On the geometry of radiative and thermally conducting gas flows

After formulation of the various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the streamline trajectories, the expressions for the tangent, principal normal and binormal vectors and the curvature and torsion of the streamlines have been obtained in terms of the velocity components, pressure, density, thermal conductivity and radiation variables. This is followed by the determination of the pressure gradient along the streamlines, their principal normals and binormals. It has been shown that the radiating character of the gas decreases the pressure gradient whereas thermal conductivity increases it along the streamlines but the pressure remains constant along the binormals and if the streamlines are straight lines, the trajectories of the principal normals lie on the surface of the constant pressure. Finally, the expressions for the vorticity components in terms of the curvature of the streamline and the velocity gradients along the streamline, their principal normals and binormals have been obtained.