An mhd boundary-layer compatibility condition

Abstract

The viscous Reynolds numbers Re used were 100, 1000, and oo. The range of magnetic interaction parameters where solutions were possible was rather limited. At the larger magnetic interaction parameters, the quasi-linearization solution was not a solution of the original nonlinear differential equations and was not included. However, a number of conclusions can be drawn from the solutions that were obtained. The numerical calculations of standoff distance as a function of interaction parameter are illustrated in Fig. 1. These results are in general agreement with previous works; i.e., the shock-wave standoff distance increases with increasing magnetic interaction parameter for a given viscous Reynolds number, and, for a constant magnetic interaction parameter, the standoff distance decreases with increasing viscous Reynolds number, as expected by physical reasoning.3-4 There are possibly two features of this plot which are new. In previous works, a critical value of the interaction parameter appears at which the shock standoff distance recedes to infinity asymptotically as the applied magnetic field is increased.3 The critical interaction parameter in the present plot no longer appears as in Ref. 3. Secondly, for Qm < 1, the standoff distance increases much more rapidly for increasing Qm m this solution than in the work by Bush. 1 If these results are applicable, it would indicate that the magnetic field, even for Qm < 1, is a more effective method of controlling the hypersonic flow than previously thought. Table 1 gives the computed values of the ratio of the resultant magnetic-field components at the shock to the dipole field at the body and also the ratio of the undistorted dipole field at the shock to that at the body. It is evident from this table that the standoff distance depends essentially upon the product of Rm and MPJ i.e., Qm. A similar result has appeared in previous calculations.li3-4 One further inter