The velocity distribution between two sidewalls is; M-shaped for the MHD channel flows with rectangular cross section and thin conducting walls in a strong transverse magnetic field. Assume that the dimensionless numb...The velocity distribution between two sidewalls is; M-shaped for the MHD channel flows with rectangular cross section and thin conducting walls in a strong transverse magnetic field. Assume that the dimensionless numbers R(m) much less than 1, M, N much greater than 1, and sigma* much less than 1 and that the distance between two perpendicular walls is very long in comparison with the distance between two sidewalls. First, the equation for steady flow is established, and the solution of M-shaped velocity distribution is given. Then, an equation for stability of small disturbances is derived based on the velocity distribution obtained. Finally, it is proved that the stability equation for sidewall how can be transformed into the famous Orr-Sommerfeld equation, in addition, the following theorems are also proved, namely, the analogy theorem, the generalized Rayleigh's theorem, the generalized Fjortoft's theorem and the generalized Joseph's theorems.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘The velocity distribution between two sidewalls is; M-shaped for the MHD channel flows with rectangular cross section and thin conducting walls in a strong transverse magnetic field. Assume that the dimensionless numbers R(m) much less than 1, M, N much greater than 1, and sigma* much less than 1 and that the distance between two perpendicular walls is very long in comparison with the distance between two sidewalls. First, the equation for steady flow is established, and the solution of M-shaped velocity distribution is given. Then, an equation for stability of small disturbances is derived based on the velocity distribution obtained. Finally, it is proved that the stability equation for sidewall how can be transformed into the famous Orr-Sommerfeld equation, in addition, the following theorems are also proved, namely, the analogy theorem, the generalized Rayleigh's theorem, the generalized Fjortoft's theorem and the generalized Joseph's theorems.
