Development of magnetohydrodynamic boundary layers associated with the sudden initiation or deceleration of a supersonic flow at the boundary of a half-space
- 31 Downloads
The problem of nonstationary magnetohydrodynamic flow of a viscous fluid in a half-space resulting from the motion of an infinite plate has received much attention. In , for example, solutions are presented for the case of isotropic conductivity, while in  a solution of the Rayleigh problem is offered for the case of anisotropic conductivity. In these instances the fluid was assumed incompressible and uniform, and the system of equations was found to be linear. In problems involving nonstationary flow of a gas in a transverse magnetic field resulting from the deceleration of a high-velocity gas flow at the boundary of a half-space or the motion of an infinite plate at supersonic speed relative to a stationary gas it becomes necessary to take into account the compressibility of the gas and the temperature dependence of the conductivity. It is then possible to have flows in which the gas becomes electrically conducting and begins to interact with the magnetic field solely as a result of the increase in temperature due to viscous dissipation of energy. The magnetic field, interacting with the conducting gas, exerts an effect on the drag and heat transfer to the surface of the plate. At sufficiently low gas pressures and strong magnetic fields a Hall effect may be observed. The system of equations describing the motion of a compressible gas with variable conductivity is essentially nonlinear. The present article is devoted to a study of such motions.
KeywordsMagnetic Field Viscous Dissipation Supersonic Flow Strong Magnetic Field Transverse Magnetic Field
Unable to display preview. Download preview PDF.
- 1.I. B. Chekmarev, “Nonstationary flow of a viscous incompressible conducting fluid in a half-space in the presence of a transverse magnetic field,” Zh. tekhn. fiz., Vol. 30, No. 8, pp., 920–924, 1960.Google Scholar
- 2.Z. G. Sakhnovskii, “Allowance for conductivity anisotropy in the magnetohydrodynamic Rayleigh problem,” Zh. tekhn. fiz., Vol. 33, No. 5, pp., 631–635, 1963.Google Scholar
- 3.V. B. Baranov, G. A. Lyubimov, and Hu Yü-yin, “Calculation of the boundary layer on a dielectric plate in a flow of incompressible, anisotropically conducting fluid in the presence of a uniform magnetic field normal to the plate,” PMM, Vol. 27, No. 3, pp., 509–522, 1963.Google Scholar
- 4.A. S. Predvoditelev, E. V. Stupochenko, et al., Tables of Thermodynamic Functions for Air [in Russian], Pt. 1, Izd-vo AN SSSR, 1962.Google Scholar
- 5.W. B. Bush “Compressible flat-plate boundary layer flow with an applied magnetic field,” J. Aero-Space Sci., Vol. 27, No. 1, pp., 49–58, 1960.Google Scholar
- 6.E. Jahnke, Handbood of Ordinary Differential Equations [Russian translation], Fizmatgiz, p. 424, 1961.Google Scholar
- 7.H. Schlichting, Boundary Layer Theory [Russian translation], IL, 1956.Google Scholar
- 8.L. M. Simuni, “Some problems in the hydrodynamics of a viscous fluid and heat transfer,” Inzh.-fiz. zh., Vol 7, No. 6, pp., 55–62, 1964.Google Scholar
- 9.V. J. Rossow, “On magneto-aerodynamic boundary layers.” Z. angew. Math. und Phys., Vol. 96, pp., 519–527, 1958.Google Scholar
- 10.V. J. Rossow, “On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field.” NACA, Report 1358, 1958.Google Scholar