
Archive issue  vol.9, No.4
1.
A STUDY OF TWO DIMENSIONAL UNSTEADY DUSTY FLUID FLOW UNDER VARYING TEMPERATURE
C.S. BAGEWADI and B.J. GIREESHA
Department of Studies and Research in Mathematics, Kuvempu University
Jnana Sahyadri  577 451, Shimoga, Karnataka, INDIA
email: university@sancharnet.in
A twodimensional unsteady dusty fluid flow in the Frenet frame field system of the threedimensional Euclidean space E^{3} is studied. Basic equations are decomposed into intrinsic forms and flow analysis is carried out by varying i) the velocities of dust and fluid in different directions, ii) the temperature of both the fluid and the dust cloud. The graphs for temperatures of dust with respect to time are plotted.

Key words: 
Frenet frame field system, dusty gas, velocity of dusty gas and fluid phase, unsteady dusty fluid, temperature, pressure, relaxation zone and density. 
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2.
PERMANENT MAGNET BEARING DESIGN: OPTIMISING THE MAGNETISATION DIRECTION
F. DI PUCCIO
Department of Mechanical, Nuclear and Production Engineering
University of Pisa, Diotisalvi 2 Str., 56126 Pisa, ITALY
email: dipuccio@ing.unipi.it
Permanent magnet bearings may be conveniently employed in several mechanical applications when friction and wear have to be avoided. The mechanical behaviour of these components is defined by the force acting between the elements of the bearing and by the stiffness of the system. In order to get the desired performance of the bearing a compromise of force and stiffness can be achieved, e.g. by selecting the magnetisation direction of the elements. The paper reviews some general criteria for permanent magnet bearing design and proposes a method for evaluating the most suitable magnetisation direction, based on the equivalent current method and employing Finite Element analyses. Three sample cases of annular and tapered bearing are reported, for which design maps for axial and radial bearings are also presented.

Key words: 
magnetic bearings, permanent magnets, magnetic force evaluation, bearing stiffness. 
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3.
PREDICTION OF UNSTEADY VAWT AERODYNAMICS BY LIFTING LINE THEORY
H. DUMITRESCU and V. CARDOS
Institute of Statistics and Applied Mathematics of the Romanian Academy
P.O. Box 124, RO70700, Bucharest, ROMANIA
email: vcardos@gheorghita.ima.ro
Based on the lifting line theory and a free vortex wake model, a method including dynamic stall effects is presented for predicting the performance of a threedimensional verticalaxis wind turbine. A vortex model is used in which the wake is composed of trailing streamwise and shedding spanwise vortices, whose strengths are equal to the change in the bound vortex strength as dictated by Helmholtz and Kelvin's theorems. Performance parameters are calculated by applying the BiotSavart law along with the KuttaJoukowski theorem and a semiempirical dynamic stall model. Predictions are shown to compare favorably with the existing experimental data. The method can predict local and global performances more accurately than the previous momentum models.

Key words: 
aerodynamics, wind turbines, vortex methods, unsteady flow, dynamic stall. 
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4.
VISCOUS TRANSONIC AIRFOIL FLOW SIMULATION
H. DUMITRESCU
Institute of Statistics and Applied Mathematics
13 September Street, Sect. V, Bucharest, ROMANIA
email: horiad@gheorghita.ima.ro
F. FRUNZULICĂ
Department of Aerospace Engineering, University "POLITEHNICA" of Bucharest
1 Gh. Polizu Street, Sect.1, ROMANIA
email: ffrunzi@yahoo.com
A calculation method for the subsonic and transonic viscous flow over airfoil using the displacement surface concept is described. This modelling technique uses a finite volume method for the timedependent Euler equations and laminar and turbulent boundarylayer integral methods. Additionally special models for transition, laminar or turbulent separation bubbles and trailing edge treatment have been selected. However, the flow is limited to small parts of trailing edgetype separation. Comparisons with experimental data and other methods are shown.

Key words: 
transonic viscous flow, Euler equation, boundary layer. 
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5.
SYNERGY ANALYSIS OF VAPORISATION PROCESSES
V.V.I. HOFFMANN, G. HUMINIC
Transilvania University of Brasov, Faculty of Mechanics
Thermodynamics and Fluid Mechanics Department, Ro  500 036, ROMANIA
email: gabi.p@unitbv.ro
In this paper, the authors present a new expression of the vaporisation heat in the case of isobarisothermal processes, the identification of the components of the vaporisation heat and the correct description of the phenomena, which are happening at the critical state.

