Electrical parameters of a channel with finite electrodes with allowance for the electrode potential drop
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Spatial problems involving the electric field in an MHD channel were formulated in  with allowance for the electrode potential drop. It was assumed that the electrode layer had a small thickness, so that relationships on the boundary of the layer could be applied to the surface of the electrode. It was assumed that the electrode potential drop δϕ° could be represented as a function of the current density jn at the electrode in the form of a known function δϕ° =f (jn) determined experimentally or deduced from the appropriate electrode-layer theory. An approximate method was then put forward for solving such problems by reducing them to the determination of the electric field from a known distribution of the magnetic field and the gas-dynamic parameters. It was shown that when ɛ=δϕ°/ E is small (E is the characteristic induced or applied potential difference), the solution can be sought in the form of series in powers of ɛ. In the zero-order approximation, the electric field is determined without taking into account the electrode processes. The first approximation gives a correction of the order of ɛ. The quantity δϕ°, which is present in the boundary conditions on the electrode in the first-order approximation, is determined from the current density calculated in the zero-order approximation.
One of the problems discussed in  was concerned with the electric current in a channel with one pair of symmetric electrodes. Its solution was found in the first approximation in the form of the integral Keldysh-Sedov formula. In this paper we report an analysis of the solution for δϕ° taken in the form of a step function.
KeywordsBoundary Condition Magnetic Field Mathematical Modeling Mechanical Engineer Electric Current
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