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Applied Mathematics Research eXpress (2006) Vol. 2006 : article ID 96131, 24 pages, doi:10.1155/AMRX/2006/96131
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

On the structure of detonation waves in magnetohydrodynamics

A. Aghajani and M. Hesaaraki

School of Mathematics, Damghan University of Basic Sciences P.O. Box 36715-364, Damghan, Iran E-mail address: aghajani{at}dubs.ac.ir
Department of Mathematical Sciences, Sharif University of Technology P.O. Box 11365-9415, Tehran, Iran E-mail address: hesaraki{at}sina.sharif.edu

The mathematical question of the existence of detonation waves in magnetohydrodynamics for rectilinear motion is stated in terms of a six-dimensional system of ordinary differential equations, which depends on six viscosity parameters, the bulk viscosity, the heat transfer coefficient, the coefficient of thermal conductivity, the coefficient of electrical conductivity, the diffusion rate for the reactant, and the reaction rate coefficient. In this paper, we will show that strong and weak detonation waves for fast, switch-on, and, in the case of transverse magnetic field, exothermic reactions exist. Along these waves, the density and the temperature are always increasing. These kinds of detonations occur in jet engine problems.


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