
Archive issue  vol.9, No.3
1.
MULTISCALING ANALYSIS OF A NONLINEAR BOUNDARY VALUE PROBLEM IN LUBRICATION THEORY
E. ALIU, J.J. SHEPHERD and H.J. CONNELL
Applied and Numerical Modelling Group, Department of Mathematics
Royal Melbourne Institute of Technology, Melbourne, 3000, AUSTRALIA
email: jshep@ems.rmit.edu.au
The method of multiple scales, a long standing alternative to the method of matched expansions, is applied to the nonlinear boundary value problem modelling the operation of a onedimensional gas lubricated slider bearing, at large values of the bearing number. Approximate expansions for the pressure profile, load bearing capacity and the location of the centre of pressure are obtained, and compared with the results of applying matched expansions and numerical techniques.

Key words: 
bearing, lubrication, multiscaling, perturbations. 
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2.
THERMOPHORESIS FREE CONVECTION FROM A VERTICAL CYLINDER EMBEDDED IN A POROUS MEDIUM
A.J. CHAMKHA
Manufacturing Engineering Department
The Public Authority for Applied Education and Training
P. O. Box 42325, Shuweikh, 70654, KUWAIT
M. JARADAT and I. POP
Faculty of Mathematics, University of Cluj
R3400 Cluj, CP 253, ROMANIA
email: popi@math.ubbcluj.ro
This paper deals with the steady free convection over an isothermal vertical circular cylinder embedded in a fluidsaturated porous medium in the presence of the thermophoresis particle deposition effect. The governing partial differential equations are transformed into a set of nonsimilar equations, which are solved numerically using an implicit finitedifference method. Comparisons with the previously published work are performed and the results are found to be in excellent agreement. Many results are obtained and a representative set of these results is displayed graphically to illustrate the influence of the various physical parameters on the wall thermophoretic deposition velocity and concentration profiles.

Key words: 
free convection, thermophoresis, vertical cylinder, boundary layer, porous medium. 
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3.
UNSTEADY FREE CONVECTION FLOW OF A DUSTY GAS PAST A SEMIINFINITE INCLINED PLATE WITH CONSTANT HEAT FLUX
P. GANESAN
School of Mathematics, Anna University, Chennai  600025, INDIA
email: ganesan@annauniv.edu
G. PALANI
#5 (New No.19) 4th Street
Rajaji Nagar, Villivakkam, Chennai  600 049, INDIA
email: gpalani32@yahoo.co.in
A numerical solution for the flow of fluid with dusty particles past a semiinfinite inclined plate with a constant heat flux is obtained by an implicit finite difference method, which is unconditionally stable. Gasvelocity, dustvelocity, temperature, skin friction and Nusselt number are shown graphically. It is observed that the velocity of the dustygas decreases with decreasing the inclination angle 'phi' to the horizontal. An increase in the mass concentration of dust also causes a fall in the gasvelocity.

Key words: 
finitedifference, dusty gas, steady state, skin friction, Nusselt number. 
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4.
THE STUDY OF THERMAL PROCESSES AS A BASIS FOR QUALITY PRODUCTION OF TOOLS OF LOWALLOY HIGHSPEED STEELS
J. JAWORSKI
Technical University of Rzeszów
Department of Mechanical Engineering and Production Organization
Ul. W. Pola 2, 35959 Rzeszów, POLAND
email: jjktmiop@prz.rzeszow.pl
In the paper, the range of application of tools made of lowalloy high speed steels has been determined on the basis of the investigation of the temperature field distribution in the cutting edge, hardness measurement of the cutting edge, the hot hardness and the assumed systematisation of wear causes. The most effective surface treatment methods have been proposed.

Key words: 
highspeed steel, hot hardness, temperability, durability. 
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5.
BLOOD FLOW IN A VESSEL WITH ASYMMETRIC ANEURYSM
B.V. Rathish KUMAR ^{1,3}, Takami YAMAGUCHI ^{2}, Hao LIU ^{3} and Ryutaro HIMENO ^{3}
^{1}Department of Mathematics and Scientific Computing
Indian Institute of Technology, Kanpur  208016, U.P., INDIA
email: bvrathishkumar@yahoo.pl
^{2}Department of Mechanical and Systems Engineering
NIT, Gokisocho, Showaku, Nagoya, 4668555, JAPAN
^{3}Division of High Performance Computing
Computer and Information Center, Riken, Wakoshi, 3510198, JAPAN
Blood flow in an asymmetrically dilated fusiform artery has been investigated under pulsatile inflow conditions for a full cycle of period T. The coupled nonlinear partial differential equations governing the conservation of mass and momentum of a viscous incompressible fluid flow has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of nonlinear terms and the pseudocompressibility technique in the current numerical scheme makes it robust both in space and time. The combined influence of asymmetric geometry and Reynolds number on the hemodynamic factors like WSS, pressure and velocity has been analyzed. Vortices favoring the thrombogenesis are seen to periodically manifest with 3D shedding in the diastolic phase of the flow cycle. During the whole cycle, relatively high WSS is noticed at the head and toe of the aneurysm. Further for the entire period (T) considerable pressures, with relatively large ones on the distal portion, are noticed on the hull of the aneurysm.

