Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
31
6
2004
Double-Diffusive Convective Flow of a Micropolar Fluid Over a Vertical Plate Embedded in a Porous Medium with a Chemical Reaction
529-551
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
Ali F.
Al-Mudhaf
Manufacturing Engineering Department, The Public Authority for Applied Education and Training, P. O. Box 42325, Shuweikh, 70654 Kuwait
Jasem
Al-Yatama
Manufacturing Engineering Department, The Public Authority for Applied Education and Training, P. O. Box 42325, Shuweikh, 70654 Kuwait
The problem of steady, laminar, double-diffusive natural convection boundary-layer flow of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-Darcian and thermal dispersion effects is investigated. Also, the model problem allows for possible heat generation or absorption and first-order chemical reaction effects. Both the wall temperature and wall concentration are assumed to have linear variations with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations into a non-similar form that can be solved as an initial-value problem. The resulting equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the microrotation material parameter, concentration to thermal buoyancy ratio, chemical reaction parameter, Schmidt number, heat generation or absorption and the surface suction or injection effects on the fluid velocity, microrotation, temperature and solute concentration as well as the local skin-friction coefficient, local wall microrotation coefficient and the local wall heat and mass transfer coefficients is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.
Rheological Effects on Tear Film Rupture
552-562
Madhu Sudan Reddy
Gorla
Chicago Glaucoma Consultants Evanston, Illinois 60201
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 drainage of the precorneal tear film in humans is studied. A fluid dynamic model for the drainage of the aqueous layer is developed that includes rheological effects. The Ostwald de Waele type power law model is employed to model the tear film. The nonlinear evolution equation for the film is formulated using the balance equations including a body force term due to van der Waals molecular attractions, lubrication theory and perturbation expansion method. The governing equation was solved by the finite difference method as part of an initial value problem for spatial periodic boundary conditions. The influence of the power law exponent on rupture is discussed. The results indicate that the rheological effects of the tear film fluid affect the film drainage process and therefore be included in models for tear film drainage.
Analytic Solutions of Free Convection Boundary Layer Flow Over a Vertical Flat Plate Embedded in a Porous Medium
563-573
V.
Kumaran
Department of Mathematics, National Institute of Technology Tiruchirappalli-620 015, India
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
Additional analytical solutions are given for the problem of steady free convection boundary layer over a vertical flat plate embedded in a fluid-saturated porous medium. Both the cases of variable surface temperature (VST) and variable surface heat flux (VHF) are considered. The resulting ordinary differential equations are solved analytically and the flow and heat transfer characteristics are discussed. The obtained results for the heat transfer at the plate and, respectively, for the surface temperature are compared with those of Na and Pop [1]. The agreement is very good especially at large distances from the leading edge of the plate.
Features of Wave Propagation in Liquid-Filled Cylinders with Compliant Walls
574-590
G. L.
Komissarova
S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The data about properties of normal waves in a composite elastic-liquid cylindrical waveguide are presented. Shear wave velocity in the cylinder's material is supposed to be less than wave velocity in the liquid (perfect fluid) filling the waveguide. The dispersion properties of the normal waves are determined on the basis of the dispersion equation analysis. The complete set of equations of the dynamic elasticity theory is used to describe the elastic cylinder's deformation. The waves in the liquid filling the waveguide are described by the Helmholtz equation. Such approach provides the effective analysis of interaction of wave motions in the elastic shell and liquid core for wide frequency and wavelength ranges. The data about the kinematic and power characteristics of the normal waves are presented. The technique for systematizing the data about the dispersion properties of the normal waves is offered using the idea of the partial subsystems. The obtained results are compared with the data for a waveguide with sufficiently rigid elastic cylinder (the transverse wave velocity in the cylinder's material exceeds the sound speed in the liquid). The essential differences in evolution of wave coupling effects in the cylinder and the liquid for the cases of rigid and compliant materials are shown.
Mathematical Models of the Soil Water-Air Regime Regulation Based on Calculating of Water-Salt Flow in the Aeration Zone
591-598
Yu. I.
Kalugin
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
S. N.
Kurganskaya
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. S.
Siry
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The aim of this paper is to develop the simple imitation-optimization mathematical models for substantiating the drainage-irrigation systems on the basis of predicting the optimal soil water-salt regimes considering the water-air and thermal conditions of growing plants. This estimation is made by forecasting the water balance components in the root layer. Their values are determined by mathematical modeling of the moisture and salt transfer in the layer of active water-salt exchange (aeration zone), that is caused by natural and irrigation water.
Calculation of the Electrical Discharge Channel Expansion in Liquid Described in Potential Approach
599-607
L. A.
Kamenskaya
Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
V. M.
Kosenkov
Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
An algorithm of calculation of the space liquid flow affected by the pulse loading is proposed. Solution of a system of gas dynamics equations is reduced to the solution of a non-linear equation with respect to a velocity potential. The results of the algorithm testing using the known solutions of 1D and 2D problems are presented. A comparison of the testing results evidences for a possibility to use it for investigation of the processes occurring at the electric discharges in fluid.
Wave Propagation and Reflection in Systems of Compliant
608-620
N. N.
Kizilova
V. N. Karazin Kharkiv National University, Ukraine
Axisymmetric wave motion of a viscous incompressible liquid in a system, which is consisted of a long thin elastic tube and a terminal element with a complex admittance is investigated. Expression for the input admittance of the system taking into account wave reflection at the end of the tube is obtained. The dependence of the input admittance on geometrical and mechanical parameters of the system is investigated. The equation for calculation the socalled resonant harmonics where the input admittance reaches its extreme is obtained. The harmonics is considered as resonant, when any alteration in terminal admittance causes a significant variation in its amplitude. The influence of variations of the model parameters on the amplitude and the phase of the input admittance is closely investigated. Possible applications of the proposed model for biomechanical interpretation of novel methods of medical pulse diagnosis are discussed.
Calculation of Two-Dimensional Unsteady Supercavities at Arbitrary Time Dependence
621-632
V. N.
Semenenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A technique is proposed for calculating the length and shape of a two-dimensional unsteady supercavity past a slender wedge at arbitrary time dependence. A finite-difference discretization with respect to time is used. In each time step the solution is calculated by the method of discrete singularities, and varying cavity length is found from the condition of the cavity pressure constancy. The computational examples for natural supercavity evolution at different types of the cavitating wedge deformations are presented. A comparison with the simplified version of this approach is given for the case of periodic time dependence.
Hydrodynamic Characteristics of the Electric Discharge in the Liquid at Energy Supplied to the Channel in a Form of Repeating Pulses
633-644
A. A.
Vovchenko
Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
V. G.
Kovalev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv; and Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
V. A.
Pozdeev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv; and Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
An external hydrodynamic problem of electric discharge in water is considered under the condition of energy supplied in the cylindrical channel as a sequence of pulses. The corresponding initial-boundary problem with mobile boundary for wave equation is formulated. The problem analytical solution is obtained by the method of nonlinear time transformation. It is shown how the small pulsations imposed on the linear law of channel radius growth affect the process development. Peculiarities of hydrodynamic characteristics of the electric discharge are revealed.