Key words: 
entropy, synergy, vaporisation, critical state and magnetisation. 
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6.
THERMALRADIATION EFFECTS ON FORCED CONVECTION HEAT TRANSFER ON A FLAT PLATE EMBEDDED IN POROUS MEDIA FOR POWERLAW FLUIDS
M.A. MANSOUR
Mathematics Department, Assiut Faculty of Science, Assiut University, Assiut, EGYPT
N.A. ELSHAER
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, EGYPT
An analysis is presented to investigate the combined effect of the thermal radiation and the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate to a powerlaw nonNewtonian fluid saturated porous medium. The Forchheimer extension is also considered in the flow equations. The rosseland approximation is used to describe the radiative heat flux in the energy equation. Numerical results are presented for the velocity distribution and temperature profiles within the boundary layer. The effects of the flow index, radiation, first and secondorder resistance on the velocity, and temperature profiles are discussed. The missing wall values of the velocity and thermal functions are tabulated.

Key words: 
radiation, boundarylayer, nonNewtonian powerlaw fluid, heat transfer porous medium. 
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7.
RECURSIVE BACKSTEPPING STABILIZATION OF A WHEELED MOBILE ROBOT
F. MNIF (1,3) and A.S. ALYAHMADI (2)
(1) Department of Electrical and Computer Engineering, Sultan Qaboos University
P.O. Box 33, Muscat 123, OMAN
email: mnif@squ.edu.om
(2) Department of Mechanical and Industrial Engineering, Sultan Qaboos University
P.O. Box 33, Muscat 123, OMAN
email: amery@squ.edu.om
(3) Intelligent Control, Design and Optimization of Complex Systems Research Unit, TUNISIA
email: faical.mnif@insat.rnu.tn
This research is aimed at the development of a dynamic control to enhance the performance of the existing dynamic controllers for mobile robots. System dynamics of the carlike robot with nonholonomic constraints is employed. A backstepping approach for the design of discontinuous state feedback controller is used for the design of the controller. It is shown that the origin of the closed loop system can be made stable in the sense of Lyapunov. The control design is made on the basis of a suitable Lyapunov function candidate. The effectiveness of the proposed approach is tested through simulation on a carlike vehicle mobile robot.

Key words: 
backstepping approach, mobile robot, chained form systems, nonholonomic systems. 
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8.
STEADY LAMINAR WATER BOUNDARY LAYER FLOW OVER A YAWED CYLINDER
S. ROY and P. SAIKRISHNAN
Department of Mathematics, Indian Institute of Technology Madras
Chennai  600036, Tamilnadu, INDIA
email: sjroy@iitm.ac.in
The aim of this work is to study the influence of temperaturedependent viscosity and the Prandtl number on the steady nonsimilar laminar forced convection flow over a yawed infinite circular cylinder starting from the origin of the streamwise coordinate to the point of separation (zero skin friction in the streamwise direction). The results show that the effect of variable viscosity and the Prandtl number is to move the point of separation downstream and the yaw angle has very little effect on the location of the point of separation. The heat transfer rate is found to depend strongly on viscous dissipation, wheras skin frictions are comparatively less affected. In general, the results pertaining to variable fluid properties differ significantly from those of constant fluid properties.

Key words: 
water boundary layer, yawed cylinder. 
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9.
PLANE HARMONIC WAVES IN TRANSVERSELY ISOTROPIC PIEZOTHERMOELASTIC MATERIALS
J.N. SHARMA and M. PAL
Department of Applied Sciences, National Institute of Technology
Hamirpur (HP)  177 005, INDIA
email: jns@recham.ernet.in
The aim of the paper is to study the propagation of plane harmonic waves in homogeneous, piezothermoelastic materials having hexagonal symmetry. After deriving the secular equation, it is found that four dispersive modes are possible. The low and high frequency approximations for the propagation speeds and attenuation coefficients have been obtained for quasilongitudinal (QL), quasitransverse (QT), and quasithermal (Tmode) by using the theory of algebraic functions. The limiting cases of the frequency equation have also been discussed in addition to the paths of particles during the motion. The paths of particles during the motion have been found to be elliptic, in general. The velocities and attenuation coefficients for various waves have been computed numerically for cadmium selenide material (6mm class) having hexagonal symmetry and are represented graphically. The inclinations of major axes of the paths of particles of QL and QT waves during the motion with wave normal have also been computed and represented graphically with respect to frequency.

Key words: 
harmonic waves, piezothermoelastic materials, particle paths, attenuation, cadmium selenide. 
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10.
FIELDINDUCED STRUCTURING AND LIGHT TRANSMISSION IN A GRAVITATIONALLY STRATIFIED FERROSUSPENSION: AN APPLICATION IN POLYMER FILM VISCOMETRY
Z.P. SHULMAN, S.B. KASHEVSKI and I.V. PROKHOROV
National Academy of Sciences of Belarus
A.V. Luikov Heat and Mass Transfer Institute
15 P. Brovka Str., Minsk 220072, BELARUS
email: bekas@itmo.by
The dynamics of structuring and light transmission in response to a transverse magnetic field applied to a gravitationally stratified layer of a ferromagnetic suspension is studied numerically and experimentally. The results obtained have been used to substantiate and implement in practice a magnetooptical method of measuring the fluid viscosity in thin films. This method is employed to investigate the viscosity kinetics of a polymer solution in a drying film.

