY BETWEEN THE SINGLETERM
AND HIGHER ORDER GALERKIN METHODS
I.S. SHIVAKUMARA and S.P. SUMA
UGCDSA Centre in Fluid Mechanics,
Central College, Bangalore University,
Department of Mathematics,
Bangalore560 001, INDIA
email: isshivakumara@hotmail.com
Effects of nonuniform temperature gradient, vertical transport of momentum and vertical transport of perturbation temperature due to throughflow are investigated on the RayleighBénard convection for different hydrodynamic boundary conditions. The eigenvalue problem for the conducting boundaries is solved by the higherorder Galerkin method. It is shown that the throughflow in one particular direction destabilizes the system depending on the value of the Prandtl number. Also a comparison between the results of singleterm and higher order Galerkin methods is made and limitations of the singleterm Galerkin method are clearly brought out.

Key words: 
longitudinal vibration, exact solutions, nonuniform bars, natural frequency, mode shape. 
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3.
EXACT SOLUTIONS FOR FREE LONGITUDINAL VIBRATION OF
BARS WITH NONUNIFORM CROSSSECTIONS
Q.S. LI
City University of Hong Kong,
Department of Building and Construction,
Tat Chee Avenue, Kowloon, HONG KONG
email: bcqsli@cityu.edu.hk
Using appropriate transformations, the differential equations of free longitudinal vibration of bars with variably distributed mass and axial stiffness are reduced to Bessels equations or ordinary differential equations with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of mass and axial stiffness. Exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for a one step nonuniform bar are derived and used to obtain the general solution and the frequency equation of a multistep nonuniform bar with various boundary conditions, including nonclassical cases. This approach which combines the transfer matrix method and closed form solutions of one step bars leads to a single frequency equation for any number of steps.

Key words: 
longitudinal vibration, exact solutions, nonuniform bars, natural frequency, mode shape. 
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4.
CALCULATION OF RESIDUAL STRESSES IN THERMOPLASTIC
MATRIX COMPOSITE LAMINATED PLATES
UNDER INPLANE LOADING
H. AYKUL
Celal Bayar University,
Department of Mechanical Engineering, Manisa, TURKEY
email: haykul@hotmail.com
R. ÖZCAN
Uludag University,
Department of Mechanical Engineering,
Bursa, TURKEY
Residual stress analysis is carried out in a thermoplastic composite laminated plate for inplane loading. Low density polyethylene thermoplastic matrix (LDPE) and steel fibers are used to produce the composite plates by using moulds. The first order shear deformation theory and nine node Lagrangian finite element are used. Mathematical formulation is given for the residual stress analysis of a laminated plate for small deformations. Yield points and stresses are obtained for symmetric and antisymmetric laminated plates without and with a circular hole. Elastic, elastoplastic and residual stresses in plates are given in tables. The expansion of plastic zones is illustrated for 100, 200 and 300 load steps. Yield points and the expansion of plastic zones are compared for different plates without and with a circular hole.

Key words: 
residual stress, elastoplastic stress analysis, finite element method, thermoplastic composites, inplane loading. 
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5.
A SECOND KIND INTEGRAL EQUATION FORMULATION FOR
THE INTERACTION BETWEEN A SOLID PARTICLE AND
A COMPOUND DROP AT LOW REYNOLDS NUMBER
M. KOHR
"BabaeşBolyai" University of ClujNapoca,
Faculty of Matematics, 3400 ClujNapoca, ROMANIA
email: mkohr@math.ubbcluj.ro
In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.

Key words: 
Stokes flow, Green tensor, doublelayer potentials, compact operators, Fredholm's alternatives. 
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6.
TRANSIENT CONJUGATE FORCED CONVECTION AND CONDUCTION
IN A CIRCULAR PIN UNDER RADIATIVE EFFECT
R.S.R. GORLA
Cleveland State University, Fenn College of Engineering,
Department of Mechanical Engineering,
Euclid Avenue at East 24th Street, Cleveland, Ohio 44115, USA
email: gorla@csaxp.erg.csuohio.edu
An analysis is presented for the unsteady heat transfer characteristics of a laminar forced convective flow over a circular pin by the conjugate convectionconduction theory including radiative effects under the optically thick limit approximation. The dimensionless form of the governing equations is solved numerically and results are presented for the temperature distribution and local heat transfer rates. Both constant root temperature and constant root heat flux boundary conditions are considered. The radiative effect tends to increase the surface temperature.

