Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
33
2
2006
Exponentially Fitted Modified Upwind Scheme for Singular Perturbation Problems
119-136
P. Pramod
Chakravarthy
Department of Mathematics, Kakatiya Institute of Technology and Science, Warangal, 506 015, India
Y. N.
Reddy
Department of Mathematics, National Institute of Technology, Warangal, 506 004, India
In this paper, an exponentially fitted modified upwind scheme is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a modified upwind scheme and is obtained from the theory of singular perturbations. A tridiagonal finite difference scheme is obtained and is solved by using the Thomas algorithm. Several linear and nonlinear problems are solved and observed, which show that the present method approximates the exact solution very well.
Transient Non-Boussinesq Magnetohydrodynamic Free Convection Flows Over a Vertical Surface
137-152
Hamzeh M.
Duwairi
Mechanical Engineering Department, Faculty of Engineering and Technology, The University of Jordan, 11942, Amman, Jordan
R. A.
Damseh
Mechanical Engineering Department, Al-Huson University College, Al-Balqa Applied University, P. O. Box 50, Al-Huson 19117 Irbid, Jordan
Bourhan
Tashtoush
Mechanical Engineering Department, JUST, Irbid, Jordan
The majority of studies of transient laminar magnetohydrodynamic (MHD) free convection over a vertical isothermal plate concern gases and air. The existing results for water have been produced assuming a linear relationship between fluid density and temperature. However, it is known that the density relationship for water is nonlinear at low temperatures. In this study, the problem of transient laminar MHD free convection over a vertical isothermal plate in water is investigated in the temperature range between 20 °C and 0 °C. The results are obtained with the numerical solution of the boundary layer equations. Comparison with previous works shows excellent agreement. The variation of the magnetic field parameter has strong effects on the results.
Magnetohydrodynamic Free Convection of a Large Prandtl Number Liquid Over a Nonisothermal Two-Dimensional Body
153-167
Mohamed F.
El-Amin
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 81258; King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia
M. A.
EL-Hakiem
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, 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
A boundary layer analysis is presented to investigate the free convection over a nonisothermal two-dimensional body under the action of a transverse nonuniform magnetic field. Two simplifications are used in this work: the first one is used due to the fact that many of the industrial liquids have large Prandtl number and, therefore, the terms that are divided by Pr in the nondimensional governing equations could be neglected; the second simplification is used to treat the shear stress for power law non-Newtonian fluids τ = K(∂u/∂y)n as a shear stress model. Solutions are obtained with variations in surface temperature or with variations in heat flux. The effects of the magnetic parameter M, the body shape parameter m, and the surface thermal variation parameter ρ as well as the heat flux parameter s are examined. Velocity profiles as well as temperature distributions are shown graphically for two cases: variable wall temperature condition (VWT) and variable wall flux condition (VWF). The numerical values of the wall shear stress and the heat transfer rate are entered in tables for the two cases.
Self-Induced Oscillations of Elastic Immersed Axisymmetric Shell-Like Jet
168-174
Yu. M.
Dudzinskii
Odessa National Polytechnic University, Odessa, Ukraine
A. O.
Sukharkov
Odessa National Polytechnic University, Ukraine
A. A.
Nazarenko
I. I. Mechnikov Odessa National University, Odessa, Ukraine
A model of axially symmetric hydrodynamic acoustic sound sources of a direct-flow design (with a circular nozzle and stepwise obstacle) and counter-flow one is considered. The basic frequency of acoustic signal is calculated as a function of working fluid properties, geometric and hydrodynamic parameters of the jet. The numerical data are compared with experimental results. A criterion of conformity of the model with real sound sources of considered types is proposed.
Effect of Properties of Alveolar Walls on Sound Velocity in Pulmonary Parenchyma
175-185
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
An acoustic model of parenchyma is offered, modified by the allowance for elastic properties of alveolar walls, transpulmonary pressure and surface tension forces acting on the gas-tissue interface. The problem of acoustic modeling of the lung tissue is reduced to considering an individual spherical bubble with a supported surface pulsing in an infinite liquid. It is proved that the basic role in the alveole's surface reinforcement is played by the longitudinal rigidity of its walls. A calculated increase of sound velocity in mammalian parenchyma caused by the alveole reinforcement does not exceed 20 %. It is shown that the reinforcement influences properties of the lungs most strongly in large mammals, which alveoles contain the greater share of elastin and collagen. Comparing of theoretical data with the experimental ones has shown a satisfactory agreement between them.
On Methods for Analysis of Supercavitation in a High-Speed Motion in Water: Incompressible Approximation
186-210
V. V.
Serebryakov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The report presents results of development of approximate analysis methods and a review of possibilities to predict flow/motion processes which take place during a high-speed motion of bodies in water with a well-developed cavitation. Two characteristic velocity ranges are under consideration: moderate and ultra-high, the Mach numbers in water being M ∼ 0.5−2.5; each of the ranges corresponds to its field of applications and issues of the theory. The preferable approach is to analyze the problem as a whole on the basis of the simplest physical models. The consideration is based on a “Matched Asymptotic Expansion Method” in the approximation of a “Slender Body Theory”, in combination with other approximations and simple heuristic models, the analysis of dimensions and integral laws of conservation. The research uses the model of an ideal incompressible fluid. The covered problems include elongated, mainly axisymmetric, steady and unsteady cavities under a number of influences, and cavities with induced blowing.