
Archive issue  vol.6 No.2
No. 
Author(s)  Title 
Pages 
1. 
Sharma R.C. and Sharma S.  On electrically conducting couplestress fluid heated from below in porous medium in presence of uniform horizontal magnetic field 
251263 
2. 
Fetecău C.  Poiseuille flows of second grade fluids in heated cylindrical domains 
265277 
3. 
Jha B.K.  Transient freeconvective flow in a vertical channel with heat sinks 
279286 
4. 
Ingham D.B., Bradean R., Wen X., Russell S.J. and Pourmohammadi A.  Mathematical and computational modelling of fluid and fibre dynamics in a sifting airlaying process 
287309 
5. 
Teter A. and Kołakowski Z.  Stability and load carrying capacity of a thinwalled corrugated trapezoidal plate 
311323 
6. 
Esendemir Ü.  An elastoplastic stress analysis in a thermoplastic composite beam of arbitrary orientation subjected to transverse uniformly distributed load 
325344 
7. 
Erdogan M.E.  On the unsteady unidirectional flows due to sudden application of a pressure gradient 
345368 
8. 
Kamiński M. and Spanos P.D.  Stochastic second order perturbation approach to the finite difference based vibration analysis 
369393 
9. 
Naeem R.K. and Ali S.A.  A class of exact solutions to equations governing the steady plane flows of an incompressible fluid of variable viscosity via von Mises variables 
395436 
10. 
Malashetty M.S., Umavathi J.C. and Leela V.  Magnetoconvective flow and heat transfer between vertical wavy wall and a parallel flat wall 
437456 
11. 
Massoudi M. and Rao C.L.  A nonlinear constitutive relation for flowing granular materials 
457471 
12. 
Anghel M., Hossain M.A., Zeb S. and Pop I.  Combined heat and mass transfer by free convection past an inclined flat plate 
473487 
13. 
Kravchuk A.S.  Contact problem for rough rigid disk and plate with thin coating on the cylindric hole 
489497 
14. 
Kiełbasa J.  Dynamics of bridgeless constant temperature anemometers 
499511 

1.
ON ELECTRICALLY CONDUCTING COUPLESTRESS FLUID HEATED FROM BELOW IN POROUS MEDIUM IN PRESENCE OF UNIFORM HORIZONTAL MAGNETIC FIELD
R.C. SHARMA and S. SHARMA
Department of Mathematics
Himachal Pradesh University, Summer Hill
Shimla171 005, INDIA
A layer of electrically conducting couplestress fluid heated from below in porous medium is considered in the presence of uniform horizontal magnetic field. The medium permeability hastens the onset of convection whereas the magnetic field and couplestress postpone the onset of convection, for the case of stationary convection. The oscillatory modes are introduced by the magnetic field which were not present in the absence of the magnetic field. The overstable case has been considered and a sufficient condition for the nonexistence of overstability is obtained.

Key words: 
couplestress fluid, thermal convection, porous medium, hydromagnetics. 
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2.
POISEUILLE FLOWS OF SECOND GRADE FLUIDS IN HEATED CYLINDRICAL DOMAINS
C. FETECĂU
Department of Theoretical Mechanics
"Gh.Asachi" Tehnical University , Iaşi, ROMANIA
email: cfetecau@diac.tuiasi.ro
The thermal convection of a second grade fluid in a concentric pipe flow is studied in this paper. The motion of the fluid and its state of stress are not influenced by the variation of temperature. In steady flows, both the velocity and the fluid temperature distribution are identical to those resulting from the NavierStokes theory.

Key words: 
fluid, flow, heat, temperature. 
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3.
TRANSIENT FREECONVECTIVE FLOW IN A VERTICAL CHANNEL WITH HEAT SINKS
B.K. JHA
Department of Mathematics
Banaras Hindu University, Varanasi  221 005, INDIA
email: rspathak@banaras.ernet.in
This paper investigates analytically heat sinks effect on transient free convective flow in a vertical channel. Laplace transform technique has been used to solve the governing momentum and energy equations. The expressions for velocity field, temperature field, skinfriction and rate of heat transfer have been obtained in closed form for two different cases. The influence of heat sinks and time parameter on velocity, temperature, skinfriction and rate of heat transfer is extensively discussed.

