Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
29
6
2002
Effects of Magnetic Field and Heat Generation/Absorption on Natural Convection from an Isothermal Surface in a Stratified Environment
13
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
The problem of steady, laminar, buoyancy-induced flow by natural convection along a vertical permeable surface immersed in a thermally-stratified environment in the presence of magnetic field and heat generation or absorption effects is studied numerically. Conditions for similarity solutions are determined for arbitrary stable and unstable thermal environment stratification. Numerical solution of the resulting similarity equations is performed using an implicit, iterative, tridiagonal finite-difference method. Comparisons with previously published work are performed and the results are found to be in excellent agreement. The effects of the Hartmann number, heat generation or absorption coefficient, ambient temperature power index, and the wall mass transfer parameter on the velocity and temperature profiles as well as the skin-friction coefficient and Nusselt number are presented in graphical form. It is found that both the magnetic field and heat absorption effects eliminate the occurrence of the fluid backflow and temperature deficit in the outer part of the boundary layer predicted for the non-magnetic case.
Spline-Wavelet Solutions for Diffusion Equation
8
E.
Laserra
Dipartimento di Matematica e Informatica, Univ. di Salerno, Via S.Allende, 1-84121 Baronissi (SA), Italy
M.
Pecoraro
Universita di Salerno, Via S.AUende, 1-84081 Baronissi (SA), Italy
Carlo
Cattani
Dipartimento di Matematica "G. Castelnuovo", Univ. di Roma "La Sapienza'' P. Ie A. Moro 5,1-00185 Roma ; and DiFarma, University of Salerno Via Ponte Don Melillo, 84084 Fisciano (SA), Italy
In this paper, the Fourier solution of a mixed parabolic diffusion problem is considered and compared with the wavelet solution and with a cardinal cubic spline solution. The wavelet solution is obtained using the discrete Haar transform and the Haar wavelets are regularized by natural splines. The cubic spline solution is obtained defining a fast Spline Haar transform via matrix product.
Multidimensional Wavelet Bases in Diffusion Theory
6
E.
Laserra
Dipartimento di Matematica e Informatica, Univ. di Salerno, Via S.Allende, 1-84121 Baronissi (SA), Italy
The theory of diffusion of reacting solutes in porous media described by a multidimensional differential system is discussed in a multidimensional Haar wavelet basis.
A Model of Dispersion in the Unsteady Separated Shear Flow past Complex Geometries
18
L.
Zannetti
Dipartimento di Ingegneria Aeronautica, Politecnico di Torino 10129 Torino, Italy
P.
Franzese
Institute for Computational Sciences and Informatics George Mason University, Fairfax, Virginia 22030, USA
The chaotic dynamics of separated flows past complex geometries is studied by means of a low order model. The flows are assumed to be rotational and inviscid, and a technique is described to determine the stream functions for linear shear profiles. The geometry considered is a snow cornice, whose edge allows for the separation of the flow and reattachment downstream of the recirculation region. A free point vortex has been added to the flows in order to constrain the separation points to be located at the edge. Unsteadiness is imposed by displacing the vortex from equilibrium. The trajectories of passive scalars continuously released upwind of the separation point and trapped by the recirculating bubble are numerically integrated, and concentration time series are calculated at fixed locations downwind of the reattachment point. The heteroclinic tangle and lobe dynamics of the recirculation region appear to be among the causes of intermittent trapping and release of scalars, in agreement with the simulation performed by higher order models.
Effect of Electrostatic Field on Rupture of Thin Power-Law Liquid Film
11
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
Earnest N.
Poulos
Department of Mechanical Engineering Cleveland State University Cleveland, Ohio 44115, USA
Nonlinear thin power-law type non-Newtonian liquid film rupture is analyzed by investigating the stability under the influence of a non-uniform electrostatic field 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 effect of the electric field is included in the analysis only in the boundary condition at the liquid vapor interface. 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 electric field stabilizes the film and increases the time to rupture when a long wavelength perturbation is introduced. The influence of the power law exponent on rupture is discussed.
Combined Convection from a Vertical Flat Plate with Temperature Dependent Viscosity and Thermal Conductivity
17
M. S.
Munir
Department of Mathematics, University of Dhaka Dhaka 1000, Bangladesh
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
We consider a two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity and thermal conductivity past a vertical impermeable flat plate. The equations governing the flow are transformed for three different regimes appropriate to the forced convection, free convection and forced-free convection regimes. The reduced equations for the forced convection and free convection regime are solved using the perturbation technique treating x the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained using the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. The effects of the viscosity variation parameter, e, and thermal conductivity parameter, g, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 1 to 100 are shown. The perturbation solutions obtained for small and large values of x are found in excellent agreement with the finite difference solutions for the entire x regime. We also present the values of the dimensionless velocity, viscosity and thermal conductivity showing the effects of viscosity and thermal conductivity parameter.
