
Archive issue  vol.6 No.3
2.
COMBINED THERMAL AND DIFFUSION BUOYANCY EFFECTS IN MICROPOLAR FLUIDS
M.A. MANSOUR
Mathematics Department, Faculty of Science,
Assuit University, Assuit, EGYPT
A.A. MOHAMMADEIN and S.M. EL KABEIR
Mathematics Department, Faculty of Science,
South Valley University, Aswan, EGYPT
R.S.R. GORLA
Mechanical Engineering Department, Cleveland State University,
Cleveland Ohio 44115, USA
email: Rama.Gorla@grc.nasa.gov
A regular perturbation analysis is presented for the laminar natural convection flows of micropolar fluids with temperature dependent viscosity: a freelyrising plane plume, the flow above a horizontal line source on an adiabatic surface (a plan wall plume) and the flow adjacent to a vertical uniform flux surface. While these flows have wellknown powerlaw similarity solutions when the fluid viscosity is taken to be constant, they are nonsimilar when the viscosity is considered to be a function of temperature. A flow adjacent to a vertical isothermal surface is also analyzed for comparison in order to estimate the extent of validity of the perturbation analysis. The formulation used here provides a unified treatment of variable viscosity effects on those four flows. Computed firstorder perturbation quantities are presented for all four flows. The velocity, microrotation distribution, temperature and concentration profiles are shown. Numerical results are presented for the local Nusselt number and Sherwood number, wall shear stress and wall couple stress.

Key words: 
combined convection, micropolar fluids, heat transfer. 
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3.
EXACT SOLUTIONS FOR THE CONVECTIVE FLOW OF FLUIDS OF DIFFERENT PRANDTL NUMBERS NEAR AN INFINITE VERTICAL PLATE IN A ROTATING SYSTEM
P. CHANDRAN and N.C. SACHETI
Department of Mathematics and Statistics
College of Science, Sultan Qaboos University
PC 123, Muscat, SULTANATE OF OMAN
email: chandran@squ.edu.om
A.K. SINGH
Department of Mathematics, Banaras Hindu University
Varanasi  221005, INDIA
The partial differential equations governing the unsteady convective flow of a fluid have been solved exactly when the flow takes place near an infinite vertical plate in a system rotating with a constant angular velocity. Exact analytical solutions for the boundary layer velocity variables and skin friction components have been presented separately for the cases of fluids whose Prandtl numbers are less than or greater than unity. The influence of rotation on the temporal and spatial variations of these physical quantities has been discussed for two specific fluids, each belonging to the two separate Prandtl number categories considered. It is seen that the rotation parameter and the Prandtl number have significant effects on the boundary layer velocity and skin friction.

Key words: 
convective flow, rotational thermal buoyancy, magnetic force, skin friction. 
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4.
THERMOSOLUTAL INSTABILITY OF WALTERS' (MODEL B') ROTATING FLUID WITH VERTICAL MAGNETIC AND VARYING GRAVITY FIELD IN A POROUS MEDIUM
V. SHARMA and S. SHARMA
Department of Mathematics, Himachal Pradesh University
Shimla 171 005, INDIA
The thermosolutal instability of Walters' (model B') elasticoviscous rotating fluid in a porous medium is considered in the presence of a uniform magnetic field and varying gravity field. For the case of stationary convection, the solute parameter delays the onset of convection. The system is stable or unstable as gravity increases or decreases in the presence of rotation and magnetic field stabilizes the system for T_{A1} < [(1+x_{0})+PQ_{1}]^{2} [(1+x_{0})P^{2}] as gravity increases or decreases. The porous medium permeability is also found to stabilize the system under certain conditions in the presence of rotation and magnetic field; whereas the kinematic viscoelasticity has no effect on the onset of convection. The magnetic field, rotation, porous medium permeability, kinematic viscoelasticity, the solute parameter and varying gravity field introduce oscillatory modes in the system, which were nonexistent in their absence. The case of overstability is also considered wherein the sufficient conditions for the nonexistence of overstability are obtained. The variation of the Rayleigh number with respect to the solute parameter, rotation, magnetic field and porous medium permeability for the stationary convection is also shown graphically.

