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We study the problem of convective movement of a reacting solute in a viscous incompressible fluid occupying a plane layer and subjected to a vertical magnetic field. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. 相似文献
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Transport in Porous Media - This study features a model for double-diffusive convection in a bidisperse porous medium where a vertical magnetic field chemical reaction’s effects are present.... 相似文献
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Transport in Porous Media - The object of this study is to investigate the question of convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated... 相似文献
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Akil J. Harfash 《Annales Henri Poincare》2014,15(12):2441-2465
This paper deals with two fundamental models for convection in a reacting fluid and porous medium with magnetic field effect. We demonstrate that the solution depends continuously on changes in the chemical reaction and the electrical conductivity coefficients. The continuous dependence is unconditional in two dimensions but conditional in three dimensions. 相似文献
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A.J. Harfash 《Acta Mechanica Sinica》2014,30(2):144-152
The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold. 相似文献
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A compact finite difference scheme is developed to the three-dimensional microscale heat transport equation. This new scheme is fourth order in space and second order in time. It is proved to be unconditionally stable with respect to initial values. Numerical results are provided for comparison testing purpose. 相似文献
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A. J. Harfash 《Transport in Porous Media》2014,102(1):43-57
A convection problem in anisotropic and inhomogeneous porous media has been analyzed. In particular, the effect of variable permeability, thermal diffusivity, and variable gravity with respect to the vertical direction, has been studied. A linear and nonlinear stability analysis of the conduction solution has been performed. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three- dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold. 相似文献
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A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient. 相似文献
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A. J. Harfash 《Transport in Porous Media》2014,103(3):361-379
The problem of convection in a variable gravity field with magnetic field effect is studied using methods of linear instability theory and non-linear energy theory. Then, the accuracies of both the linear instability and global non-linear energy stability thresholds are tested using a three-dimensional simulation. The strong stabilizing effect of gravity field and magnetic field is shown. Moreover, the results support the assertion that the linear theory is very accurate in predicting the onset of convective motion, and thus regions of stability. 相似文献