Key words: 
magnetic suspension, fieldinduced structuring, magnetooptics, polymer solution, viscometry. 
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11.
FULLY DEVELOPED FLOW AND HEAT TRANSFER IN A HORIZONTAL CHANNEL CONTAINING AN ELECTRICALLY CONDUCTING FLUID SANDWICHED BETWEEN TWO FLUID LAYERS
J.C. UMAVATHI, M.S. MALASHETTY and A. MATEEN
Department of Mathematics, Gulbarga University
Gulbarga  585 106, Karnataka, INDIA
email: malashettyms@yahoo.com
The problem of fully developed flow and heat transfer in a horizontal channel consisting of an electrically conducting fluid layer sandwiched between two fluid layers is studied analytically. The fluids in all phases are assumed to be incompressible and immiscible. Further the fluids are assumed to have different viscosities and thermal conductivities. The governing differential equations are linear and exact solutions are obtained. The expressions for velocity and temperature distributions are computed numerically for different values of physical parameters and the results are presented graphically. The effect of increasing the Hartmann number M is to decrease the velocity and temperature field. It is found that with suitable values of ratios of viscosities and thermal conductivities, the velocity and temperature can be increased.

Key words: 
threephase, MHD, heat transfer, horizontal channel. 
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12. Brief note
ANALYTICAL APPROXIMANTS FOR A BOUNDARY LAYER FLOW ON A STRETCHING MOVING SURFACE WITH A POWER LAW VELOCITY
LIANCUN ZHENG, XUEHUI CHEN
Department of Mathematics and Mechanics
University of Science and Technology Beijing, Beijing 100083, CHINA
email: liancunzheng@hotmail.com
XINXIN ZHANG
Mechanical Engineering School
University of Science and Technology Beijing, Beijing 100083, CHINA
email: xxzhang@me.ustb.edu.cn
This paper presents an efficient analytical decomposition and numerical procedure technique for solving a selfsimilarity boundary layer on a moving surface with power law velocity. The types of potential flows necessary for similar solutions to the boundary layer equations and the existence conditions of the Pad e' approximants [2/2] of degree 4 are determined. Furthermore, the analytical approximations and numerical solutions are presented for different velocity parameters. The results demonstrate the reliability and efficiency of the proposed algorithm.

Key words: 
boundary layer, stretching surface, similarity solution, analytical approximants. 
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13. Technical paper
APPLICABILITY OF A FEW ANALYTICAL FORMULATIONS FOR DYNAMIC CHARACTERISTICS OF ELEVATED TANKS WITH BATTERED STAGINGS
S.C. DUTTA
Department of Applied Mechanics
Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
email: scdind@netscape.net
R. ROY
Department of Applied Mechanics
Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
email: rroybec@yahoo.com
S. DUTTA
Department of Applied Mechanics
Bengal Engineering College (Deemed University)
Howrah 711 103, West Bengal, INDIA
email: somdutta68@hotmail.com
The applicability of available analytical formulations for elevated tanks with vertical stagings is shown to the similar tanks with battered stagings. The formulation includes the dynamic characteristics like lateral and torsional stiffness and natural periods. Both frame and shaft supported stagings for elevated tanks are considered with and without accounting for the effect of soilstructure interaction. The values obtained through analytical formulation are compared to the results of finite element analysis and found to have reasonable performance. Thus the study yields handy formulations to be used for seismic design of elevated tanks with battered stagings.

Key words: 
elevated tanks, frame staging with battering, shaft staging with battering, lateral and torsional stiffness, lateral and torsional periods. 
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14. Letter to the Editor
COMMENTS ON MHD PLASMA FLOW IN A ROTATING ENVIRONMENT IN THE PRESENCE OF AN INCLINED MAGNETIC FIELD
S.K. GHOSH
Department of Mathematics, Narajole Raj College, P.O.: Narajole
Dist : Midnapore (West), West Bengal, INDIA
email: g_swapan@rediffmail.com
I. POP
Faculty of Mathematics, University of Cluj
R3400 Cluj, CP 253, ROMANIA
email address: popi@math.ubbcluj.ro
This note adds some comments to the papers published by Ghosh (1997; 2001). It is shown that the inertial frequency becomes significant when forced oscillation is taken into account. This emerges from the backbone of a remarkable approach of designing a spacecraft subject to a controlled thermonuclear reaction.

Key words: 
neutral plasma stability parameter, Ghosh inertial frequency parameter, resonance, electrical discharge, turbulence. 
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