Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
32
5
2005
Natural Convection Flow in a Rotating Fluid Over a Vertical Plate Embedded in a Thermally Stratified High-Porosity Medium
511-527
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
Harmindar S.
Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
Girishwar
Nath
Professor S. K. Sinha, KNIT Campus, IV/17, KNIT, Sultanpur 228118, India
An analysis has been carried out to study the natural convection flow in a rotating fluid over a vertical plate embedded in a thermally stratified high-porosity medium. The nonlinear coupled parabolic partial differential equations have been solved numerically by using an implicit finite-difference scheme. The flow and temperature fields are strongly influenced by the thermal stratification, porosity, inertia, Rossby number, and Prandtl number, whereas they are weakly dependent on the permeability parameter.
Influence of Magnetic Field on the Onset of Convection in a Porous Medium
528-537
Salah Abd El-Aziem
El-Kholy
Department of Mathematics, Faculty of Science, Menoufia University Shebin El-Kom, Egypt
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
The aim of the paper is to investigate the influence of a magnetic field on the buoyancy instability of an electrically conducting fluid in a porous medium. This is based on a parallel flow assumption and the Brinkman model for the porous flow. The stability of a convection fluid saturating a porous medium is considered. The critical Rayleigh-Darcy number Rc as a function of Darcy number Da and Hartmann number H is obtained when the onset of instability occurs.
Stagnation-Point Flow Towards a Heated Stretching Sheet with Variable Fluid Viscosity
538-548
Gorachand C.
Layek
Department of Mathematics, University of Burdwan Burdwan, West Bengal, India
Swati
Mukhopadhyay
Department of Mathematics, The University of Burdwan, India
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
The influence of temperature-dependent fluid viscosity on a steady stagnation-point flow over a heated stretching sheet is investigated. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations of motion and energy. Using the invariants, third- and second-order ordinary differential equations corresponding to the momentum and energy equations are obtained. These equations are then solved numerically. It is found that the horizontal velocity increases with the increasing value of the ratio of the free-stream velocity ax and the stretching velocity cx, but the temperature decreases in this case. The important findings of the present study are that at a particular point of the heated stretching sheet, the fluid viscosity decreases with an increase of the temperature-dependent fluid viscosity parameter A near the stagnation point when the free-stream velocity is less than the stretching velocity, but with increasing η, the horizontal velocity increases in this case with the increasing temperature-dependent fluid viscosity parameter A. When the free-stream velocity is greater than the stretching velocity, the opposite behavior of horizontal velocity is noted.
Sound Field in an Inhomogeneous Hydroacoustical Waveguide with a Stepped Bottom
549-564
S. O.
Papkov
Sevastopol National Technical University, Ukraine
Yu. I.
Papkova
Sevastopol National Technical University, Ukraine
A. A.
Yaroshenko
Sevastopol National Technical University, Ukraine
The paper deals with an asymptotic behavior of unknowns in an infinite system of linear equations which defines the weight factors in the Fourier expansion of the acoustic potential for a model of a waveguide with a stiff stepped bottom and a sound velocity profile variable over the depth. Knowing the asymptotic behavior of the unknowns one can use an enhanced reduction method to calculate the coefficients for normal modes. A numerical study of sound fields was performed with variable parameters of the problem.
A Hydrodynamic Instability of a Vortex in Open Systems with a Volumetric Sink and Unlimited Inflow of Matter as a Possible Mechanism of Tornado Emergence
565-578
E. A.
Pashitskii
Institute of Physics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Several exact unsteady solutions of the Navier-Stokes and continuity equations are obtained for a vortex in an incompressible viscous two-component (or two-phase) medium with a volumetric sink of matter caused by phase transition (for instance, vapor condensation in humid air at temperatures below the dew point) and with unlimited inflow of the matter from the environment. These solutions describe an exponential or “explosive” hydrodynamic instability of a “solid-body” rotation of matter in the vortex core caused by the action of convective and Coriolis forces arising as a result of nonlinear interaction between the rotating matter and radial flows, which provide constant density and composition throughout the medium (in particular, constant air humidity). This kind of hydrodynamic instability can be considered as a possible mechanism of creation and development of powerful atmospheric vortices - tornados and typhoons - during the formation of dense cloud systems when intense condensation of air moisture plays the role of a volumetric sink (convergence) of the matter.
Propagation of Unsteady Hydroelastic Waves in Semi-Infinite Cylindrical Shell with an Insertion
579-587
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
O. V.
Zvonareva
Transport University, Dnipropetrovsk, Ukraine
An unsteady wave propagation from the end face of a semi-infinite cylindrical shell in the presence of insertion at some distance is investigated. It is assumed that the shell material is viscoelastic and fluid is viscous. The motion of shell is described by the Kirchhoff-Love theory, the fluid motion by the equations averaged over the cross-section. The problem is solved by the Laplace transform in time with a consequent numerical inversion. The analysis of numerical results for the shell radial displacement in the presence of elastic insertion is carried out.
Sound Radiation by an Array Formed by Coaxial Cylindrical Piezoceramic Shells with the End Baffles
588-633
I. V.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. T.
Matsypura
National Engineering University of Ukraine "KPI", Kyiv, Ukraine
A problem on sound radiation by an array consisting of piezoceramic shells with the end baffles in the form of truncated spherical sectors is solved on the basis of the modified method of partial domains. The significant distinctions between the vibration velocities and radiated powers of the particular shells is shown in the case when all of them are excited by equal electric voltages, that is caused by interaction through the acoustic field. It is proved that at certain frequencies some shells may change their operation mode from power radiation to its absorption from the environment. The far field of sound radiation by the shell is studied and directivity patterns for the arrays with various properties of the surface baffles are calculated. It is found that the most effective baffles are those with completely soft surfaces. A problem on sound radiation by the array which shells are excited by periodic sequence of radio-pulses. It is shown that in the case when all the shells are supplied by equal radio-pulses time dependencies for the vibration velocities of the shells (within radio-pulse duration interval) essentially differ both from the exciting pulse and from each other. It is found that at pulse supply of the shells the pressure time evolution in the far field significantly depends on direction. The pronounced acoustic reverberation is discovered in pulse-to-pulse interval. Some specific techniques for controlling the array acoustic properties are considered.