Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
32
6
2005
Multiparameter Perturbation Analysis of Unsteady Oscillatory Magnetoconvection in Porous Media with Heat Source Effects
635-661
O. Anwar
Bég
Fluid Mechanics, Nanosystems and Propulsion, Aeronautical and Mechanical Engineering,
School of Computing, Science and Engineering, Newton Building, University of Salford,
Manchester M54WT, United Kingdom
Harmindar S.
Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
Ajay Kumar
Singh
Department of Mathematics, C. L. Jain College, Firozabad-283 203, India
Unsteady natural convection flow of a viscous, incompressible, electrically conducting fluid past an infinite vertical porous plate embedded within a saturated, highly porous medium under the influence of a uniform magnetic field, Eckert heating, and a heat-absorbing sink is studied. It is assumed that the suction velocity is subjected to small-amplitude oscillations in time about the steady nonzero mean suction velocity. Approximate solutions for the velocity and temperature field are obtained using the multiparameter perturbation technique. Expressions for skin friction and rate of heat transfer are also derived. Mean temperatures are boosted by both magnetic field and heat-source parameter, but are lowered by a rise in the Prandtl number, Grashof number, and permeability parameter (k). The effects of all parameters on velocity, temperature, skin friction, and heat transfer rate (Nusselt number) are graphically presented and tabulated, and are discussed in detail. The model finds applications in nuclear heat transfer processes, metallurgy, aerospace/aval propulsion, and energy systems.
Rupture of Thin Liquid Films Utilizing Binary Fluid Mixtures
662-674
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
Larry W.
Byrd
Thermal Structures Branch, Air Vehicles Directorate, Air Force Research Laboratory, Wright Patterson Air Force Base, OH 45433, USA
David
Kost
Department of Chemical & Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115-2425
Bahman
Ghorashi
Department of Chemical & Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115-2425
The dynamic rupture process of a thin liquid film involving a binary fluid has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. The results indicate that the interfacial surface tension gradients with concentration and temperature have significant effect on the film rupture. Film rupture may be delayed by introducing a small amount of a less volatile fluid with a higher surface tension into the working fluid.
Convection of Micropolar Heated Fluid with Rotation in Hydromagnetics
675-690
Neela
Rani
Department of Mathematics, MCMDAV College Chandigarh - 160 036, India
S. K.
Tomar
Department of Mathematics, Panjab University, Chandigarh 160 014, India
In this paper, the thermal instability of electrically conducting incompressible micropolar fluid heated from below in the presence of uniform magnetic field under the action of rotation in porous and non-porous medium is investigated. Frequency equations are derived and Rayleigh number is determined. It is found that in both porous and non-porous medium, the variation of Rayleigh number with wavenumber is decreasing. However, the Rayleigh number is found to increase with increase of rotation parameter. This shows that the rotation has stabilizing effect in both cases. The results of some earlier workers have been reduced from the present formulation.
Gravity-Modulated Thermo Capillary Convection in a Liquid Bridge
691-702
K. N.
Shukla
Karunya Institute of Technology and Sciences Coimbatore-641114, India
The problem of thermo capillary convection in a liquid bridge has been studied in a gravity-modulated environment. The half zone consists of a liquid bridge held between two solid, planar end walls across which a temperature gradient is applied. Thus the basic state of thermo capillary convection consists of a single toroidal roll with the surface motion directed downwards from the hot upper disc to the cold lower one. The interface deformation caused by the gravity jitters depends on the volume of the liquid bridge and cause changes in the basic state of the fluid. The deformation of free surface of the liquid column may introduce oscillatory flow field, which may induce convection. The paper discusses the effect of recirculatory flow inside the bridge on the stability of liquid bridges.
Two-Dimensional Modeling of Rainfall Runoff and Sediment Transport in Small Catchment Areas
703-717
Sergey L.
Kivva
Institute of Mathematical Machines and Systems of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Mark J.
Zheleznyak
Institute for Problems of Mathematical Machines and Systems of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A mathematical model of rainfall runoff formation in small catchments is developed; the model is physically valid. The model gives an adequate description of such processes as interception of rainfall by vegetation; storage in relief micro-depressions; infiltration; overland runoff; wash off, transport and re-deposition of soil particles. Numerical simulation of formation of the surface runoff involves the solution of two-dimensional nonstationary shallow water equations, the infiltration equation, and the sediment transport equation. The shallow water equations and the sediment transport equation are integrated numerically using conservative implicit first-order finite-difference schemes. The finite-difference scheme for the shallow water equations allows simulating an open flow with a free boundary. Verification of the model is based on observed data for rain-induced high water in catchment areas of the Butenya river.
Computer Simulation on the Basis of Hamilton-Type Equations of Nonlinear Fluid Oscillations in a Rectangular Tank
718-741
G. F.
Zolotenko
Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The subject of consideration comprises nonlinear systems of ordinary integral-differential equations which appear in dynamics of relative motion of ideal homogeneous incompressible fluid in connection with a variational method by Bateman−Luke−Whitham; the equations are similar to Hamiltonian equations. The paper presents an analysis of properties of the said simultaneous equations and a known method for their approximate solution − by excluding quasi-velocities of the fluid and reducing the system to certain simultaneous equations of second order with respect to the coordinates of a free surface. An alternative approach is presented for a rectangular vessel partially filled with fluid. It is based on a direct integration of the original exact equations by the Runge-Kutta technique. An algorithm for numerical solution of the equations has been developed and is demonstrated by the example of nonlinear free oscillations (sloshing) of fluid in a tilted rectangular vessel after its being accelerated.