Key words: 
(for subject classification) 1. NavierStokes equations (3D, unsteady, incompressible), 2. biological fluid mechanics (Blood Flow, Aneurysm), 3. numerical (FVM). 
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6.
VIBRATIONAL EFFECT ON HEAT TRANSFER AND ENTROPY GENERATION IN A CIRCULAR POROUS CAVITY
S. MAHMUD
Department of Mechanical Engineering, University of Waterloo
200 University Avenue West, Waterloo, Ontario, N2L3G1, CANADA
email: smahmud@engmail.uwaterloo.ca
R.A. FRASER
Department of Mechanical Engineering, University of Waterloo
200 University Avenue West, Waterloo, Ontario, N2L3G1, CANADA
email: rafraser@engmail.uwaterloo.ca
We investigate the nature of heat transfer and entropy generation for natural convection in a twodimensional circular section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zerogravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of the average Nusselt number (Nu_{av}), entropy generation number (Ns_{av}), Bejan number (Be_{av}), and kinetic energy (KE_{av}).

Key words: 
convection, heat transfer, entropy generation, irreversibility, porous media, vibration. 
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7.
FREE CONVECTION INSIDE A VERTICAL INPHASE WAVY CAVITY
S. MAHMUD
Department of Mechanical Engineering, University of Waterloo
200 University Avenue West, Waterloo, Ontario, N2L3G1, CANADA
email: smahmud@engmail.uwaterloo.ca
R.A. FRASER
Department of Mechanical Engineering, University of Waterloo
200 University Avenue West, Waterloo, Ontario, N2L3G1, CANADA
email: rafraser@engmail.uwaterloo.ca
We examined the heat transfer and fluid flow characteristics inside a bent cavity made of two horizontal straight walls and two vertical bent walls. Bent walls are assumed to follow a profile of cosine curve. Horizontal straight walls are kept adiabatic, while the bent walls are isothermal but kept at different temperatures. Laminar nature convection inside the cavity is considered. Governing equations were discretized using the Finite Volume method with collocated variable arrangement. Simulation was carried out for a range of wave ratio 'lambda' = 0.000.6, aspect ratio A = 1.04.0, and Rayleigh number Ra = 10^{0}10^{7} for a fluid having Prandtl number 1.0. Streamlines and isothermal lines are used to present the corresponding flow and thermal field inside the enclosure. Local and global distributions of Nusselt number are presented for the above configuration. Lastly, velocity profiles are presented for some selected cases of A and 'lambda' inside the enclosure for better understanding of the influence of flow field on the thermal field.

Key words: 
bent cavity, finitevolume method, laminar flow, natural convection, wavy wall. 
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8.
THE LOCATION OF ANOMALOUS SPIKES ON A WORKING ROTOR: A THEORICALEXPERIMENTAL TEST
V. NIOLA
Department of Mechanical Engineering for Energetic
University of Naples "Federico II"
Via Claudio 21, 80125, Napoli, ITALY
Email: vniola@unina.it
G. QUAREMBA
University of Naples "Federico II"
Via Pansini 5, 80131, Napoli, ITALY
Email: quaremba@unina.it
R. OLIVIERO
Departament of Mathematics for Economic, Financial and Insurance Decisions
University of Rome "La Sapienza"
Via del Castro Laurenziano 6, 00161, Roma, ITALY
Email: rolivier@scec.eco.uniromal.it
An efficient and efficacious response to the continuous request of "high performance", in terms of qualitative standards, becomes one of the most important factors in determining the profit of a business.
The aim of this paper is to check the reliability of a signal analysis method based on a Discrete Wavelet Transform (DWT). This algorithm appears useful in revealing anomalies that are added to a regular signal. Such anomalies, characterized by high frequency, small amplitude and short period, generally are filtered in a data logging or sampling.
Moreover, it has been illustrated how, for each level of the DWT, the maximum value of the entropy allows the location as well as the best graphical representation of the phenomenon in study. In this paper the results obtained during the functioning of an experimental equipment will be shown.

