Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
34
6
2007
Transient Rotating Hydromagnetic Partially-Ionized Heat-Generating Gas Dynamic Flow with Hall/Ion-Slip Current Effects: Finite Element Analysis
493-505
Harouna
Naroua
Université Abdou Moumouni
Harmindar S.
Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
P. C.
Ram
Department of Mathematics and Computer Science, The Catholic University of Eastern Africa, P. O. Box 62157, Nairobi, Kenya
Tasveer A.
Beg
Engineering Mechanics Associates, Manchester, M16, England, United Kingdom
O. Anwar
Bég
Fluid Mechanics, Nanosystems and Propulsion, Aeronautical and Mechanical Engineering,
School of Computing, Science and Engineering, Newton Building, University of Salford,
Manchester M54WT, United Kingdom
Rama
Bhargava
Department of Mathematics, Indian Institute of Technology, Roorkee-247667, India
A mathematical model is presented for the unsteady magnetohydrodynamic heat-generating free convection flow of a partially-ionized gas past an infinite vertical porous plate in a rotating frame of reference. Hall and ion-slip current effects are incorporated in the model. A finite element solution to the coupled non-linear differential equations is presented under physically realistic boundary conditions. The effects of Hall current parameter, ion-slip current parameter, Prandtl number, heat generation parameter, rotational parameter, Grashof (buoyancy) parameter and also time on the velocity and temperature fields are presented graphically. Primary velocity profile (u) decreases due to an increase in the Hall parameter and the ionslip parameter; however it is boosted with time for positive Grashof numbers (cooling of the plate by free convection currents) and decreases with time for negative Grashof numbers (heating of the plate by free convection currents). Secondary velocity profile (v) is also reduced with rising Hall parameter and ionslip parameter but boosted with time and stronger rotation. The temperature profile (θ) is enhanced with a rise in the heat generating parameter and also increases with time. The flow regime has important applications in MHD energy systems, plasma aerodynamics and induction flow meter technologies.
Behavior of Magnetic Fluid Based Squeeze Film Between Porous Circular Plates with Porous Matrix of Variable Thickness
506-514
G. M.
Deheri
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India
H. C.
Patel
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India
R. M.
Patel
Department of Mathematics, Gujarat Arts and Science College, Ahmedabad-380006, Gujarat, India
Efforts have been made to study and analyze the performance of a magnetic fluid based squeeze film between porous circular plates with porous matrix of variable film thickness. The associated Reynolds equation is solved with appropriate boundary conditions and the expressions for pressure, load carrying capacity and response time are obtained. The results are presented graphically as well as in tabular form. It is observed that these performance characteristics increase with the increasing magnetization parameter thereby, indicating that the performance of the bearing with magnetic fluid lubricant is better than that with the conventional lubricant. Moreover, there is a very significant observation that for a proper selection of the thickness ratio parameter, a magnetic fluid based squeeze film bearing with variable porous matrix thickness can be made to perform considerably better than that of a conventional porous bearing with a uniform porous matrix thickness working with a conventional lubricant.
Thermal Radiation of an Optically Thick Gray Gas in the Presence of Indirect Natural Convection
515-520
Ioan
Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
S. K.
Ghosh
Department of Mathematics, Narajole Raj College, Narajole, District - Midnapore (West)-721211, West Bengal, India
The effects of thermal radiation of a viscous incompressible fluid occupying a semi-infinite region of space bounded by an infinite horizontal moving hot plate in the presence of indirect natural convection by way of an induced pressure gradient, is considered. The fluid is a gray, absorbing-emitting radiation but a non-scattering medium. An exact solution is obtained for the flow by applying Laplace transform technique. The numerical results of velocity distributions are depicted graphically for different values of radiation parameter K1 and Grashof number Gr, taking the Prandtl number Pr = 0.71 and t = 0.2 are kept fixed. It is observed that the velocity slightly decreases with increasing the value of radiation parameter while the velocity is slightly decreases with increase in Gr whereas there exists a reverse flow on increasing Gr due to the presence of induced pressure gradient.
Effects of Wall Conductance on MHD Fully Developed Flow with Asymmetric Heating of the Wall
521-534
Mrinmoy
Guria
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721102, West Bengal, India
B. K.
Das
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721102, West Bengal, India
Rabindra N.
