Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
30
4
2003
Three-Dimensional Micropolar Flow due to a Stretching Flat Surface
10
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
M.
Jaradat
Faculty of Mathematics, University of Cluj R-3400 Cluj, CP 253, Romania
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
A numerical solution of the steady boundary layer equations under similarity assumptions is obtained for the three-dimensional flow of a micropolar fluid over a continuous stretching surface. The case when microrotation vector is zero on the solid surface is considered. Using properly similarity variables, the three-dimensional Navier-Stokes equations are reduced to a set of four coupled non-linear ordinary differential equations. A very efficient numerical solution has been used to solve the boundary layer equations and a comparison is made with earlier results for a Newtonian fluid.
Stokes Flow past an Array of Annular Disks
14
A. M.
Gomilko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. S.
Malyuga
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. V.
Meleshko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
M. G. J.
Verbruggen
Eindhoven University of Technology, the Netherlands
An axisymmetric Stokes flow past three thin annular disks is considered. With use of the theory of hydrodynamic potential and the method of orthogonal polynomials the boundary-value problem is reduced to an infinite system of linear algebraic equations of the second kind. To this end, the expansions of the unknown densities in terms of the Chebyshev polynomials are employed. A dependence of the drag force on geometrical parameter is analyzed. The streamline patterns, describing the kinematics of the flow, are presented.
Nonsimilar Solutions for Natural Convection in Micropolar Fluids on a Vertical Plate
14
I. A.
Hassanien
Department of Mathematics, Faculty of Science, Assiut University, Assiut, 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 buoyancy effects on the forced convective micropolar fluid flow and heat transfer on a vertical plate with a vectored surface mass transfer are studied using the theory of micropolar fluids formulated by Eringen. The governing momentum, angular momentum and energy equations have been solved numerically by a finite difference method. Buoyancy effects on the flow, temperature and angular velocity fields are presented and discussed. The influence of uniform mass transfer from the surface is also considered. Wall friction, heat transfer and wall couple stress results are presented for a Prandtl number of 0.7 for various cases representing the relative effects of blowing or suction.
Dynamics and Energetics of Heavy Gas Dispersion in Bottom Atmospheric Boundary Layer
15
Ivan V.
Kovalets
Institute for Problems of Mathematical Machines and Systems Problems of National Academy of Sciences of Ukraine, Kyiv
Vladimir S.
Maderich
Institute of Problems of Mathematical Machines and Systems of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The results of simulation of the heavy cloud dispersion in the atmospheric boundary layer are presented. The model of the turbulent dynamics of the heavy cloud is described. The Favre - Reynolds averaging procedure is used, that results in the less complicated form of equations than the Reynolds averaging procedure. The first-order turbulence model is applied for the calculation of turbulent fluxes and stresses. The numerical algorithm of the problem solution is briefly described with use of the the conservative implicit finite-difference scheme. The splitting method upon the space directions and physical processes is used. The results of calculations are compared with the results of laboratory and field experiments. The analysis of the energetics of the heavy gas dispersion processes is given.
Numerical 3D Model for Heavy Gas Dispersion in the Atmosphere with the Use of the Conservative Splitting Schemes
15
Ivan V.
Kovalets
Institute for Problems of Mathematical Machines and Systems Problems of National Academy of Sciences of Ukraine, Kyiv
Vladimir S.
Maderich
Institute of Problems of Mathematical Machines and Systems of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The numerical three-dimensional model of heavy gas dispersion is considered. The conservative (upon mass) splitting method was used, solving pressure equation instead of the equation for temperature. The results of simulations compared with the laboratory experiments data. The comparison of the results against of calculations by the non-conservative splitting method is presented.
On Mechanisms of Formation of Acoustic Properties of Pulmonary Parenchyma
18
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
The anatomic structure of human respiratory system is analyzed. For frequencies typical for the respiratory sounds a possibility of representing of lung's respiratory zone as a continuum with microstructure is justified. An acoustic model of pulmonary parenchyma is developed on the basis of physical study of sound dispersion and attenuation in emulsions. For the case of thermal independence of grains of emulsion (alveoles) the analytical expression describing the sound speed and attenuation decrement in the parenchyma is obtained. It is shown that behavior of the sound speed foreseen in the emulsion model is similar to tendencies depicted by simple gas-liquid models. A strong dependence of the attenuation decrement on the frequency and concentration of parenchyma's gas phase is shown. It is outlined that at low values of air filling of lungs the frequency dependence of damping in the studied range is a square law. As for high air filling, a transition to the square root tendency with the increase of frequency is demonstrated. This peculiarity is conditioned by strong resizing of the alveoles during the respiratory cycle. A considerable decrease of the sound attenuation at deep inspiration is stated.
Thermal Dispersion and Dissipation of a Sound in Concentrated Dispersion Liquid and Liquid-Gas Media
19
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
On the basis of classical model of emulsion developed by M. A. Isakovich the physical and mathematical models of forming of acoustical properties of emulsions, bubble media, and aerosols are worked out with allowance for local thermal interaction of their microstructural elements. It is shown that model by Isakovich can be regarded as a limiting case of the model accounting for microstructural interaction, which describes the bubble medium. A numerical analysis demonstrates that at small and moderate interspaces between the grains of emulsion the model, accounting for thermal interaction, displays much better correlation with general physical interpretation of low-frequency sound propagation in dispersed mixtures than classical one, considering the microstructural elements to be independent.