Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
42
6
2015
Unsteady MHD Hartmann − Couette Flow Due to Time Dependent Movement of the Plate of a Darcian Channel with Hall Current and Ion-Slip Effects
463-484
Jitendra
Singh
Vijayanagara Sri Krishnadevaraya University
Naveen
Joshi
Department of Mathematics, V.S.K. University Bellary-583105, Karnataka, India
S. Ghousia
Begum
Department of Mathematics, V.S.K. University Bellary-583105, Karnataka, India
Unsteady MHD Hartmann−Couette flow of a viscous, incompressible and electrically conducting fluid within parallel plate porous Darcian channel with Hall current and ion-slip effects is carried-out. Fluid flow within the channel is induced due to time dependent movement of the upper plate of the channel and by a constant pressure gradient applied along the axis of the plates of the Darcian channel. Fluid flow within the Darcian channel is permeated by a uniform transverse magnetic field, which is fixed relative to the stationary plate. Laplace transform technique is used to obtain an exact solution of the governing equations. The expression for the shear stress at the moving plate due to primary and secondary flows is also derived. To highlight the transient approach to the final steady state flow and the effects of Hall current, ion-slip, magnetic field, permeability and suction/injection, asymptotic behavior of the solution is analyzed for small and large values of time. It is noticed that, at the starting stage, secondary velocity is independent of permeability and there are no flows in the secondary flow direction in the absence of Hall current. At the final stage, fluid flow is in quasi-steady state. Steady state flow executes spatial oscillations in the flow-field whereas unsteady state flow exhibits spatial as well as inertial oscillation in the flow-field. Inertial oscillations in the flow-field are due to presence of Hall current. Numerical values of primary and secondary fluid velocities and that of shear stress at the moving plate of the Darcian channel due to primary and secondary flows are represented graphically for various values of pertinent flow parameters.
Effectiveness and Economic for Using Ag-Nanoparticles in Porous Media inside Enclosure with Present Heat Generation and Magnetic Field under Natural Convection Conditions
485-508
Ali Meerali Jasim
Al-Zamily
University of Babylon, Iraq
In the present study, the effect of the magnetic field and the heat generation on the effectiveness and the economics of using Ag-nanoparticles in porous media under a natural convection with heat flux is studied numerically using finite element method. Four different enclosure shapes are studied. The uniform heat flux is applied partly at the base wall. The vertical or sloped walls are maintained at a constant cold temperature. New criteria are used to evaluate the effectiveness of using nanoparticles depending on the nanoparticles cost and the heat transfer. The results are based on visualization of heat flow via isotherms, heatfunctions and Nusselt number; fluid flow via streamfunctions; and irreversibility via Bejan number. Comparisons with previous published works are performed and the results are found in a good agreement. The influence of main pertinent parameters is investigated, such as: Rayleigh number Ra = (104 ... 107), Hartmann number Ha = (0 ... 60), heat generation constant (λ = 1 and 10) and nanoparticles volume fraction Φ = (0 ... 0.15) on the flow, heat transfer and entropy generation for constant Darcy number Da = 10−4. The results show that the benefit of using nanoparticles on the system stability (effectiveness-Be) decreases as the n increases. Also, for most cases, the maximum cost-heat appears at λ = 0.05 and it reduces as nanoparticles volume fraction increases except for high Ra = 107. The results show at n = 0 (square cavity) and Ra = 104, the streamfunction of pure fluid increases 45.2 times between λ = 1 and 10, while at Ra = 107, the streamfunction of pure fluid increases 1.1 times.
Flow Characteristics Study and Mathematical Correlation Development in Different Suddenly Expanded and Contracted Configurations
509-536
Bishnu Pada
Biswas
Kalyani Government Engineering College
Kalyani, Nadia-741235, West Bengal, India
Somnath
Chakrabarti
Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology Shibpur, Howrah, 711103, West Bengal, India
A comprehensive numerical study of the flow characteristics of an incompressible fluid flowing through different configurations of combined sudden expansion and contraction has been carried out in this paper along with relevant mathematical correlation development. The two-dimensional steady differential equations for conservation of mass and momentum have been solved for the Reynolds number Re ranging from 50 to 350, fence restriction FR of 10 %, tab restriction TR of 20 %, tab length L*t of 0.25, the expansion length L*exp of 9, aspect ratio AR of 2 and fully developed velocity profile at inlet. The effect of Reynolds number on average static pressure, average stagnation pressure, wall pressure and streamline contour has been studied in detail. From the study, it is revealed that the maximum magnitude of average static pressure rise for sudden expansion and contraction with rectangular tab configuration (Model-3) is more compared to the considered two configurations of plain sudden expansion and contraction (Model-1), and sudden expansion and contraction with fence (Model-2). The average stagnation pressure drop across a section is always more for Model-3 compared to Model-1 and Model-2. The maximum magnitude of wall pressure and the size of the corner recirculating bubble for Model-3 is more compared to other two models. The predicted magnitude of maximum average static pressure rise P*av−max, average stagnation pressure drop P*sav−drop, maximum wall pressure P*w−max and corner recirculating bubble length L*R from the developed mathematical correlations are having error below 10 % in all the cases of considered configurations.
Magnetohydrodynamics of a Mixed Convection Flow in a Vertical Microannulus: An Exact Solution
537-552
Basant K.
Jha
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
Babatunde
Aina
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria
An exact solution of steady fully developed mixed convection flow of viscous, incompressible, electrically conducting fluid in a vertical microannulus in the presence of transverse magnetic field by taking in to consideration of velocity slip and temperature jump at the vertical microannulus surfaces is obtained. The momentum and energy equations representing the present physical situation are presented in dimensionless form along with relevant boundary conditions. The mathematical model is solved using the method of undetermined coefficients. Exact solution is expressed in terms of modified Bessel function of first kind and second kind. The solution obtained is graphically represented and the effects of radius ratio, magnetic field, Knudsen number, and mixed convection on the flow is investigated. It is interesting to remark that as magnetic field increases, there is decrease in the fluid velocity at the outer surface of inner cylinder while there is an increase at the inner surface of the outer cylinder. Furthermore, it is also discovered that an increase in magnetic field parameter leads to decrease in the rate of heat transfer at outer surface of inner cylinder while it increase at inner surface of outer cylinder.
INDEX FOR VOLUME 42, 2015
553-556