
Archive issue  vol.10, No.1
No. 
Author(s)  Title 
Pages 
1. 
R. Balevicius and V. Simbirkin  Nonlinear physical relations for reinforced concrete elements under longterm loading 
520 
2. 
L. Cheng and A.V. Kuznetsov  Investigation of a laminar flow of a nonNetonian fluid in a helical pipe 
2137 
3. 
C. Chiera, H.J. Connell and J.J. Shepherd  Perturbation methods applied to the helical flow of a Casson fluid 
3951 
4. 
G.M. Deheri, P.I. Andharia and R.M. Patel  Transversely rough slider bearings with squeeze film formed by a magnetic fluid 
5376 
5. 
M.F. ElAmin  Thermal dispersion effects on nonDarcy axisymmetric free convection in a porous medium saturated with a nonNewtonian fluid 
7786 
6. 
B. Kalita and A.K. Borkakati  Transient free convection MHD flow through a porous medium between two vertical plates 
8794 
7. 
R. Kumar and P. Ailawalia  Effects of viscosity with moving load at micropolar boundary surface 
95108 
8. 
R. Kumar and P. Ailawalia  Interactions due to inclined load at micropolar elastic halfspace with voids 
109122 
9. 
P. Kumar and P. Sharma  The instability of streaming Walters B' viscoelastic fluids in hydromagnetics through porous media 
123131 
10. 
S.S. Ray and R.K. Bera  Application of Adomian method on the solution of wave propagation in a linear random nonhomogeneous viscoelastic semiinfinite rod 
133143 
11. 
N. Rudraiah and D.V. Chandrashekhar  Flow past an impermeable sphere embedded in a porous medium with Brinkmann model 
145158 
12. 
H.V. Ersoy  Unsteady flow of a Maxwell fluid induced by noncoaxial rotation of a disk and the fluid at infinity 
159165 

1.
NONLINEAR PHYSICAL RELATIONS FOR REINFORCED CONCRETE ELEMENTS UNDER LONGTERM LOADING
R. BALEVICIUS
Vilnius Gediminas Technical University
Sauletekio al. 11, 2040 Vilnius, LITHUANIA
email: Robertas.Balevicius@st.vtu.lt
V. SIMBIRKIN
Belarusian Research Institute for Construction (BelNIIS)
Staroborisovsky trakt 15, 220114 Minsk, BELARUS
email: simbirkin@hotmail.com
The paper presents a method for modelling material nonlinearity for use in the analysis of loadcarrying capacity and deformations of reinforced concrete beams, columns and membranebending plates subjected to longterm loads. Physical relationships expressing relations between internal forces and stresses, strains and stiffness are derived on the basis of the fracture and creep theories for concrete and using nonlinear stressstrain diagrams modified for time effects. A specific implementation technique of a genetic algorithm is developed to find multiple solutions to nonsmooth problems under consideration.
The computation technique proposed is found to be effective in numerical examples, and an adequate accuracy of the analysis is verified by comparison with experimental data.

Key words:  reinforced concrete, physical nonlinearity, longterm loading, strength, genetic algorithm. 
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2.
INVESTIGATION OF A LAMINAR FLOW OF A NONNEWTONIAN FLUID IN A HELICAL PIPE
L. CHENG and A.V. KUZNETSOV
Department of Mechanical and Aerospace Engineering, North Carolina State University
Campus Box 7910, Raleigh, NC 276957910, USA
email: avkuznet@eos.ncsu.edu
This paper presents a numerical study of a fully developed laminar flow of a nonNewtonian fluid in a helical pipe. An orthogonal helical coordinate system is utilized and the NavierStokes equations for the nonNewtonian fluid in this coordinate system are derived. The SIMPLE algorithm with a staggered grid is adopted to solve the governing equations. The effects of the pressure gradient, the curvature, and the torsion on the fully developed laminar flow in helical pipes are investigated. The comparison of flow dynamics between Newtonian and nonNewtonian fluids is presented.

