
Archive issue  vol.4 No.3
1.
FLOWS OF BUBBLY LIQUIDS
L. TAO and K.R. RAJAGOPAL
Department of Mechanical Engineering
Texas A&M University
College Station, Texas 778433123, USA
This paper deals with the modeling of flows of a Newtonian liquid dispersed with bubbles. We provide an averaging procedure that combines and gainfully exploits area, volume and ensemble averaging methods, and arrives at the governing equations for bubbly liquids. Expressions are suggested for the interaction mechanisms and other constitutive quantities that appear as a consequence of the averaging. Restrictions on the constitutive quantities due to the second law of thermodynamics are delineated and a specific boundary value problem solved within the context of the theory. It is found that the prediction of the theory compares favorably with experimental observations for the specific boundary value problem under consideration.

Key words: 
averaging procedure, constitutive functions, equations of motion, Newtonian bubbly liquids. 
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2.
GRADUALLY VARIED FLOW OF UNLOADED MUD IN OPEN CHANNEL
B. Nsom
Université de Savoie, UFR SFA (Dép. Mécanique),
Campus Scientifique du Technolac,
BP 73076, Le Bourget du Lac, Cedex, FRANCE
K. Debiane, J.M. Piau and A. Ayadi
Laboratoire de Rhéologie (CNRSUJFINPG) BP 53,
Grenoble Cedex, FRANCE
We present a theoretical and experimental study of unloaded free surface mudflow in gradually varied conditions. First of all, a polymer gel following the same rheological law as the natural mud was identified, and its severe rheometric characterization was performed. Then the flow of this synthetic mud was generated in a 1D open channel. The velocity and depth profiles were then systematically investigated. The theoretical study consisted in determining the velocity profiles in terms of the rheological parameters in uniform conditions as well as in determining the form parameter characterizing the gradually varied flow of yield stress fluids in open channels.

Key words: 
gradually varied flow, LaserDoppler velocimetry, mudflow, ultrasounds, yield stress fluid. 
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3.
EFFECTS OF TEMPERATUREDEPENDENT VISCOSITY
AND HETEROGENEOUS CHEMICAL REACTION ON
UNSTEADY CONVECTIVE DIFFUSION IN A NONISOTHERMAL
PLANEPOISEUILLE FLOW
P.G. SIDDHESHWAR
Department of Mathematics, Central College Campus, Bangalore University,
Bangalore 560 001, INDIA
S. MANJUNATH
Department of Mathematics, R.V. College of Engineering, Mysore Road,
Bangalore 560 059, INDIA
A closedform solution is obtained for the problem of dispersion of solute in a nonisothermal flow of a Newtonian fluid with temperaturedependent viscosity. The effect of wallcatalysed reaction on dispersion is investigated against the background of the noreaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent. The Taylor (1953) and Aris (1956) regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering nonasymptotic alltime analysis. The results of the study indicate that heating from above is an effective means of controlling dispersion in variableviscosity liquids.

Key words: 
variableviscosity, mass transfer, dispersion, heat exchangers, biomechanics. 
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4.
TANGENTIAL FORCES ON THE DIE  WORKPIECE CONTACT SURFACE
DURING ROTARY FORGING
T. BALAWENDER and F. STACHOWICZ
Rzeszów University of Technology,
35959 Rzeszów, ul. W. Pola 2, POLAND
Theoretical considerations of the kinematic relationship between a rocking die and workpiece during rotary forging are described in here. According to friction conditions the skid or slip may cause the rising of circumferential forces at the dieworkpiece interface. It was confirmed by the results of experimental invegations of the rotary forging process.

Key words: 
rotary forging, orbital forging, planetary forging, tangential forces. 
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5.
EFFECT OF A TRANSVERSE MAGNETIC FIELD ON
NATURAL CONVECTION BOUNDARY LAYER FLOW
OF A MICROPOLAR FLUIDS IN A POROUS MEDIUM
M.A. ELHakiem
Mathematics Department, Faculty of Science, South Valley University,
AswanEGYPT
A boundary layer analysis is presented to study the effects of a transverse magnetic field on natural boundary layer flow of a micropolar fluid in a porous medium. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall plume. The governing equations for momentum, angular momentum and energy have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters, Prandtl number and magnetic parameter of the fluid. A comparison has been made with the corresponding results for Newtonian fluids. Micropolar fluids display drag reduction and reduced surface heat transfer rate in a porous medium as compared with Newtonian fluids.

