Magnetograph Transformation in Variably Inclined Two Phase MFD Flows

Abstract

The steady plane variably inclined two phase MFD flow is considered. Magnetograph transformation is employed to obtain the solution of governing partial differential equations of second order and also to find the solution for the vortex flow. The non-linear partial differential equations have been converted into solvable form by employing Legendre’s transform function as well as the polar co-ordinates. Two different forms of Legendre transform function in terms of components of magnetic field are taken as two applications of the developed theory. The components of fluid velocity, components of magnetic field, vorticity function, current density function, the fluid pressure and the number density of dust particles are found out in both the cases. The variation of components of fluid velocity with one component of magnetic field, keeping the other component constant, is plotted for different angles. The magnetic field lines are also plotted which are found out to be concentric circles for both the cases.