
Archive issue  vol.4 No.4
1.
A BOUNDARY INTEGRAL EQUATION FORMULATION OF
MODERATELY THICK LAMINATED ANISOTROPIC SHALLOW SHELLS
J. WANG
Department of Civil Engineering,
Hefei University of Technology 230009, Hefei, Anhui,
People's Republic of CHINA
K. SCHWEIZERHOF
Institut fur Mechanik, Universitat Karlsruhe,
D76128, Karlsruhe, GERMANY
In this paper, a boundary integral equation formulation of moderately thick laminated anisotropic shallow shells including transverse shear deformation is presented using the method of weighted residuals. Numerical computation of the boundary integral equation presented is discussed in detail. Some of numerical examples are given and compared with the exact solutions and the solutions available in the literature. The numerical results show that the method presented has good accuracy and high efficiency.

Key words: 
anisotropy, laminated shallow shells, transverse shear deformation, boundary integral equations, boundary element methods. 
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2.
COMBINED FREE AND FORCED CONVECTION FLOW PAST
A SEMIINFINITE VERTICAL PLATE EMBEDDED
IN A HOMOGENEOUS POROUS MEDIUM
S.N. RAY
Sr. Programming Office, Regional Computer Centre
ONGC Ltd., P32, Transport Depot Road
Calcutta 700 088, INDIA
V.M. SOUNDALGKER
31A12, Brindavan Society, Thane 400 601, INDIA
Combined free and forced convection flow of a viscous incompressible fluid past a semiinfinite vertical plate embedded in a homogeneous porous medium is studied here. With usual boundary layer transformations, the equations are reduced to local nonsimilar forms and these are solved numerically on a computer. Velocity and temperature profiles are shown graphically and the numerical values of the skinfriction and the rate of heat transfer are listed in a table. The effects of the parameters Gr/Re^{2} (Gr  Grashof number Re  the Reynolds number), 'alpha' (coefficient of viscosities of the fluid and porous medium), 'sigma' (the Darcy number), Pr (the Prandtl number) and E (the Eckert number) on the flow field are discussed.

Key words: 
combined convection, dissipation heat, semiinfinite, vertical plate. 
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3.
MHD MIXED CONVECTION BOUNDARY LAYER FLOW
OF A MICROPOLAR FLUID FROM A HORIZONTAL CYLINDER
M.A. MANSOUR
Department of Mathematics, Faculty of Science, Assiut University,
Assiut, EGYPT
R.S.R. GORLA
Department of Mechanical Engineering, Cleveland State University,
Cleveland, OH 44115, USA
A boundary layer solution is presented to study the mixed convection from a horizontal cylinder embedded in electrically conducting micropolar fluid. The governing conservation equations have been solved numerically. Details of the velocity, microrotation and temperature fields are presented for various material parameters. Missing values of the velocity, angular velocity and thermal functions are tabulated.

Key words: 
mixed convection, micropolar fluids, MHD effects, heat transfer. 
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4.
MICROPOLAR FLUID FLOW PAST A CONTINUOUSLY MOVING PLATE
IN THE PRESENCEOF MAGNETIC FIELD
M.A. MANSOUR
Department of Mathematics, Faculty of Science,
Assiut University, Assiut, EGYPT
R.S.R. GORLA
Department of Mechanical Engineering, Cleveland State University,
Cleveland, OH 44115, USA
A similarity analysis of the flow and heat transfer with magnetic field past a continuously moving semiinfinite permeable plate in a micropolar fluid is presented. The velocity, microrotation distribution, the temperature profiles, the skin friction and the rate of heat transfer are shown on graphs. Also the numerical values of the skin friction and the rate heat transfer are entered in tabular form.

