| Abstract: | A considerable number of papers are devoted to the problem of the deformation of a plane flow of a conducting liquid moving through a channel |x| <  , 0  y h=const in a zone of entry into a magnetic field B=(0, 0, B.  (x)), where (x) is the Heaviside unit function((x)=0 for x < 0 and (x)=i for x < 0). Apparently the first paper in this direction was that of Shercliff 1, 2] in which the asymptotic (for x .o- )profile of a perturbed velocity was. determined for a flow of an isotropic conducting liquid in a channel with nonconducting walls. The flow considered by Shemliff takes place in magnetohydrodynarnic flowmeters. Complete calculation of the perturbed flow of an isotropie conducting liquid in the channel of a magnetohydrodynamic generator is carried out in 3]. Asymptotic velocity profiles in the channel of a magnetohydrodynamic generator, with ideally segmented electrodes and the flow of an anisotropically conducting medium along them, were found in 4]. General formulas for the calculation of the asymptotic velocity profile, from the known distribution of the perturbing forces along the channel, are presented in 5]. In 6, 7] the Green function is proposed for the solution of the equation for the stream function of the perturbed flow. Finally, in 8], the solution for the perturbed flow of an anisotropically conducting liquid in a channel with continuous electrodes is described by means of the Green function, and the asymptotic profiles of the velocity are calculated.In this paper the flow of anauisotropically conducting liquid is determined in a channel with ideally segmented electrodes. The solution is set up with the aid of the Fourier method. The resulting series, in which the slowly converging part can be related to the asymptotic profile 4] calculated from the solution of an ordinary differential equation, make it possible to determine the velocity field rapidly. A detailed deformation pattern of the velocity profile is set up. Certain general properties of the flow in a zone of entry into a magnetic field are noted; with the aid of these it is possible to discover the error in the calculations 8]. |
