Abstract:

: Hartmann’s work on magnetohydrodynamic channel flow is extended to include the case with a time-dependent pressure gradient. Cases treated are: 1) suddenly applied pressure gradients which are periodic in time, and 2) pressure gradients which, with respect to time, are step and delta functions. The channel walls are assumed to be perfectly conductive. As a limiting case, the solution for hydrodynamic channel flow with a time-dependent pressure gradient is also given. The nature of viscous and magnetic drag on the wall is discussed. By use of the convolution integral and superposition principle, solutions can be obtained for any arbitrary time-dependent pressure gradient Figyres show the physical consequence of the solutions.

Keywords: Magnetohydrodynamic channel; Pressure gradient; Flow; Laplace transformation