Key words: 
wavelet analysis, vibrations, discrete wavelet transform, spike analysis, entropy. 
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9.
NUMERICAL STUDY OF VISCOUS FLOW THROUGH A LOCALLY EXPANDEDCHANNEL
S. PRAMANIK and G.C. LAYEK
Department of Mathematics, Burdwan University
Burdwan  713104, West Bengal, INDIA
T. RAY MAHAPATRA
Department of Mathematics, R.B.C College
Naihati, 24  Parganas (N), West Bengal, INDIA
H.P. MAZUMDAR
Physics and Applied Mathematics Unit, Indian Statistical Institute
203 B.T. Road, Kolkata  700108, INDIA
The numerical solution to the problem of viscous incompressible flow of a Newtonian fluid in a locally expanded channel has been obtained for low and moderate high Reynolds numbers under laminar conditions. The wellknown finite difference scheme in a staggered grid due to Harlow and Welch (1965) is used to discretize the equations of fluid flow. The present algorithm is of twostages. In the first stage, Poisson equation for pressure has been solved iteratively and then pressure velocity corrections are made in the second stage. The flow characteristics such as the wall shear stress, velocity distribution and pressure distribution are then calculated. The results are presented graphically and discussed.

Key words: 
staggered grid, twostage numerical algorithm, locally expanded channel and viscous flow separation. 
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10. Dedicated to Professor A.Z. Szeri on his seventieth Birthday
COUETTE FLOWS OF FLUIDS WITH PRESSURE DEPENDENT VISCOSITY
K.R. RAJAGOPAL
Department of Mechanical Engineering
Texas A&M University, College Station, TX 778433123, USA
email: krajagopal@mengr.tamu.edu
For liquids such as water, for a range of pressures for which the density remains nearly constant, the viscosity could change by several orders of magnitude. Thus, such liquids could be approximated as incompressible liquids whose viscosity depends on the pressure. Stokes (1945) recognized this possibility and the fact that the viscosity could be considered to be independent of the pressure in only special flows. That this is indeed so has been verified in the case of numerous liquids (Bridgman, 1931). In this short study, we allow the viscosity of the fluid to be dependent on the pressure and investigate the consequence of the effect of gravity in simple flows such as Couette flows between parallel plates. We find that gravity can have a profound effect on the structure of the flow. Its presence leads to the concentration of vorticity adjacent to one of the plates.

Key words: 
pressure dependent viscosity, implicit constitutive equations, boundary layers, Reynolds number, elastohydrodynamics. 
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11.
FLEXURAL AND EXTENSIONAL WAVES PROPAGATION IN TRANSVERSELY ISOTROPIC PLATES IN GENERALIZED THERMOELASTICITY
K.L. VERMA
Department of Mathematics, Government Post Graduate College
Hamirpur (H.P.).  177 005, INDIA
klverma@sancharnet.in
S.C. VERMA
Electrical Power Research and Development
Center, Chubu Electric Power Co. Inc.
201, Kitasekiyama, OdakaCho, Midoriku, Nagoya4598522, JAPAN
N. HASEBE
Department of Civil Engineering
Nagoya Institute of Technology
GokisoCho, ShowaKu, Nagoya 466, JAPAN
In this paper, the boundary value problem concerning the propagation of plane harmonic thermoelastic waves in flat infinite homogeneous transversely isotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations for a heat conducting thermoelastic plate corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. The horizontally polarized SH wave gets decoupled from the rest of motion and propagates without dispersion or damping, and is not affected by thermal variations on the same plate. A numerical solution to the frequency equations for an aluminum plate (isotropic) and zinc plate (transversely isotropic) is given, and the dispersion curves are presented. The three motions namely, longitudinal, transverse and thermal of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves is modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.

Key words: 
generalized thermoelasticity, thermal relaxation times, frequency equations, dispersion, extensional waves, and flexural waves. 
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12. Brief note
THE FLOW OF VISCOUS INCOMPRESSIBLE FLUID CONFINED BETWEEN A ROTATING DISK AND A POROUS MEDIUM
R.C. CHAUDHARY and P.K. SHARMA
Department of Mathematics, University of Rajasthan
Jaipur  302004, INDIA
email: ramadiaranchaudharyfglrediffmail.com
email: pawkumar20@yahoo.eo.in
The flow of a viscous fluid induced by the rotation of a disk bounded by a porous medium fully saturated with the liquid is discussed. It is assumed that the flow between the disk and the porous medium is governed by NavierStokes equations and that in the porous medium by Brinkman (1947) equations. Flows in the two regions are matched at the interface by the conditions suggested by OchaoTapia and Whittaker (1995a; b). Analytical expressions for velocity and skinfriction are obtained and discussed.

Key words: 
incompressible fluid flow, porous medium, rotating disk. 
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13. Brief note
MAGNETIC FLUID PRESSURE ON FINGERING PHENOMENON THROUGH HOMOGENEOUS POROUS MEDIA
Rajesh C. SHAH
Department of Mathematics, Institute of Technology
Nirma University of Science and Technology
SarkhejGandhinagar Highway, Ahmedabad  382 481, Gujarat State, INDIA
email: dr_rcshah@yahoo.com
This paper studied theoretically the net effect of pressure and the consequences arising due to the addition of a layer of a magnetic fluid to the fingering phenomenon through homogeneous porous media by comparing the model with the conventional one.

Key words: 
magnetic fluid, fingering phenomenon, porous media. 
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