Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
38
1
2011
Exact Solution for the Oscillating Creeping Flow between Concentric Spheres
1-12
Sokrates
Tsangaris
Lab. of Biofluid-Mechnics and Biomedical Engineering of National Technical University of Athens
D.
Kondaxakis
School of Mechanical Engineering, Fluids Section, National Technical University of Athens Athens
N. W.
Vlachakis
School of Mechanical Engineering, Fluids Section, National Technical University of Athens Athens
The Navier-Stokes equations are solved to obtain an analytical solution of the developed unsteady oscillating flow within the gap formed between two concentric spheres. This flow field spatially evolves between the north and the south poles of the geometrical configuration. The present paper contributes to the mathematical as well as to the mechanical characterization of the flow in spherical gaps and provides exact solutions for unsteady cases when convection effects are neglected. The results are mainly illustrated by representing the velocity as a function of two non-dimensional parameters: the gap spacing parameter and the reduced frequency parameter (Womersley number).
Effusion in Dense Fluids
13-25
Pirooz
Mohazzabi
Department of Physics, University of Wisconsin-Parkside
Molecular dynamics simulations as well as theoretical considerations reveal that Graham's law of effusion holds in fluids with much less stringent conditions than previously stated. This includes fluids with densities exceeding that of solids and high enough to cause localization of the particles. One- and two-component fluids are investigated and some subtleties are reported.
Efflux Time Comparison for Tanks of Different Geometries
26-37
Ch. V.
Subbarao
Department of Chemical Engineering, MVGR College of Engineering
P. V. Gopal
Singh
Department of Chemical Engineering, MVGR College of Engineering
S.
Kishore
Department of Chemical Engineering, MVGR College of Engineering
C. Bhaskara
Sarma
Gayatri Vidya Parishad College of Engineering Mudhurawada
V. S. R. K.
Prasad
Anil Neerukonda Institute of Technology & Sciences (ANITS)
Based on macroscopic balances, mathematical equations for efflux time during gravity draining of a Newtonian liquid (below its bubble point) from large open storage tanks of different geometries through exit pipe of same length and cross sectional area (the flow in the exit pipe being laminar) located at the centre of the bottom of the respective storage tanks are developed. The equations so developed are useful in arriving at the maximum time required for draining the contents of the respective storage vessels. To drain the same volume of liquid, the mathematical equations so developed are compared to find out "which of the tanks considered empty faster".
Unsteady Motion of a Single Rising Bubble in Low Reynolds Numbers: An Analytical Study
38-55
M.
Jalaal
Department of Mechanical Engineering, University of Tabriz
Davood
Ganji (D.D. Ganji)
Babol University
The rising behavior of bubbles is of fundamental importance in many natural and industrial phenomenon. In current study, the unsteady motion of a single spherical air bubble rising in a stationary viscose liquid has been studied for low Reynolds numbers region. Considered nonlinear equation of motion involved added-mass term and neglected the Basset term. An exact solution is derived for instantaneous velocity using homotopy perturbation method. Therefore, acceleration and position of the bubble were achieved. Equation was solved generally and for some practical conditions while air was assumed to be the gas phase and glycerin solutions with different concentrations were considered as liquid phases. Present investigation shows the effectiveness of HPM and exhibit a new application of it for nonlinear problems arising in two-phase flows. Current analytical expression for rising bubble can be used in different further investigations on rising bubbles.
Effect of Inlet Flow Angle on the Flow Characteristics in Chamber
56-70
A.
Abdel-Fattah
Department of Mechanical Power Engineering, Faculty of Engineering Menoufiya University, Shebin El-Kom
In the present study, a steady laminar and incompressible fluid flow issues from wall injection in a circular chamber has been studied experimentally and numerically. The water is injected from injection system into the chamber through the wall jets. The static pressure variation along the chamber length is measured and calculated for different values of Reynolds numbers and inlet flow angles. The average heat transfer variation with Reynolds number has been obtained for different values of the inlet flow angle. The velocity vectors, velocities and temperature contours are found. The flow Reynolds number in this study is found to vary between 433 and 910 at inlet flow angle of 0,15, 30, 45 and 60°. The results indicate that the pressure recovery coefficient decreases as both Reynolds number and inlet flow angle increase. The average heat transfer coefficient increases with increasing both Reynolds number and inlet flow angle. Numerically, the results showed that two recirculation zones occur in the sides of center line of the chamber behind the step. The size of these recirculation zones increases by increasing Reynolds number. As Reynolds number increase, the flow temperature decreases in down stream direction.
Exact Solutions for Laminar Periodic Non-Axisymmetric Slip Flow of a Viscous Incompressible Fluid due to a Porous Rotating Disk
71-84
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
A. A.
Farooq
COMSATS Institute of Information Technology University Road
A. R.
Ansari
Department of Mathematics & Statistics, College of Informatics & Electronics, University of Limerick, Limerick, Ireland
Tahira
Haroon
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
An exact analytical solution of the steady, three-dimensional Navier-Stokes equations is obtained for the case of flow due to a porous disk rotating with a constant angular velocity, where the disk surface admits partial slip. The basic equations have been solved by reducing them to second order ordinary differential equations with appropriate boundary conditions. The temperature distribution in the flow field is also investigated in the case when the disk is maintained at constant temperature and heat is being transferred from the disk to the fluid. The influence of the slip parameter and other pertinent parameters on the velocity and the temperature profiles are discussed. Finally, the results obtained are shown graphically for various parameters. The main finding is that the velocity and temperature profiles are greatly influenced by the slip parameter.
Examination of Anisotropy of Reynolds Stress Tensor Downstream of a Short Roughness Strip and Concentrated Wall Suction in a Turbulent Boundary Layer
85-92
O. M.
Oyewola
School of Chemical Engineering, University of New South Wales NSW
Hot wire measurements have been made in a turbulent boundary layer subjected to concentrated wall suction and impulse in form of a short roughness strip with the aim of examining their effects on the anisotropy of the Reynolds stress tensor. The results indicate that, while suction increases the anisotropy of the layer, the degree of the anisotropy is altered at the present of the roughness strip. The combination of suction and roughness strip modified the scale of the near-wall structures as reflected in the change in the streamwise and wall-normal integral length scales.