Key words: 
micropolar fluids, heat transfer, moving plate, magnetic effects. 
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5.
AXIAL MIXING IN THE PROCHEM MULTISTAGE
MECHANICALLY  AGITATED GAS/LIQUID CONTACTOR
A.M. Al TAWEEL, Y.H. CHENG and A.E. GHALY
Faculty of Engineering, Dalhousie University
Halifax NS, B3J 2X4, CANADA
The axial mixing characteristics of a pilotscale multistage mechanicallyagitated gas/liquid contactor (the PROCHEM column) was investigated over a wide range of design and operating conditions. The experimental results, obtained using the dynamic response method, were analyzed using three models. The tanks in series model were identified as the one most suitable for describing the axial mixing in this type of column and a general correlation describing the effect of various design and operating conditions on the axial mixing characteristics was developed. A comparison with other multiphase column contactors indicates that the axial mixing characteristics of this column are superior to those of unagitated bubble columns operating under similar conditions. Means for further improvement in column performance were also identified.

Key words: 
gas/liquid contactors, bubble columns, mechanical agitation, axial mixing, dispersion, backmixing. 
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6.
INFLUENCE OF VARIABLE PERMEABILITY
ON COMBINED CONVECTION ALONG A NONISOTHERMAL
WEDGE IN A SATURATED POROUS MEDIUM
F.S. IBRAHIM and I.A. HASSANIEN
Department of Mathematics,
Faculty of Science, Assiut University,
Assiut, EGYPT
Mixed convection along a vertical nonisothermal wedge embedded in a fluid  saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter 'ksi' and a pseudosimilarity variable 'eta' are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter 'ksi'=[1+(Ra_{x}/Pe_{x})^{1/2}]^{1} from pure forced convection ('ksi'=1) to pure free convection ('ksi'=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as the local Nusselt number are presented. The wedge angle geometry parameter ranged from 0 to 1.

Key words: 
mixed convection, porous media, heat transfer, nonsimilar solution. 
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7.
NONSIMILAR BOUNDARY LAYER SOLUTIONS FOR MIXED
CONVECTION IN NONNEWTONIAN FLUIDS
ALONG A VERTICAL PLATE IN A POROUS MEDIUM
M.A. MANSOUR
Mathematics Department, Faculty of Science,
Assiut University, Assiut, EGYPT
R.S.R. GORLA
Mechanical Engineering Department,
Cleveland State University,
Cleveland, Ohio 44115, USA
Nonsimilarity solutions for mixed convection in powerlaw type nonNewtonian fluids from a vertical flat plate embedded in a porous medium are reported for a variable wall temperature of the power law form. The governing equations, including internal heat generation, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finitedifference scheme. Numerical results are presented for the fluid velocity and temperature fields.

Key words: 
mixed convection, nonNewtonian fluids, porous medium, boundary layer.

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8.
THERMAL DISPERSION EFFECTS ON NONDARCY AXISYMMETRIC
FREE CONVECTION IN A SATURATED POROUS MEDIUM
WITH LATERAL MASS TRANSFER
M.A. MANSOUR
Mathematics Department, Faculty of Science,
Assiut University, Assiut, EGYPT
M.F. ELAMIN
Mathematics Department, Aswan Faculty of Science,
South Valley University, Aswan, EGYPT
An analysis is presented to study the effects of thermal dispersion and lateral mass flux on nonDarcy axisymmetric free convection on permeable horizontal surfaces in a fluid saturated porous medium. 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 or when heat flux is constant. The effects of the dispersion, lateral mass flux and nonDarcy parameters on the velocity and temperature are shown on graphs. The numerical values of the rate of heat transfer as well as the total energy convected through the boundary layer are entered in tables.

Key words: 
porous medium, thermal dispersion, permeable surfaces, axisymmetric flow, free convection. 
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9.
EFFECTS OF BUOYANCY AND HETEROGENEOUS CHEMICAL
REACTION ON UNSTEADY CONVECTIVE DIFFUSION
OF SOLUTE IN A BOUSSINESQ FLUID 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 closed  form solution is obtained for the problem concerning buoyancy  affected dispersion of solute in a Boussinesq fluid flow with wall  catalysed reaction. The long time Taylor (1953) and Aris (1956) regimes of dispersion for the present problem are obtained as limiting cases. 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 results have applications in heat exchangers, sediment  laden flows and extra  corporeal biomechanical situations.