Jana
Department of Applied Mathematics, Vidyasagar University, Midnapore-721 102, West Bengal, India
S. K.
Ghosh
Department of Mathematics, Narajole Raj College, Narajole, District - Midnapore (West)-721211, West Bengal, India
Effect of wall conductance on hydromagnetic fully developed flow of a viscous incompressible electrically conducting fluid through a vertical channel, is studied. The generalized similarity solutions for velocity and induced magnetic field are obtained in a closed form. Limiting case of a MHD forced and free convection are analyzed with regard to non-conducting as well as perfectly conducting walls. A limiting consideration of a MHD mixed convection flow confined to non-conducting as well as perfectly conducting walls are analyzed for rT = 1 and M << 1. It is interesting to note that since the rate of flow is constant, the critical Grashof number at the cold and hot wall becomes identical. This indicates that the rate of flow is influenced by spanwise temperature variations along the cold and hot wall and the buoyancy force is balanced by the constant rate of flow.
Hydromagnetic Flow Due to Eccentrically Rotating Porous Disk and a Fluid at Infinity
535-547
Mrinmoy
Guria
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721102, West Bengal, India
B. K.
Das
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore - 721102, West Bengal, India
Hydromagnetic flow due to non-coaxial rotations of a porous disk and a fluid at infinity rotating about an axis passes through a fixed point in the presence of a uniform magnetic field is considered. An exact solution of the Navier-Stokes equations obtained for the velocity and temperature field when there is a uniform suction/blowing at the disk. It is seen that the main velocity component f/Ωy1 increases with increase in either magnetic parameter M2 or suction parameter S. On the other hand, the cross velocity component g/Ωy1 decreases with increase in either magnetic parameter or suction parameter. The flow has a boundary layer structure even in the presence of a blowing at the disk. It is observed that f/Ωy1 decreases while g/Ωy1 increases with increase in blowing parameter S1. This implies that blowing at the disk causes reduction in the cross velocity of the flow. The expressions of the force and the torque exerted by the fluid on the porous disk is also obtained and discussed for several values of suction/blowing parameter and magnetic parameter. It is seen that no torque is exerted by the fluid on the disk. It is found that temperature profile θ decreases with increase in suction parameter whereas it increases with increase in magnetic parameter.
Couette Flow of a Burgers' Fluid with Rotation
548-561
Rahmat
Ellahi
Center for Modeling and Computer Simulation, Research Institute, King Fahd University of
Petroleum & Minerals, Dhahran-31261, Saudi Arabia; Department of Mathematics, Faculty of Basic and Applied Sciences, IIU, Islamabad, Pakistan
Saleem
Ashgar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan
An exact solution of the oscillatory flow for an electrically conducting Burgers' fluid is developed in a rotating frame. A magnetic field is applied transversely to the fluid motion. The fluid motion between the two infinite plates is induced due to the small-amplitude oscillation of the upper plate. The primary and secondary velocities for steady and unsteady flows are developed. It is noted that the steady solution is independent of the nature of the fluid, whereas the fluctuating part of the solution depends strongly. Finally, the graphs are plotted and discussed in detail.
Dominating Singularity Behavior of Flow in a Nonaligned Straight Rotating Pipe
562-571
Md. Abdul Hakim
Khan
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh
M. A.
Hye
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh
The dominating singularity behavior of flow in a nonaligned straight rotating pipe has been studied by means of approximate methods. A series in powers of the rotational Reynolds number is obtained by using the algebraic programming language MAPLE. The series is then summed by using the various generalizations of the Padé method. It is observed that the convergence of the series is limited by a pair of singularities located along the imaginary axis in the complex plane. One can approximately depict the critical behavior of the flow near the (unphysical) singularity point.
Liquid Filtration in a Microcirculatory Cell of the Plant Leaf: A Lumped Parameter Model
572-588
N. N.
Kizilova
V. N. Karazin Kharkiv National University, Ukraine
Stationary filtration of a viscous incompressible liquid in the system consisting of the channel with impermeable walls, surrounded by a non-uniform anisotropic porous medium is investigated. The liquid flow along the channel and in the medium is determined by gradients of hydrostatic and osmotic pressures. The problem is related to the sap flow in plant leaves. The considered system is a generalization of Krogh's cylinder for plant tissues. By averaging the initial system of equations the quasi-one-dimensional model is obtained. Various modes of the dynamic system behavior are investigated at different parameters of the model. Expressions are obtained for the averaged pressure, volumetric rate of the fluid and concentration of the osmotically active component.
On Water Wave Suppression by Local Bottom Inhomogeneities
589-598
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
V. A.
Tkachenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
S. A.
Savchenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
The influence of regular bottom peaks or inclined part of the bottom surface on suppression of surface gravity waves is investigated on the basis of potential theory in the framework of the model of finite depth water. The method of spline-collocation is used for solving the problem in the region of variable depth. The influence of the number of local peaks and their height on the reflection coefficient is investigated. Also, the influence of inclined or inclined polygonal part is investigated. An analysis of characteristic features of the phenomenon and the possibility of effective wave suppression are presented.