Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
39
6
2012
Effect of Rotation on the Onset of Convection in Rivlin − Ericksen Fluid Heated from below in a Brinkman Porous Medium
467-477
G. C.
Rana
Department of Mathematics, Government College Hamirpur, Himachal Pradesh, India
V.
Sharma
Himachal Pradesh University Shimla, Himachal Pradesh, India
The effect of rotation on the onset of convection in Rivlin − Ericksen elastico-viscous fluid heated from below in porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, rotation, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation and Darcy number has stabilizing effect whereas the medium permeability has destabilizing/stabilizing effect on the system under certain conditions. The effects of rotation, Darcy number and medium permeability has also been shown graphically.
Suppression of Secondary Flow through Sidewall Converging in Model Horizontal Longitudinal MOCVD Processes
478-493
Jyh-Long
Tuh
Department of Living Services Industry, Asia-Pacific Institute of Creativity Miaoli, Taiwan 35153, ROC
Experimental flow visualization has been conducted to investigate how the sidewall converging affects the buoyancy induced return flow structure and stabilization of vortex flow in mixed convection of gas in a horizontal rectangular duct. The buoyancy driven secondary flow including the return flow and vortex flow is driven by a heated circular disk embedded in the bottom plate of the duct, simulating that in a horizontal longitudinal MOCVD reactor. Specifically, the sidewalls of the duct are inclined toward the duct core so that the gas flow in the duct is accelerated, causing the local buoyancy-to-inertia ratio to decrease in the main flow direction. In the experiment the Reynolds and Rayleigh numbers of the flow at the duct inlet are respectively varied from 5.1 to 51.2 and from 7200 to 21000, and the duct aspect ratio is reduced from 20 at the inlet to 16 or 12 at the exit. The results show a substantial delay in the onset of the return flow and the effective suppression of the buoyancy driven unstable longitudinal and transverse vortex flows by the sidewall converging. Moreover, the sidewall converging can weaken the return flow more effectively at slightly higher Reynolds numbers. An empirical equation is provided to correlate the present data for the onset condition of the return flow in the converging duct. The reduction in the size and intensity of the return flow is prominent. Besides, the onsets of longitudinal and transverse vortex rolls are delayed substantially.
Magnetic and Permeability Effects on a Weakly Nonlinear Magneto-Convective Flow in an Active Mushy Layer
494-520
Dambaru
Bhatta
UTRGV
S. Mallikarjunaiah
Muddamallappa
Department of Mathematics, Texas A&M University College Station, Texas
Daniel N.
Riahi
School of Mathematical and Statistical Sciences,
One West University Boulevard, University of Texas Rio Grande Valley, Brownsville, Texas 78520 USA
Here we consider a mushy layer which is formed during solidification of binary alloys in presence of a magnetic field. The mushy layer is treated as active. The original boundary value problem consisting of five partial differential equations with five unknowns are converted to four partial differential equations with four unknowns after eliminating the pressure variable. A Landau type nonlinear evolution equation for the amplitude based on weakly nonlinear theory is derived. We also present computational results for marginal stability curves and other dependent variables for different permeability parameter and Chandrasekhar number. These results suggest that higher permeability parameter and Chandrasekhar number enhance the marginal stability. This analysis also indicates a possible slow transition to turbulence in such flow system since the computed Landau constants are positive.
A FSI Model on the Casson Fluid Flow through an Elastic Stenosed Artery
521-534
Sachin
Shaw
Botswana International University of Science and Technology
S. C.
Pradhan
Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, India
P. V. S. N.
Murthy
Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, 721302, India
In the present work, flow of a pulsatile Casson fluid through a stenosed artery has been investigated. The artery is assumed to be a cylinder of finite length and uniform diameter. Stenoses are considered to be present on inner side of the artery wall. Artery wall is assumed to be elastic in nature. The governing momentum equation is expressed in terms of the shear stress. The momentum equation along with the initial and boundary conditions are solved numerically. Finite element analysis is employed and artery wall displacements are computed. The fluid solid interaction (FSI) and convergence study is carried out. Influence of (i) the radial displacement of artery wall (ii) the location of the stenosis, (iii) the height of the stenosis and (iv) the magnitude of artery wall elastic coefficients on the radila deformation and the wall shear stress have been investigated.
Effect of Gravity Modulation on the Onset of Thermal Convection in Rotating Viscoelastic Fluid and Porous Layer
535-557
S . N.
Gaikwad
Department of Mathematics, Gulbarga University, Jnana Ganga, Gulbarga-585106, India
Irfana
Begum
Department of Mathematics, Gulbarga University Gulbarga 585 106, India
The combined effect of gravity modulation and rotation on the onset of thermal convection in a viscoelastic horizontal fluid layer and a fluid-saturated porous layer is studied analytically using linear stability theory. The regular perturbation method based on small amplitude of modulation is employed to compute the critical value of Rayleigh number and wavenumber. The correction critical Rayleigh number is calculated as a function of Deborah number, Taylor number, Prandtl number, Darcy number, frequency of the modulation and normalized porosity. It is shown that in general the gravity modulation produces a stabilizing effect in case of viscous fluid and Darcy porous layer and both destabilizing and stabilizing effects in case of Brinkman porous layer. It is shown that the onset of convection can be advanced or delayed by proper tuning of various governing parameters.