Key words: 
transient free convective flow, heat sinks. 
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4.
MATHEMATICAL AND COMPUTATIONAL MODELLING OF FLUID AND FIBRE DYNAMICS IN A SIFTING AIRLAYING PROCESS
D.B. INGHAM, R. BRADEAN
Department of Applied Mathematical Studies
University of Leeds, Leeds, LS2 9JT, UK
email: amt6dbi@amsta.leeds.ac.uk
X. WEN
Environment Centre
University of Leeds, Leeds, LS2 9JT, UK
S.J. RUSSELL and A. POURMOHAMMADI
School of Textile Industries,
University of Leeds, Leeds, LS2 9JT, UK
In this study we develop a fundamental understanding of an aerodynamic method of forming fibrous web structures from short fibres. Computational fluid dynamics is employed to model the air flow in the system and based on this analysis the fibre dynamics in the process are then modelled. Experimental results were obtained by using high speed photography and we have found reasonable agreement between the theoretical predictions and the experimental findings.

Key words: 
fibre dynamics, turbulent flows, mathematical modelling, CFD, airlaying processes, fibrous web structures. 
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5.
STABILITY AND LOAD CARRYING CAPACITY OF A THINWALLED CORRUGATED TRAPEZOIDAL PLATE
A. TETER
Technical University of Lublin
Department of Applied Mechanics
20618 Lublin, ul. Nadbystrzycka 36, POLAND
email: teter@archimedes.pol.lublin.pl
Z. KOŁAKOWSKI
Technical University of Łód
Department of Strength of Materials and Structures (K12)
90924 Łód, ul. Stefanowskiego 1/15, POLAND
email: kola@orion.p.lodz.pl
The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. The present paper deals with a nonlinear analysis of stability and load carrying capacity for a sheetmetal section with trapezoidal repeating elements when the distortional deformations are taken into account. The plates are assumed to be simply supported at the ends. The investigation is concerned with the stability of thinwalled structures based on the second order nonlinear approximation of the asymptotic theory of stability. The asymptotic expansion established by Byskov and Hutchinson (1977) is employed in the numerical calculations performed using the transition matrix method. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of crosssectional distortions and the shear lag phenomenon are included.

Key words: 
stability, load carrying capacity, thinwalled structures, corrugated plate. 
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6.
AN ELASTOPLASTIC STRESS ANALYSIS IN A THERMOPLASTIC COMPOSITE BEAM OF ARBITRARY ORIENTATION SUBJECTED TO TRANSVERSE UNIFORMLY DISTRIBUTED LOAD
Ü. ESENDEMIR
Department of Mechanical Engineering
Süleyman Demirel University, Isparta, TURKEY
email: esen@mmf.sdu.edu.tr
Beam is a structural element loaded transversely in general conditions. This loading causes shear forces and bending moments. In this study, an elastoplastic stress analysis is carried out in a low density polyethylene thermoplastic composite beam reinforced by woven steel fibers subjected to a uniformly distributed load in transverse direction. In the elastoplastic solution, the material is assumed to be perfectly plastic. The expansion of the plastic region and the residual stress component of 'sigma'_{x} are determined for 0°, 15°, 30°, and 45° orientation angles. Yielding begins for 0° and 45° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. It starts though first at the upper surface for 15° and 30° orientation angles. The intensity of the residual stress component of 'tau'_{xy} is maximum on or around the x axis of the beam, but the residual stress component of 'sigma'_{x} is maximum at the upper and lower surfaces.