Key words: 
circular pin, conjugate convection and conduction, laminar flow, radiative effect.

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7.
TWO COMPUTATION METHODS FOR OSCILLATORY AIRFOILS
H. DUMITRESCU and V. CARDOŞ
"CAIUS IACOB" Institute of Applied Mathematics
P.O. Box 124, Ro70700, Bucharest, ROMANIA
email: vcardos@ns.IMA.Ro
Two commonly used methods for predicting unsteady airloads are:
1) the panel method based on the surface distribution of singularity elements and
2) the indicial method for unsteady problems governed by the linearized partial differential equation and linearized boundary conditions. The panel method considered here involves a piecewise linear continuous distribution of singularities (sources and doublets) over the airfoil surface. Since the linearity assumptions of the indicial method do not allow for variations in the form of the chordwise pressure, this approach seems to be more economical from the computational point of view. The present study is aimed at the systematic assessment of the two approaches by considering a number of unsteady twodimensional flows. Good agreement was found with measured airloads data for the two methods.

Key words: 
aerodynamics, unsteady flows, incompressible fluids, airfoil theory, subsonic flows. 
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8.
CALCULATION OF RESIDUAL STRESSES
IN THERMOPLASTIC MATRIX COMPOSITE LAMINATED
PLATES UNDER INPLANE LOADING
H. AYKUL
Celal Bayar University,
Department of Mechanical Engineering,
Manisa, TURKEY
email: haykul@hotmail.com
R. ÖZCAN
Uludag University,
Department of Mechanical Engineering,
Bursa, TURKEY
Residual stress analysis is carried out in a thermoplastic composite laminated plate for inplane loading. Low density polyethylene thermoplastic matrix (LDPE) and steel fibers are used to produce the composite plates by using moulds. The first order shear deformation theory and nine node Lagrangian finite element are used. Mathematical formulation is given for the residual stress analysis of a laminated plate for small deformations. Yield points and stresses are obtained for symmetric and antisymmetric laminated plates without and with a circular hole. Elastic, elastoplastic and residual stresses in plates are given in tables. The expansion of plastic zones is illustrated for 100, 200 and 300 load steps. Yield points and the expansion of plastic zones are compared for different plates without and with a circular hole.

Key words: 
residual stress, elastoplastic stress analysis, finite element method, thermoplastic composites, inplane loading. 
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9.
SOLVING THE NOLINEAR PROBLEM
OF GASLUBRICATED HYBRID CIRCULAR BEARINGS.
PART I: STEADY CASE
S. NEDELCU
Air Force Academy, Department of Mathematics,
2200 Brasov, ROMANIA
A. POSTELNICU
Transilvania University of Brasov,
Department of Fluid Mechanics,
2200 Brasov, ROMANIA
e.mail: adip@unitbv.ro
In hybrid bearings, the carrying effect is produced by supplying under pressure and by the relative motion of the bearing surfaces. Because the pressure distribution in the bearing is the solution to a nonlinear partial differential equation of second order, the two causes cannot be studied separately and solving the problem is a difficult task. The mathematical model considered by us is the Reynolds equation for compressible fluids in a multiple connected domain. The boundary conditions on the inner boundaries are derived from the flowrate continuity through the supplying orifices and are expressed as nonlinear integraldifferential equations, which are solved numerically.

