The onset of thermal instability of a two-dimensional hydromagnetic stagnation point flow

The aim of the present paper is to examine the effects of a constant magnetic field on the thermal instability of a two-dimensional stagnation point flow. First, it is shown that a basic flow, described by an exact solution of the full Navier–Stokes equations exists under some conditions relating the orientation of the magnetic field in the plane of motion to the obliqueness of free stream. The stability of the basic flow is then investigated in the usual fashion by making use of the normal mode decomposition. The resulting eigenvalue problem is solved numerically by means of a pseudo spectral collocation method based upon Laguerre’s functions. The use of this procedure is warranted by the exponential damping of disturbances far from the boundary layer and the appropriate distribution of the roots of Laguerre’s polynomials to treat boundary layer problems. It is found through the calculation of neutral stability curves that magnetic field acts to increase the stability of the basic flow.