Characteristics of Normal Waves in Elastic-Fluid Cylindrical Waveguide
18
G. L.
Komissarova
S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Properties of normal waves in the thin-walled elastic cylinder filled with an ideal liquid are considered. The analysis is carried out in a wide range of frequencies. To describe the wave field in the elastic cylinder the complete set of equations of the dynamic theory of elasticity is used. It allows to study comprehensively the effects of interaction between waves in an elastic body and liquid. The basic attention is given to the cases concerning thin cylinders. The arrangement of numerical calculation data is carried out on the basis of known properties of some partial subsystems. Manifestation of the interaction effects and physical properties of normal waves in compound waveguide become sufficiently informative when the empty elastic cylinder and cylindrical acoustic waveguides with soft or rigid external boundaries as partial subsystems are chosen. Using the soft boundary model is justified in case of a thin-walled elastic cylinder and concerning low frequencies. At increase of rigidity of the cylinder or increase of frequency the waveguide with rigid wall is more suitable as a partial subsystem. The detailed analysis of the kinematic and power characteristics of normal waves is given. Their change depending on geometrical and physical parameters shows the role of the effects of elastic-liquid interaction in compound waveguides. Special attention is given to the lowest normal waves having the special properties and being most strongly the subject of the influence of the interaction between the solid and fluid parts of the waveguides.
Velocity Distribution in Horizontal Pipes Conveying Non-Uniform Particles
19
Rakesh
Mishra
Department of Applied Mechanics, M. N. Regional Engineering College, Allahabad, India
Sidh
Singh
Indian Institute of Technology Delhi
V.
Seshadri
Department of Applied Mechanics, IIT Delhi Hauz Khas, New Delhi, India
Velocity distribution in a flow of multi-sized particulate solid-liquid mixtures was measured in horizontal pipes using an impact-type of probe with a modified pressure sensing mechanism. Measurements were done over a wide range of solid concentrations (0 to 40 % by weight) and flowrates. Quantitative data on the degree of asymmetry in the velocity profile and the location and magnitude of maximum velocity are presented. Results show that at a given concentration the degree of asymmetry in the velocity profile in the mid vertical plane reduces with the increase in flowrate and the point of maximum velocity shifts towards the center. At any given flowrate, the extent of asymmetry increases with the increase in solid concentration up to 30 % (by weight) and reduces thereafter marginally at higher concentration.
Solutions of Polymers under the Conditions of Wall Turbulence. Mechanism of Drag Reduction
19
Volodymyr G.
Pogrebnyak
Donbass State Academy of Building Industry and Architecture, Donetsk, Ukraine
Anatoly A.
Pisarenko
Donbass State Academy of Building Industry and Architecture, Donetsk, Ukraine
Results of a polarization-optical investigation of a wall turbulent flow of the solutions of polyethylene oxide (PEO) are presented in the paper. They prove that, within certain zones of the boundary layer, the macromolecules are subjected to a strong deformation effect of the hydrodynamic field. The experimental findings presented in the paper support the idea that the mechanism of drag reduction is uniquely related to the process of strong deformation of the macromolecules, which give rise to the nonlinear effects of elasticity. The adequate experimental verification of unrolling of the molecules under the conditions of wall turbulence illustrates that the employment of non-turbulent flows with stretching for studying the interaction between the macromolecules and the hydrodynamic field has some advantages. This allows an experimental investigation into the "anomalous" effects under the controlled conditions and provides a way of simulating the basic properties of the turbulent boundary layer. The velocity, velocity gradient fields and the degree of the unrolling of the macromolecules in the entry zone of a short capillary (under the modeled conditions of wall turbulence) are studied experimentally. If the flow is converging, the macromolecules are subjected to the considerable unrolling (up to 60 %) under the action of the hydrodynamic field, which leads to reconfiguration of this field. It is found that the behavior of the macromolecules in a flow with a longitudinal velocity gradient along with the effects of elastic deformations, which manifest themselves in this case, are essential for understanding of nature of the "anomalously" low turbulent friction observed in a flow of polymer solutions.
Mathematical Simulation of the Admixture Transfer by Turbulent Boundary Layer
13
Eugene Alexeyevich
Shkvar
Higher and Computational Mathematics Chair, National Aviation University 1 Cosmonaut Komarovave., 03058, Kiev, Ukraine
A semiempirical model of a turbulent boundary layer with a nonuniform distribution of liquid or fine-dispersed admixtures of low concentrations over a layer's thickness is suggested. The modifications of the algebraic model of turbulent viscosity, which allow for influence of the complex of phases carried by the flow on the turbulent viscosity to be taken into account, are developed. The general characteristic of these phases is that the gradients of their concentrations are normal to the surface flowed around. A noniterative march method for the simulation of a multiphase boundary layer taking into account the influence of the transferred phases on the parameters of the main flow is developed in the paper. It is demonstrated that the algorithms of parallel computing can be successfully applied within the frames of the suggested method. The execution time on the multiprocessor computer is estimated. Some examples of the numerical simulation of the turbulent flows are considered.