Key words: 
residual stress, elastoplastic stress analysis, thermoplastic composites, cantilever beam, uniformly distributed load. 
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7.
ON THE UNSTEADY UNIDIRECTIONAL FLOWS DUE TO SUDDEN APPLICATION OF A PRESSURE GRADIENT
M.E. ERDOGAN
Istanbul Teknik Üniversitesi, Makina Fakültesi, 80191, Gümüşsuyu
Istanbul, TURKEY
Some properties of unsteady unidirectional flows of viscous fluids are discussed for flows impulsively started from rest by a constant pressure gradient in the direction of the flow. Three illustrative examples are given. The first example is the unsteady Poiseuille flow, the second is the unsteady generalized Couette flow and the third is the unsteady flow in a circular pipe. It is found that the expressions of the quantities such as velocity, flux and skin friction are in series forms which may be rapidly convergent for large values of the dimensionless time but slowly convergent for small values of the dimensionless time or vice versa. It is shown that if their expressions can be found for one of large values of the dimensionless time or small values of the dimensionless time, these expressions can also be used for the other.

Key words: 
viscous flow, Poiseuille flow, pipe flow, generalized Couette flow. 
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8.
STOCHASTIC SECOND ORDER PERTURBATION APPROACH TO THE FINITE DIFFERENCE BASED VIBRATION ANALYSIS
M. KAMIŃSKI
Division of Mechanics of Materials, Technical University of Łód
al. Politechniki 6, 93590 Łód, POLAND
email: marcin@kmmlx.p.lodz.pl
P.D. SPANOS
Department of Mechanical Engineering
George Brown School of Engineering, Rice University
6100 Main Street, Houston, 770051892 Texas, USA
email: spanos@ruf.rice.edu
The second order perturbation second probabilistic moment analysis of stochastic vibrations problems in the context of the Finite Difference Method (FDM) is presented. The approach can be successfully used in all engineering analyses where FDM modelling of vibrations is appropriate and, in the same time, where certain structural parameters are random variables or fields. The main advantage of the Stochastic Finite Difference Method (SFDM) proposed is a relatively convenient extension of existing deterministic models of the classical theory of elastodynamics to the stochastic case. Theoretical developments are elucidated by the examples regarding the limitations on the second order random uncertainties measures of input random variables.

Key words: 
stochastic perturbation approach, Finite Difference Method, vibration analysis, beams and plates. 
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9.
A CLASS OF EXACT SOLUTIONS TO EQUATIONS GOVERNING THE STEADY PLANE FLOWS OF AN INCOMPRESSIBLE FLUID OF VARIABLE VISCOSITY VIA VON MISES VARIABLES
R.K. NAEEM and S.A. ALI
Department of Mathematics
University of Karachi, Karachi, Pakistan
A class to exact solutions of equations governing the steady plane flows of an incompressible fluid of variable viscosity are determined using von Mises variables. Applications of some of the solutions to the boundary value problems are also indicated.

Key words: 
von Mises variables, NavierStokes equations, incompressible fluid, variable viscosity, steady plane flows. 
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10.
MAGNETOCONVECTIVE FLOW AND HEAT TRANSFER BETWEEN VERTICAL WAVY WALL AND A PARALLEL FLAT WALL
M.S. MALASHETTY, J.C. UMAVATHI and V. LEELA
Department of Mathematics, Gulbarga University
Gulbarga585 106, Karnataka, INDIA
email: msshetty@blr.vsnl.net.in
The magnetoconvective flow and heat transfer between a long vertical wavy wall and a parallel flat wall in the presence of applied electric field parallel to gravity, magnetic field normal to gravity and uniform heat source is investigated. Nonlinear equations governing the motion have been solved by linearization technique wherein the flow is assumed to consist of two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and the perturbed part is solved using long wave approximation. The results are presented for various values of the Hartmann number, electric field loading parameter, heat source parameter and the wall temperature ratio. The effect of these parameters on the physical characteristics such as skin friction and the Nusselt number at the walls is studied.