Key words: 
buoyancy, mass transfer, dispersion heat exchangers, biomechanics. 
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10.
LUBRICATION OF A SLIDER BEARING WITH A
SPECIAL THIRD GRADE FLUID
M. YÜRÜSOY and M. PAKDEMIRLI
Department of Mechanical Engineering,
Celal Bayar University, 45140,
Muradiye, Manisa, TURKEY
Lubrication of a slider bearing with a nonNewtonian fluid is considered. The fluid is a third grade fluid. Under the assumptions of the order of magnitudes of the variables, it is seen that only viscous and third grade terms are effective, whereas second grade terms and inertia terms are negligible. Choosing third grade effects to be smaller than the viscous effects, a perturbation solution is constructed. The velocity profile and the pressure distribution in the bearing is calculated approximately.

Key words: 
slider bearing, third grade fluids, perturbation analysis. 
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11.
COMBINED HEAT AND MASS TRANSFER
BY MIXED CONVECTION FLOW OVERA HORIZONTAL PLATE
M. ANGEL and I. POP
Department of Applied Mathematics, University of Cluj,
R3400 Cluj, CP 253, ROMANIA
M.A. HOSSAIN
Department of Mathematics, University of Dhaka,
Dhaka1000, BANGLADESH
This paper studies combined heat and mass transfer by laminar mixed convection over a horizontal plate with uniform wall temperature and concentration. Numerical solutions of the nonsimilar boundary layer equations governing the flow, energy and concentration are obtained by employing an implicit finitedifference approximation together with the Kelley box method. Distribution of the velocity, temperature and concentration profiles as well as of the local Nusselt and Sherwood numbers are calculated. The flow characteristics are revealed to be significantly influenced by the buoyancy ratio parameter, mixed convection parameter and Schmidt number.

Key words: 
convection, thermal, diffusion, massconcentration, boundary layer. 
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12.
NATURAL CONVECTION IN A MICROPOLAR FLUID WITH
INTERNAL HEAT GENERATION AND VISCOUS DISSIPATION
M.A. ELHAKIEM
Mathematics Department, Faculty of Science,
South Valley University, Aswan, EGYPT
R.S.R. GORLA
Mechanical Engineering Department,
Cleveland State University, Cleveland,
Ohio 44115, USA
A similarity solution is presented for the flow of a micropolar fluid along an isothermal vertical plate with an exponentially decaying heat generation term and viscous dissipation. Numerical solutions are obtained for the governing equations. The data for friction factor, Nusselt number and wall couple stress have been tabulated for a range of Prandtl numbers and micropolar parameters.

Key words: 
natural convection, micropolar fluid, heat generation, viscous dissipation. 
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13.
THE INFLUENCE OF INLET BOUNDARY CONDITIONS
ON THE NEAR FIELD OF A PLANE TURBULENT JET
B.A.F. SIMPSON and A.E. HOLDO
Computational Fluid Dynamics Group,
Division of Mechanical, Aeronautical and Automotive Engineering,
The University of Hertfordshire,
Hatfield, Hertfordshire, AL10 9AB, U.K.
Numerical investigations into the sensitivity of the near field of a plane jet to the inlet boundary conditions were performed, employing both finite element and finite volume methods together with the k'epsilon' turbulence model. The study shows that the near field is insensitive to the turbulent inlet boundary conditions when a uniform velocity profile is used. However, when a nonuniform, shear dominated velocity profile is used, the assignment of turbulent parameters has a substantial effect on the solution.

Key words: 
Plane jets, computational modelling, boundary conditions. 
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14.
Brief note
RADIATION AND FREE CONVECTION FLOW PAST
A MOVING PLATE
A. RAPTIS and C.PERDIKIS
Department of Mathematics, University of Ioannina,
Ioannina, 451 10, GREECE
This paper deals with the effects of thermal radiation by taking into account the free convection flow over a moving plate. The fluid considered is a gray, absorbingemitting radiation but nonscattering medium.

Key words: 
free convection, radiation. 
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