Key words: 
nonNewtonian, helical pipe, laminar flow, orthogonal helical coordinates. 
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3.
PERTURBATION METHODS APPLIED TO THE HELICAL FLOW OF A CASSON FLUID
C. CHIERA, H.J. CONNELL and J.J. SHEPHERD
Department of Mathematics, Royal Melbourne Institute of Technology
PO Box 2476V, Melbourne, 3001, AUSTRALIA
email: jshep@ems.rmit.edu.au
The helical flow of a Casson fluid between infinitely long coaxial cylinders is analyzed, when the inner cylinder has a given constant angular velocity, and a constant axial flow rate is imposed. Perturbation methods are applied in two circumstances of physical interest  that of low axial flow rates; and that of small intercylindrical gap width  to yield approximate expressions describing the fluid velocity field; and the ReinerRiwlin equation, the fundamental relationship linking the angular velocity of the inner cylinder, the torque experienced there, and the given axial flow rate. The accuracy of these expressions is tested by comparison with solutions generated using numerical computation.

Key words: 
perturbation methods, helical flow, Casson fluid, rheometry. 
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4.
TRANSVERSELY ROUGH SLIDER BEARINGS WITH SQUEEZE FILM FORMED BY A MAGNETIC FLUID
G.M. DEHERI
Department of Mathematics, Sardar Patel University
Vallabh Vidyanagar 388 120, Gujarat State, INDIA
P.I. ANDHARIA
Bhavnagar University, S. S. Computer Center
Bhavnagar 364 002, Gujarat State, INDIA
RAKESH M. PATEL
Department of Mathematics, Gujarat Arts and Science College
Ahmedabad 380 006 Gujarat State, INDIA
email: jrmpatel@rediffmail.com
In this article it has been sought to study the effect of transverse roughness on the behaviour of slider bearings with squeeze film formed by a magnetic fluid. The roughness of the bearing surface is modelled by a stochastic random variable with non zero mean, variance and skewness. The associated Reynolds' equation is stochastically averaged with respect to the random roughness parameter. Results for bearing performance characteristics such as load carrying capacity, center of pressure, frictional force and coefficient of friction for different values of mean, standard deviation and measure of symmetry are numerically computed. In order to decipher the quantitative effect of roughness on the performance characteristics four different shapes namely; plane slider, exponential slider, hyperbolic slider and secant slider for the lubricant film are considered. The results are presented graphically. It is noticed that the bearing suffers on account of transverse surface roughness. The results show that the use of a magnetic fluid as lubricant increases the load carrying capacity, decreases the coefficient of friction and affects the center of pressure marginally. It is further observed that the effect of magnetization on the plane and secant shaped bearings is nominal while the effect on exponential and hyperbolic slider bearing is significant. In addition it is easily seen that by increasing the strength of the magnetic field the adverse impact on the bearing due to roughness can be minimized.

Key words: 
slider bearing, squeeze film, rough surfaces, magnetic fluid. 
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5.
THERMAL DISPERSION EFFECTS ON NONDARCY AXISYMMETRIC FREE CONVECTION IN A POROUS MEDIUM SATURATED WITH A NONNEWTONIAN FLUID
M.F. ELAMIN
Mathematics Department, Aswan Faculty of Science
South Valley University, Aswan 81528, EGYPT
email: mfam2000@yahoo.com
A boundary layer analysis is presented to study the effects of thermal dispersion of a nonNewtonian fluid on nonDarcy axisymmetric free convection over a horizontal surface embedded in a porous medium. The OstwalddeWaele powerlaw model is used to characterize the nonNewtonian fluid behavior. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. Similarity solutions are obtained when the surface temperature varies as the square root of the radial distance (i.e., the prescribed temperature PT) or when heat flux is constant (i.e., the prescribed heat flux PHF). The effects of the dispersion and nonDarcy parameters as well as the powerlaw index n on the velocity, temperature, the Nusselt number and the boundary layer thickness are shown on graphs. The numerical values of the rate of heat transfer through the boundary layer in terms of the Nusselt number are entered in a table.

