THEORY OF VISCOUS MAGNETOGASDYNAMIC FLOW IN SLOWLY DIVERGING TWO- DIMENSIONAL CHANNELS
A class of viscous magnetogasdynamic flows at moderate Reynolds number in slightly divergent two-dimensional channels is treated theoretically. The conducting walls of the channel serve as electrodes and are connected to an external load so that the device operates as a power generator. The main component of the applied magnetic field is perpendicular to the flow direction but parallel to the channel walls. The flowing medium is a slightly ionized gas with variable fluid properties. In particular two different mathematical models of the electrical conductivity are used. The theory pertains to low values of the magnetic Reynolds number, based on the channel height, and to moderate values of the Hall parameter. Entrance and exit effects are not considered. The equations of fluid dynamics are simplified by approximations similar to those employed in ordinary boundary-layer theory, and the resulting set of equations is then solved exactly and in closed form for a particular family of pressure variations along the channel. The main parameters appearing in the solution are the viscous Reynolds number, the Mach number, the Hartmann number and a parameter describing the pressure variation along the channel. Numerical examples pertaining to various types of boundary conditions on temperature, wall heat transfer, or potential difference across the channel are presented showing channel shapes, velocity and temperature profiles and efficiency data. (auth)
- Research Organization:
- Cornell Univ., Ithaca, N.Y. Graduate School of Aeronautical Engineering
- NSA Number:
- NSA-15-032796
- OSTI ID:
- 4837295
- Report Number(s):
- AFOSR-1332
- Country of Publication:
- United States
- Language:
- English
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