Key words: 
boundary layer, magnetic field, micropolar fluids, porous medium. 
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6.
ON THE PROBLEM OF PROPAGATION OF HEAT IN MIXTURES
D. IESAN
Department of Mathematics, University "Al. I. Cuza", Iasi, ROMANIA
R. QUINTANILLA
Department of Applied Mathematics II, Polytechnical University of Catalonia,
Terrassa, Barcelona, SPAIN
This paper is concerned with the linear theory of heat propagation in a binary mixture of rigid heat conductors. First, the equilibrium theory is studied. A solution of Galerkin type is established and fundamental solutions are derived. The potentials of singlelayer and doublelayer are used to reduce the boundary value problems to singular integral equations. Existence and uniqueness results are established. The second part of the paper is concerned with the dynamical theory. A continuous dependence result and a spatial decay estimate are derived.

Key words: 
mixture of solids, heat conduction, boundary value problems, existence, continuous dependence. 
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7.
ON FLOW PAST A CONTINUOUSLY MOVING SEMIINFINITE
VERTICAL PLATE IN THE UPWARD DIRECTION
V.M. SOUNDALGEKAR
31A12, Brindavan Society, Thane (400 601 ), INDIA
H.S. TAKHAR
Department of Engineering, Manchester University,
Manchester M13 9PL, UNITED KINGDOM
Flow past a continuously moving semiinfinite vertical plate in the upward direction is studied here. With usual boundary layer transformations, the boundary layer equations are reduced to local nonsimilar ordinary differential equations which are solved numerically. Velocity and temperature profiles are shown on graphs and the numerical values of the skinfriction and the rate of heat transfer are listed in a Table. It is observed that there occurs separation of low Prandtl number fluids at large values of Gr/Re^{2} where Gr is the Grashof number and Re is the Reynolds number. Greater viscous dissipative heat causes a fall in both the skinfriction and the rate of heat transfer.

Key words: 
boundary layer equations, vertical plate, velocity and temperature profiles. 
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8.
PRESSURE WAVES IN ELASTIC TUBE WITH POLYMERIC LIQUID
S. LEVITSKY, R. BERGMAN, O. LEVI and J. HADDAD
School of Engineering, 71 Bazel St., P.O.Box 45,
BeerSheva, 84100, ISRAEL
Propagation of acoustic waves in an elastic tube with compressible polymeric liquid is investigated. A dispersion equation is derived that accounts for viscoelastic effects in the fluid in coupling with inertia, radial and longitudinal deformations of the tube's wall. The equation is valid in the frequency range where sound wave length is greater from the tube radius and includes the Korteweg Joukowski speed of water hammer as a limiting case. Analysis of the dispersion relation has shown a strong influence of the rheological properties of the liquid on dispersion and attenuation of pressure signals. The results indicate also that the model developed could give means to characterize the rheological parameters of a polymeric liquid with sufficiently simple acoustic technique.

Key words: 
polymeric liquids, rheological effects, pressure waves, dispersion, attenuation. 
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9.
ONSET OF CONVECTION IN AN INCLINED POROUS LAYER WITH
ANISOTROPIC PERMEABILITY
L. STORESLETTEN
Department of Mathematics, Agder College, N4604 Kristiansand, NORWAY
M. TVEITEREID
Faculty of Engineering, Agder College, N4890 Grimstad, NORWAY
The present paper is concerned with the onset of RayleighBénard convection in an inclined porous layer with anisotropic permeability. Due to the temperature gradient and the inclination, a steady shear flow is set up. The critical Rayleigh number at marginal stability of this basic flow is calculated and the flow pattern occurring at convection onset is examined. It turns out that anisotropy in the permeability and the shear flow have an essential influence on the selected flow structure. Depending on the anisotropy ratio and the tilt angle, convection rolls are found either with axes parallel to the basic flow or with axes perpendicular to the flow.

Key words: 
porous layer, anisotropic permeability, RayleighBénard convection. 
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10.
NUMERICAL ANALYSIS OF THE EFFECT OF SURFACTANTS
ON A CIRCULAR LIQUID LENS (II)
M. KOHR and I. LAZĂR
BabeşBolyai University,
Faculty of Mathematics and Computer Sciences,
1 M.Kogălniceanu Str., 3400 ClujNapoca, ROMANIA
The spectrum of a twodimensional flow, due to the presence of a circular liquid obstacle in a liquid layer, is investigated by using a boundary integral equation method.

Key words: 
Stokes flow, cylindrical interface, Marangoni surface flow, interfacial tension, boundary element method. 
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