Key words: 
powerlaw fluids, porous medium, thermal dispersion, axisymmetric flow, free convection. 
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6.
TRANSIENT FREE CONVECTION MHD FLOW THROUGH A POROUS MEDIUM BETWEEN TWO VERTICAL PLATES
B. KALITA and A.K. BORKAKATI
Department of Mathematical Sciences
Tezpur University, TezpurNaapam784025, ASSAM, INDIA
email: atul@agnee.tezu.ernet.in
An analysis is presented to investigate the flow and heat transfer characteristic of a viscous incompressible and electrically conducting fluid through a porous medium bounded by two long vertical parallel plates in the presence of a uniform magnetic field applied transversely to the flow. The governing momentum and energy equations are solved by the Laplace transform technique and the solutions are presented for velocity and temperature distributions and shear stress. The effects of the four parameters, namely, the Darcy number, viscosity ratio parameter, magnetic Hartmann number, and Prandtl number on temperature and velocity distributions are shown in graphs and presented through the results and discussion. Also, the effects of these four parameters on skin friction are given.

Key words: 
transient free convection, porous medium, Laplace transformation, MHD flow, effective viscosity, heat transfer. 
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7.
EFFECTS OF VISCOSITY WITH MOVING LOAD AT MICROPOLAR BOUNDARY SURFACE
R. KUMAR
Department of Mathematics, Kurukshetra University
Kurukshetra, Haryana, INDIA
email: rajneesh_kuk@rediffmail.com
P. AILAWALIA
Department of Applied Sciences, I.E.E.T, Makhnumajra, Baddi
Distt. Solan, 173205, H.P., INDIA
email: praveen_2117@rediffmail.com
The steady state response at viscous fluid/micropolar elastic solid interface to a moving point load has been studied for subsonic, supersonic and transonic load velocities. The Fourier transform has been used to solve the problem. The displacement, microrotation and stress components for a micropolar elastic solid so obtained in the physical domain are computed numerically by using the numerical inversion technique. Viscosity and micropolarity effects on the resulting expressions have been presented graphically for a specific material.

Key words: 
steady state, viscous fluid, micropolar, Fourier transform. 
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8.
INTERACTIONS DUE TO INCLINED LOAD AT MICROPOLAR ELASTIC HALFSPACE WITH VOIDS
R. KUMAR
Department of Mathematics, Kurukshetra University
Kurukshetra, Haryana, INDIA
email: rajneesh_kuk@rediffmail.com
P. AILAWALIA
Department of Applied Sciences, I.E.E.T.
Makhnumajra, Baddi, Distt. Solan, Pin173205, H.P., INDIA
email: praveen_2117@rediffmail.com
The analytic expressions for the displacements, microrotation, stresses and volume fraction field on the free surface of a micropolar elastic halfspace with voids as a result of moving an inclined load have been obtained. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The problem has been solved by employing the Eigenvalue approach after using the Fourier transform as the use of matrix notation avoids unwidely mathematical expressions. The technique used in the present paper is simple, straightforward and convenient for numerical computations. The variations of the displacements, stresses and volume fraction field with the horizontal distance have been shown graphically for a particular model. A special case has also been discussed.

Key words: 
micropolar, voids, inclined load, Eigenvalue approach, Fourier transform. 
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9.
THE INSTABILITY OF STREAMING WALTERS B' VISCOELASTIC FLUIDS IN HYDROMAGNETICS THROUGH POROUS MEDIA
P. KUMAR and P. SHARMA
Department of Mathematics, ICDEOL, Himachal Pradesh University
Summer Hill, Shimla171005, INDIA
email: drpardeep@sancharnet.in
The instability of streaming Walters B' elasticoviscous fluids in hydromagnetics through porous medium is considered. The case of two uniform streaming fluids separated by a common horizontal interface is considered. It is found that for the special case when perturbations in the direction of streaming are ignored, the system can be stable or unstable, depending upon kinematic viscoelasticity, medium porosity and medium permeability, for both potentially unstable and stable configurations. In all other directions, a minimum value of wavenumber has been found and the system is unstable for all wavenumbers greater than this minimum wave number and the instability of the system is found to be postponed due to the presence of the magnetic field.

