Equations LORENZ IN CROSS-FERROHIDRODINÂMICA / EQUAÇÕES DE LORENZ-CROSS NA FERROHIDRODINÂMICA
AUTOR(ES)
Nélio Martins da Silva Azevedo Sasaki
DATA DE PUBLICAÇÃO
2008
RESUMO
In this work we investigated the problem of Rayleigh-Bénard for a magnetic binary fluid, i.e., a magnetic fluid, which consist of magnetic nanopartilces stably dispersed in a liquid carrier. The theoretical calculations were performed based on a Lorenz-like model, which transforms a system of partial differential equations into ordinary differential ones. The analysis of the magnetic binary fluid problem used the Navier-Stokes, thermal conduction and mass diffusion equations. The magnetic body force was obtained using the Cowley- Rosensweig tensor as well as the Maxwell equations. The mass flux had included the difusive contribution, associated to Ficks law, and also the thermal diffusion term, due to the Soret effect. Our model consist of a system of eight ordinary differential equations, which were shown to mantain the same mathematical form as the ones obtained earlier by Cross for a non-magnetic binary fluid. However, as expected, our coefficients depend on the magnetic field. According to our investigation on the site www.isiknowledge.com this is the first time in the literature that those equations are obtained, which we named the Lorenz-Cross equations on Ferrohydrodynamics. The validity of our system of equations were, also, checked in the limit of a simple fluid, where our model returns to the Lorenz equations. The only difference is the existence of an effective Rayleigh number, represented by the sum of the Rayleigh number and the magnetic Rayleigh one. Finally, the efect of magnetophoresis in the system of equations had also been discussed.
ASSUNTO(S)
fisica equações de lorenz fluidos magnéticos ferrohidrodinâmica ferrohydrodynamics, magnetic fluids, lorenz equations fluidos magnéticos
