共查询到20条相似文献,搜索用时 15 毫秒
1.
İbrahim Çelik 《国际流体数值方法杂志》2011,66(10):1325-1340
In this study, matrix representation of the Chebyshev collocation method for partial differential equation has been represented and applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Numerical solution of velocity and induced magnetic field is obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. The Chebyshev collocation method is used with a reasonable number of collocations points, which gives accurate numerical solutions of the MHD flow problem. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H≤1000. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
2.
An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution. 相似文献
3.
In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance
imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the
influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev
collocation spectral method. The critical Reynolds number Re
c, the critical wave number α
c and the critical wave speed c
c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing
effect on the fluid flow. 相似文献
4.
The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An efficient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined. 相似文献
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6.
D. A. Nield 《Transport in Porous Media》1994,14(1):85-88
A modification to the Forchheimer-Brinkman equation, for the modelling of high speed flow of a compressible fluid in a dense saturated porous medium, is proposed. The modified equation is applied to a flow in which choking can occur. 相似文献
7.
The effect of linearly polarized vibration on the stability of a plane displacement front in a porous medium is studied. The problem of the stability of the motion of a plane displacement front traveling at a constant velocity U under the action of vibration normal to the front is considered. It is shown that under the action of vibration the dynamics of the plane displacement front can be described by the Mathieu equation with a dissipative term. Using the standard averaging method, in the case of high-frequency vibration it is revealed that vibration can only increase the stability of the system. It is found that the vibration stabilizes the plane displacement front with respect to part of the perturbation spectrum. 相似文献
8.
S. CHAND 《应用数学和力学(英文版)》2013,34(3):309-326
The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters (i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter) are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M 1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained. 相似文献
9.
A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convectionReceived: 10 February 2003, Accepted: 11 March 2003, Published online: 12 September 2003 相似文献
10.
11.
In this paper, the steady flow and heat transfer of a magnetohydrodynamic fluid is studied. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field and occupies the porous space in annular pipe. The governing nonlinear equations are modeled by introducing the modified Darcy's law obeying the Sisko model. The system is solved using the homotopy analysis method (HAM), which yields analytical solutions in the form of a rapidly convergent infinite series. Also, HAM is used to obtain analytical solutions of the problem for noninteger values of the power index. The resulting problem for velocity field is then numerically solved using an iterative method to show the accuracy of the analytic solutions. The obtained solutions for the velocity and temperature fields are graphically sketched and the salient features of these solutions are discussed for various values of the power index parameter. We also present a comparison between Sisko and Newtonian fluids. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular
tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The
non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral
equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability,
and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability
of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum
pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal
to the yield stress of the fluid. 相似文献
13.
A. A. Hill 《Continuum Mechanics and Thermodynamics》2003,15(3):275-285
A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The
model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the
growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are
also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability
Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory
accurately emulates the physics of the onset of convection.
Received February 10, 2003 / Accepted February 10, 2003/ Published online May 9, 2003 / B. Straughan 相似文献
14.
V. E. Odintsova 《Fluid Dynamics》2009,44(1):103-111
The stability of the phase interface in geothermal systems is considered in the isothermal approximation with allowance for capillary effects. The dispersion relation is obtained and the domains of stability and instability of steady-state vertical flows are found. Possible types of transition to instability, namely, transitions with the most unstable mode corresponding to zero and infinite wavenumbers or to all wavenumbers simultaneously, are described. In the first case the nonlinear Kolmogorov-Petrovskii-Piskunov equation describing the evolution of a narrow strip of weakly unstable modes on the stability threshold is derived. The effect of the parameters of the system on its stability is investigated. 相似文献
15.
16.
A. A. AFIFY N. S. ELGAZERY 《应用数学和力学(英文版)》2013,34(10):1247-1262
A numerical study of a non-Darcy mixed convective heat and mass transfer flow over a vertical surface embedded in a dispersion, melting, and thermal radiation is porous medium under the effects of double investigated. The set of governing boundary layer equations and the boundary conditions is transformed into a set of coupled nonlinear ordinary differential equations with the relevant boundary conditions. The transformed equations are solved numerically by using the Chebyshev pseudospectral method. Comparisons of the present results with the existing results in the literature are made, and good agreement is found. Numerical results for the velocity, temperature, concentration profiles, and local Nusselt and Sherwood numbers are discussed for various values of physical parameters. 相似文献
17.
The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of
soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of
three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem
of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the
coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory
results.
The project supported by the National Science Foundation of China 相似文献
18.
We study the effect of fluid contact area on viscous coupling in the parallel flow of immiscible fluids in a porous media geometry. We consider flow on opposite sides of a planar interface, consisting of alternating solid and open (slit) segments. We use the analytical solution of Tio and Sadhal [15] to derive explicit expressions for viscous coupling in terms of the fractional area of contact between the fluids and the viscosity ratio,M. ForM=1, the coefficient matrix obtained is symmetric showing that Onsager's relations are satisfied. In this case, the resulting viscous coupling is typically very small, in agreement with recent experimental results. Lattice gas simulations forM=1 using theBGK model support the theoretical results and show that viscous coupling further diminishes as the wall thickness increases. Assuming the same configuration, analytical results are next derived forM1. The results confirm an existing reciprocity relation between the off-diagonal terms. Viscous coupling remains small. 相似文献
19.
A. V. Kuznetsov 《Applied Scientific Research》1996,56(1):53-67
In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles. 相似文献