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Numerical Solutions and Mathematical Theorems for Divergent, Compressible Plasma Flows
Author(s) -
Liron N.,
Wilhelm H. E.
Publication year - 1976
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19760560804
Subject(s) - polytropic process , physics , ordinary differential equation , partial differential equation , boundary value problem , nonlinear system , mathematical analysis , mathematics , compressible flow , compressibility , mechanics , differential equation , classical mechanics , quantum mechanics
The boundary‐value problem for the ordinary nonlinear differential equation of second order, resulting from the self‐similar transformation of the partial differential equations for a polytropic, compressible plasma flow in a diffuser with azimuthal magnetic field, is integrated rigorously by numerical methods. Typical velocity profiles of symmetrical outflows are given for various Reynolds, Hartmann, and polytropic numbers. Mathematical theorems are derived which prove that the selfsimilar transformation of the plasma fields of the form F(r, θ) = (r)G(θ) cannot represent pure inflows, mixed in‐ and outflows and asymmetrical flows, i.e., is applicable exclusively to symmetrical outflows without backflow regions (within the polytropic approximation).