In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption ...In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].展开更多
In this work, a numerical study for designing a new kind of MHD （Magneto-Hydrn-Dynamic） pumps is presented. This technique makes a compromise between electrolysis prevention and high flow rate performance. This tech...In this work, a numerical study for designing a new kind of MHD （Magneto-Hydrn-Dynamic） pumps is presented. This technique makes a compromise between electrolysis prevention and high flow rate performance. This technique should eliminate electrolytic bubble generation, electrodes wear and fluid propriety modification. All these side phenomena are prevented by considering isolated electrodes. The numerical presented results in this paper demonstrate that continuous MHD pumping is possible with isolated electrodes. The MHD excitation combines a high frequency altering current with a low frequency altering magnetic field. In order to validate our results, two independent theoretical methods for computing flow rate are followed. The two presented independent approaches show that high flow rate is possible even with isolated electrodes. To overcome the problem of dimensioning this kind of pumps, a generic numerical analysis is proposed. Hence, the pump performances as functions of the external parameter are studied and tools to calculate for a given fluid and the optimal high frequency regime are provided.展开更多
This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficie...This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The effects of transverse magnetic field parameter (Hartmann number Ha), Reynolds number Re (different velocities), Prandtl number Pr (different types of fluids) and dispersion parameter on the wall shear stress and the heat transfer rate are discussed.展开更多
基金supported in part by The 973 key Program(2006CB805902)Knowledge Innovation Funds of CAS(KJCX3-SYW-S03),People’s Republic of China+1 种基金supported in part by the Zheng Ge Ru Foundation and Hong Kong RGC Earmarked Research Grantsa research grant from the Center on Nonlinear Studies, Northwest University
文摘In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].
文摘In this work, a numerical study for designing a new kind of MHD （Magneto-Hydrn-Dynamic） pumps is presented. This technique makes a compromise between electrolysis prevention and high flow rate performance. This technique should eliminate electrolytic bubble generation, electrodes wear and fluid propriety modification. All these side phenomena are prevented by considering isolated electrodes. The numerical presented results in this paper demonstrate that continuous MHD pumping is possible with isolated electrodes. The MHD excitation combines a high frequency altering current with a low frequency altering magnetic field. In order to validate our results, two independent theoretical methods for computing flow rate are followed. The two presented independent approaches show that high flow rate is possible even with isolated electrodes. To overcome the problem of dimensioning this kind of pumps, a generic numerical analysis is proposed. Hence, the pump performances as functions of the external parameter are studied and tools to calculate for a given fluid and the optimal high frequency regime are provided.
文摘This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The effects of transverse magnetic field parameter (Hartmann number Ha), Reynolds number Re (different velocities), Prandtl number Pr (different types of fluids) and dispersion parameter on the wall shear stress and the heat transfer rate are discussed.