Key words: 
lubrication, hybrid bearings, compressible fluids, nonlinear equations. 
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10.
HALL EFFECT ON THERMAL INSTABILITY OF WALTERS'
(MODEL B') FLUID IN A POROUS MEDIUM
SUNIL
Regional Engineering College, Department of Applied Sciences,
Hamirpur (H.P.)  177 005, INDIA
P. KUMAR
Deen Dayal Upadhaya College, Department of Mathematics,
Mehre (Barsar) (H.P.)  174 305, INDIA
The thermal instability of Walters' (model B') fluid in a porous medium is considered in the presence of a uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has the stabilizing effect on the system, whereas the Hall currents have destabilizing effect on the system. The porous medium permeability has both stabilizing and destabilizing effects on the system depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. The kinematic viscoelasticity and magnetic field (and corresponding Hall currents) 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: 
Hall effect, thermal instability, Walters' (model B') fluid, porous medium. 
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11.
COMBINED MIXED CONVECTION FLOW PAST
A SEMIINFINITE VERTICAL POROUS
PLATE WITH OSCILLATING PLATE TEMPERATURE
N.V. VIGHNESAM
IFDD, Flight Dynamic Division,
ISRO Satellite Centre
Bangalore (560 017), INDIA
V.M. SOUNDALGEKAR
31A12, Brindavan Society, Thane (400 061), INDIA
S.N. RAY
Sr. Programming Officer, Regional Computer Centre
ONGC Ltd., P32, Transport Depot Road
Calcutta (700 088), INDIA
Mixed convection flow past a semiinfinite vertical porous plate is studied here when the plate temperature is oscillating about a nonzero mean. Mean velocity, mean temperature, inphase and out of phase components of unsteady part of the temperature are shown graphically. It is observed that an increase in suction velocity leads to an increase and an increase in injection velocity leads to a decrease in the amplitude of the rate of heat transfer. Also at large values of frequency ?, the oscillating component of temperature is superimposed on the mean temperature and is found to be unaffected by ? and suctioninjection velocity.

Key words: 
mixed convection, porous plate, oscillating plate temperature. 
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12.
GAS HOLDUP FOR SELFASPIRATING IMPELLERS
A. HEIM, CZ. KUNCEWICZ, E. RZYSKI and J. STELMACH
Technical University of £odz, Department of Process Equipment,
ul. Stefanowskiego 12/16, 90924 £ód, POLAND
Gas holdup for selfaspirating disk impellers was determined experimentally. Process parameters such as rotations frequency, impeller size and height of liquid level over the impeller were found to have the greatest impact on its value. The effect of viscosity of the liquid being aerated is much weaker  the investigations were carried out with several liquids differing in viscosity. It was also found that the width of the outlet slots of the impeller had a slight influence on gas holdup.

Key words: 
aeration, agitation, gas holdup, mixing, selfaspirating impellers. 
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13.
WEAKLY NONLINEAR HIGH FREQUENCY WAVES FOR A FIRST
ORDER QUASILINEAR SYSTEM INVOLVING SOURCELIKE TERMS:
A COVARIANT FORMULATION
F. CONFORTO
University of Messina, Department of Mathematics
Contrada Papardo, salita Sperone, 31, 98166 Messina, ITALY
email: fiamma@dipmat.unime.it
Making use of the hypersurface theory, the ray theory and the method of asymptotic expansion of multiple scales, a study of weakly nonlinear high frequency waves, through homogeneous media characterized by dissipative or dispersive hyperbolic systems of partial differential equations, is proposed in covariant formalism.
Within the present theoretical framework, asymptotic waves in a heatconducting relativistic fluid are considered.

Key words: 
asymptotic waves, relativistic thermoviscous fluid, dissipative and dispersive effects. 
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14.
THE AXISYMMETRIC COMPRESSIBLE BOUNDARY LAYER FLOW
ALONG A CIRCULAR CYLINDER
J.W. ELLIOTT
University of Hull, Department of Mathematics,
Hull HU6 7RX, UNITED KINGDOM
email: J.W.Elliott@maths.hull.ac.uk
A numerical and analytical investigation of the compressible axisymmetric boundarylager flow over a circular cylinder is presented for both adiabatic flow and the case of heated or cooled walk. First, a numerical solution to the governing equations is presented for a variety of wall conditions. The remainder and majority of the paper is then concerned with an analysis of the fardownstream flow where curvature becomes a dominant feature. Here the flow takes on a double structure, with an Oseen type of outer flow. The problem reduces to matching to an inner solution which, in contrast to the incompressible case, is found to be nontrivial. Three forms of the inner solution are constructed, firstly to justify obtaining a new result and secondly to rebut the assertion that matching is only possible for a single approach. Further the use of a general power law form for the viscosity law is considered. The resulting asymptotic forms are then compared with the numerical results of the far downstream flow.

Key words: 
boundary layer flow, circular cylinder, compressible flow. 
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