Int. 1. Engng Sci. Vol. 27, No. 9, pp. 1115-1122, 1989 Printed in Great Britain. All rights reserved OKZO-7225/89 $3.00 + 0.00 Copyright @ 1989 Pergamon Press plc zyxwvut NON-UNIFORM PROPAGATION OF WEAK DISCONTINUITIES IN RADIATION MAGNETOGASDYNAMICS S. N. OJHA and ASHOK SINGH Department of Mathematics, S.C. College, Ballia, U.P., India Abstract-The propagation of weak discontinuities headed by a wave front of arbitrary shape in three dimensions is investigated in an electrically conducting thermally radiating inviscid gas flow. The critical stage of shock formation as a result of breakdown has been determined.The role of electrical conductivity and radiationis to cause damping. Particular casesof the diverging and converging waves are discussed to explore the possibilities of the shock formation by assuming the medium to be uniform and at rest. 1. INTRODUCTION In the present space age, scientists are very much concerned with many new technological developments in the fields of hypersonic flights, gas-cooled nuclear reactors and power plants for space exploration needs, where the temperature is very high and density is low. In gaseous flow under high temperature conditions it is more realistic to take into account the thermal radiation effects. The effects of the thermal radiation on the propagation of small disturbances in gas flows have been studied by Vincenti and Baldwin Cl], Prasad [2], Nye [3] and Helliwell [4]. Using the method of characteristic Helliwell [4] determined the speed of propagation of weak discontinuities together with jump relations for the derivatives of field variables in three dimensions. Assuming the medium to be uniform and at rest, Thomas [5] studied the propagation of shock waves in ideal gases. Using the method of Thomas, Ojha and Verma [6] and Nariboli and Secrest [7] have derived and discussed the growth and decay equation of these waves in radiating gases and magnetogasdynamics, respectively. By associating the theory of singular surfaces with the ray theory of geometrical optics, Ojha and Singh [8] extended the analysis of Nariboli and Secrest [7] in radiation magnetogasdynamics. Further, Ojha and Rai [9] have discussed the effects of thermal radiation on the propagation of weak discontinuities by taking a suitable form of the energy equation. Ojha and Singh [lo] have presented the analysis of shock-wave formation in 1-D radiative magnetogasdynamic flow where the gas has been considered at such a high temperature and low pressure that radiation flux is negligible in comparison to radiation pressure and energy (Pai [ll]). In all the above investigations, the flow field has been assumed to be uniform and at rest. In fact, the flow ahead of modified gasdynamic waves will, in general, be disturbed and therefore one should take into account the non-uniform behaviour of the flow ahead of the wave. In this connection, the work of Elcrat [12] and Sharma and Shyam [13] on the propagation of sonic discontinuities in the unsteady flow of perfect gas and radiating gases, respectively, are worth mentioning. By considering the flow ahead of the wavefront to be non-uniform, the purpose of this problem is to discuss the growth and decay behaviour of weak discontinuities in radiation magnetogasdynamics. The analysis is based entirely upon the theory of singular surfaces, which in comparison to the characteristic theory, quickly leads to results of general significance. In particular cases of the uniform flow ahead of the radiating magnetogasdynamic wave, the effects of wavefront curvature and the growth and decay properties of the diverging and converging waves are studied. 1115