Key words: 
magnetoconvection, heat transfer, perturbation method. 
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11.
A NONLINEAR CONSTITUTIVE RELATION FOR
FLOWING GRANULAR MATERIALS
M. MASSOUDI
US Department of Energy
National Energy Technology Laboratory
P.O. Box 10940, Pittsburgh, PA 15236, USA
email: massoudi@netl.doe.gov
C.L. RAO
Department of Applied Mechanics
Indian Institute of Technology Madras
Chennai600036, INDIA
We study the flow of granular materials down an inclined plane. We assume steady fully developed conditions. The constitutive relation is that of Rajagopal and Massoudi (1990), where the material parameters are given by the theory of Boyle and Massoudi (1990). We do not consider the effects of granular temperature (a measure of the fluctuating component of the velocity of the grains). The material parameters are given in this model as functions of volume fraction, particle diameter, restitution coefficient, and the excluded volume. The momentum equations are nondimensionalized and the resulting coupled nonlinear ordinary differential equations are solved numerically; the results are presented for the volume fraction and velocity profiles for different dimensionless numbers.

Key words: 
granular materials, constitutive relation, inclined flow, kinetic theory, boundary value problem. 
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12.
COMBINED HEAT AND MASS TRANSFER BY FREE CONVECTION PAST AN INCLINED FLAT PLATE
M. ANGHEL
Bogdan Vodă University
R3400 ClujNapoca, ROMANIA
M.A. HOSSAIN and S. ZEB
Department of Mathematics, University of Dhaka
Dhaka1000, BANGLADESH
I. POP
Department of Applied Mathematics, University of Cluj
R3400 Cluj, CP 253, ROMANIA
email: popi@math.ubcluj.ro
The steady laminar free convection boundary layer over the upper surface of a semiinfinite flat plate which is inclined at a small angle to the horizontal under the combined buoyancy effects of thermal and mass (concentration) effects is theoretically studied in this paper. Series solutions are obtained for both positive and negative inclinations of the plate, valid near the leading edge of the plate. Also, a series solution, which is valid only for positive inclinations and far downstream from the leading edge of the plate, is determined. The Kellerbox scheme is then used to complete the solution in the regions where neither series is adequate using the full boundary layer equations. Results for the skin friction coefficient, the local Nusselt and Scherwood numbers are presented. Also, the variation of the separation point of the boundary layer with the Schmidt number is determined and shown on a graph.

Key words: 
convection, thermal, concentration, flat plate, boundary layer. 
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13.
CONTACT PROBLEM FOR ROUGH RIGID DISK AND PLATE WITH THIN COATING ON THE CYLINDRIC HOLE
A.S. KRAVCHUK
Department of Theoretical Mechanics
Belarussian State Polytechnic Academy
Skorina Avenue 65, Minsk, 220027, BELARUS
The model of elastic interior contact between a rough rigid disk and an isotropic plate with thin coating on a smooth cylindrical hole was developed. These investigations allowed us to take into account plastic deformations of a layer of the hole and probability characteristics of surface roughness of a disk. The method of complex potentials (the potentials of KolosovMuskhelishvily) and the dependence of plastic deformations of the layer obtained by Alecseev for plain joints were used. The problem was reduced to an integraldifferential equation with respect to normal contact stress.

Key words: 
contact problem, complex potentials, plastic coating, roughness. 
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14.
DYNAMICS OF BRIDGELESS CONSTANT TEMPERATURE ANEMOMETERS
J. KIEŁBASA
Department of Power Installations
University of Mining and Metallurgy
al. Mickiewicza 30, 30059 Kraków, POLAND
Strata Mechanics Research Institute, Polish Academy of Sciences
ul. Reymonta 27, 30059 Kraków, POLAND
The paper presents a new technique for measuring the time constant of the bridgeless CTA in which the overheating ratio is set digitally. The results of studies of anemometer dynamic behaviour are discussed. The overheating ratio is modulated sinusoidally with respect to its mean value. The tests were run in steady flow conditions.
Hot wire sensors are made of tungsten wire 8 micrometers in diameter, 1.52 mm long. Tests were run in the air, at flow velocities of up to 1 m/s. frequency ranged from 10500 Hz. The mean value of the overheating ratio was 1.8, while the amplitude of modulation was 10%.

Key words: 
hot wire anemometer, thermal anemometer, bridgeless anemometer circuit, time constant of an anemometer. 
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