Key words: 
thermosolutal instability, Walters' (model B') rotating fluid, magnetic field, variable gravity field, porous medium. 
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5.
ACTIVE SUSPENSION CONTROL FOR VEHICLES AND NUMERICAL CALCULATIONS BY USING ARTIFICIAL NEURAL NETWORKS
H.A. ÖZYIGIT and H.R. ÖZ
Department of Mechanical Engineering, Celal Bayar University,
45140 Muradiye, Manisa, TURKEY
B. KARLIK
International Computing Institute, Ege University,
35100 Bornova, Izmir, TURKEY
email: bkarlik@bornova.ege.edu.tr
The increase in vehicle speed, unsuitable road conditions and comfort demand have resulted in extensive research on vibration control of vehicle systems. In this paper, firstly, a specific passenger car (with a conventional suspension system) was considered including the vertical body displacements for sinusoidal road functions. Secondly, passive and active vibration control cases are studied to eliminate the body deflections. Thirdly, a new calculation method, namely artificial neural networks (ANN), for control force values was proposed for the active suspension system. In ANN application, feedforward, multilayer perceptron and backpropagation algorithm are used. By training calculated control values the required values were obtained by using ANN application. The analysis is performed in frequency domain.

Key words: 
active suspension, artificial neural networks, vibration control. 
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6.
AN INVESTIGATION ON OPTIMISATION OF A CAR RIM BY ELASTOPLASTIC ANALYSIS
H. AKBULUT
Department of Mechanical Engineering, Atatürk University, Erzurum, TURKEY
email: hamitakbulut@yahoo.com
This paper presents the optimisation of an octopus type car rim in which first critical zones have been found and then optimum thickness has been investigated using an elastoplastic analysis. In this study, three dimensional finite elements method has been used for conducting elastoplastic analysis. In the finite element analysis, the elements forming the meshes are hexahedral linear elements with eight nodes. Twelve different meshes were used. A quadrant of rim is exploited due to its symmetric shape. The theoretical results have been compared with experimental ones. It seems that the theoretical results are in agreement with the experimental ones. The results were given in tables, graphics and figures.

Key words: 
rim, finite element method, elastoplastic analysis, optimization. 
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7.
EFFECTS OF FREE CONVECTION CURRENTS ON THE OSCILLATORY FLOW OF AN ELECTRICALLY CONDUCTING FLUID PAST A STATIONARY OR STEADILY MOVING VERTICAL PLATE WITH VARIABLE SUCTION AND CONSTANT HEAT FLUX
V.M. SOUNDALGEKAR
31A12, Brindavan Society, Thane 400 061, INDIA
P.D. WAVRE
Tara Chand College, Baramati (Poona), INDIA
H.S. TAKHAR
Department of Engineering Technology
Manchester Metropolitan University
Chester Street, Manchester MI 5GD, U.K.
email: hstakhar@man.ac.uk
An approximate analysis of a twodimensional flow of an electrically conducting incompressible viscous fluid past an infinite porous plate, stationary or steadily moving in its own plane, is presented under the following conditions: i) suction velocity oscillates about a constant nonzero mean; ii) the free stream velocity oscillating in time about a constant mean; iii) constant heat flux at the plate; iv) presence of free convection currents due to the temperature difference; v) a uniform transverse magnetic field.
Approximate solutions to coupled nonlinear equations governing the problem have been derived for the transient velocity, the transient temperature, the amplitude and the phase of the skinfriction and the Nusselt number.
During the course of analysis, the effects of the Grashof number Gr, the magnetic field parameter M, the suction parameter A, the Eckert number E, the velocity of the plate V and the frequency 'omega' have been discussed.

Key words: 
oscillatory flow, conducting fluid, vertical plate, variable suction. 
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8.
RHEOLOGICAL PROPERTIES OF GELATIN GELS WITH SODIUM ALGINATE
S.R. DERKATCH and N.G. VORONKO
Murmansk State Technical University
13 Sportivnaya, 183 010 Murmansk, RUSSIA
email: derksveta@yahoo.com
V.N. IZMAILOVA
Moscow State University
Leninsky Gory, 119 899 Moscow, RUSSIA
The effect of anionic polysaccharide sodium alginate on the rheological properties of gelatin gels at pH values more than isolectric point of gelatin macromolecules has been investigated. The results of rheological measurements within the nonlinear viscoelasticity range have been studied using HershelBulkley model and Casson model. The analysis of the rheological curves allows characterizing the gelatin gels of low concentration of sodium alginate as viscoelasticplastic material. Sodium alginate additions give nonmonotonous change of the rheological parameters with clearly expressed extreme points for the multicomponent gels in comparison with the gelatin gels. In the presence of polysaccharide the rate of threedimensional structure formation increases. A range of sodium alginate/gelatin ratios with extreme values of the rheological characteristics has been discovered.