Key words: 
KelvinHelmholtz instability, Walters B' viscoelastic fluid, magnetic field, porous medium. 
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10.
APPLICATION OF ADOMIAN METHOD ON THE SOLUTION OF WAVE PROPAGATION IN A LINEAR RANDOM NONHOMOGENEOUS VISCOELASTIC SEMIINFINITE ROD
S.S. RAY
B. P. Poddar Institute of Management and Technology
Poddar Vihar, 137, V.I.P. Road, Kolkata 700052, INDIA
email: santanusaharay@yahoo.com
R.K. BERA
Technical Teachers' Training Institute
BlockFC, Sector III, Salt Lake, Kolkata 700106, INDIA
email: rasajit@hotmail.com
The aim of the present problem is to investigate the efficiency of the method of Adomian for the solution of nonlinear and complicated differential equation in a random medium. Here the problem is connected with the investigation of the mean and variance of the displacement distribution in a thin linear random nonhomogeneous Biot type viscoelastic semiinfinite rod, due to general timedependent displacement input at the rod. A truncated series solution of the wave problem following the method of Adomian after using the Laplace transform is obtained for small random variations in viscoelastic properties. Three specific cases concerning the probability measure as a function of the continuous type of random variable have been discussed.

Key words: 
random, viscoelastic, nonhomogeneous, Adomian method. 
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11.
FLOW PAST AN IMPERMEABLE SPHERE EMBEDDED IN A POROUS MEDIUM WITH BRINKMANN MODEL
N. RUDRAIAH and D.V. CHANDRASHEKHAR^{1}
UGC  CAS In Fluid Mechanics Department of Mathematics, Bangalore
University, Bangalore 560 001, Karnataka, INDIA
and
National Research Institute for Applied Mathematics (NRIAM)
#492/G, 7th Block, 7th Cross (west), Jayanagar, Bangalore  560 082, Karnataka, INDIA
^{1}Vivekananda Institute of Technology, Gudimavu, Kumbalagodu (post)
Kengeri (Hobli) Bangalore 560 074, Karnataka, INDIA
email: rudraiahn@hotmail.com
email: dvchandru@yahoo.com
The twodimensional steady incompressible flow past an impermeable sphere embedded in a porous medium is studied analytically using the Brinkmann model specifying a uniform shear away from the sphere. A closed form solution is obtained for the governing equations. It is found that the increase in the permeability of a porous medium and viscosity ratio is to increase the thickness of the Brinkman boundary layer. The analysis is also concerned with the explanation of the velocity overshoot behavior. The effects of shear stress and the separation parameter are also discussed. The streamlines are drawn for different values of the porous parameter and the viscosity ratio and some important conclusions are drawn.

Key words: 
sphere in a porous medium, Brinkmann model, uniform shear. 
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12. Brief note
UNSTEADY FLOW OF A MAXWELL FLUID INDUCED BY NONCOAXIAL ROTATION OF A DISK AND THE FLUID AT INFINITY
H.V. ERSOY
Department of Mechanics, Faculty of Mechanical Engineering, Istanbul Technical University
34437, Gümüºsuyu  Istanbul, TURKEY
email: ersoyhv@yahoo.com
In this note, the unsteady flow of a Maxwell fluid produced by noncoaxial rotation while a disk and the fluid at infinity are initially rotating with the same angular velocity about a common axis is considered. Even in the case of a nonNewtonian fluid, it is shown that there is an exact solution for this flow geometry. The velocity field is obtained with the help of the Laplace transform technique.

Key words: 
disk, fluid rotating at infinity, noncoaxial rotation, unsteady flow, Maxwell fluid. 
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