Key words: 
rheological parameters, gelatin, polysaccharide, multicomponent gel. 
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9.
EFFECT OF CROSS DIFFUSION ON THE ONSET OF DOUBLE DIFFUSIVE CONVECTION IN A POROUS MEDIUM
M.S. MALASHETTY and S.N. GAIKWAD
Department of Mathematics
Gulbarga University
Gulbarga  585 106, INDIA
email: malashetty@123india
The effect of cross diffusion and the horizontal gradients of temperature and salinity on double diffusive convection in a fluid saturated densely packed porous medium is investigated using an analytical approach. The condition for the onset of convection through stationary and oscillatory modes has been reported. The effect of Soret, Dufour parameters, and horizontal gradients of temperature and salinity on the stability of the system is shown graphically. It is shown that the maximum growth rate of instability, the slope of the wave front depend on both Soret and Dufour coefficients. Some of the known results of the former problems are discussed as special cases.

Key words: 
convection, cross diffusion, porous medium. 
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10.
ULTIMATE LOAD AND POSTFAILURE BEHAVIOUR OF THINWALLED ORTHOTROPIC BEAMS
M. KOTEŁKO
Department of Strength of Materials and Structures
Technical University of Łód
1/15 Stefanowskiego St., 90924 Łód, POLAND
email: mkotelko@cksg.p.lodz.pl
The paper contains an analysis of the ultimate load and postfailure behaviour of thinwalled orthotropic boxsection beams. The problem of postfailure behaviour is solved using the principle of virtual velocities based on the rigidplastic theory adopted and modified for the purposes of an orthotropic material  displaying strainhardening phenomenon.
The Hill yield criterion is applied in order to evaluate plastic moment capacities at yieldlines situated differently with respect to principal directions of orthotropy. Subsequently the energy of plastic deformation for different local plastic hinges is derived. A structural problem is solved in the analyticalnumerical way, using the incremental method. The bending moment capacity at the global plastic hinge is calculated in terms of the angle of rotation of two beam's parts at that hinge. Numerical calculations are carried out for beams made mainly from fibrous composites. Diagrams showing the influence of material orthotropic properties upon the beam structural behaviour are presented. The upper bound estimation of the loadcarrying capacity is performed by combining results of nonlinear elastic postbuckling analysis with the results of plastic mechanism analysis. The influence of orthoptropic properties, among others fibres orientation in fibrous composites, upon the loadcarrying capacity and postfailure behaviour of examined beams is discussed.

Key words: 
thinwalled structures, orthotropy, loadcarrying capacity, plastic mechanisms of failure. 
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11.
RADIATION EFFECTS ON FLOW PAST AN IMPULSIVELY STARTED INFINITE VERTICAL PLATE
P. GANESAN
Department of Mathematics
Anna University, Chennai 600 025, INDIA
email: ganesan@annauniv.edu
P. LOGANATHAN
Department of Mathematics
Anna University, Chennai 600 025, INDIA
email: plnathan@hotmail.com
V. M. SOUNDALGEKAR
31A12, Brindavan society
Thane 400 601, INDIA
Flow past an impulsively started infinite vertical isothermal plate in the presence of thermal radiation effects is studied here. The fluid considered is a gray, absorbingemitting radiation but a nonscattering medium. It is observed that for an increase in radiation parameter N or the Grashof number Gr, there is a fall in the velocity or temperature, but compared to the noradiation case, there is a rise in the velocity and temperature of the fluid.

Key words: 
impulsively started vertical plate, radiation. 
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12.
INERTIA EFFECTS IN THE FLOW OF A MICROPOLAR FLUID IN A SLOT BETWEEN ROTATING SURFACES OF REVOLUTION
A. WALICKA
Departament of Mechanics
Technical University of Zielona Góra
ul. Szafrana 2, 65516 Zielona Góra, POLAND
At present there exist several approaches to the formulation of fluids that contain structures. These fluids have various names such as simple microfluids, micropolar fluids, deformable directed fluids, polar fluids, anisotropic fluids, etc. In this paper the steady laminar flow of micropolar fluid in a slot between rotating surfaces of revolution, having a common axis of symmetry, is considered. To solve this problem the boundary layer equations for micropolar fluid are used and expressed for the axially symmetric case in the intrinsic curvilinear orthogonal coordinate system _ . The method of small parameter is used to solve the boundary layer equations. As a result one obtains the formulae for the velocity field and pressure. The solution to the equations of motion have been illustrated by plots of velocity components _ microrotation _ and pressure p.

Key words: 
laminar flow, micropolar fluid, small parameter, surfaces of revolution. 
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