Stability of viscous flow driven by an azimuthal pressure gradient between two porous concentric cylinders with radial flow and a radial temperature gradient

The effect of a radial temperature gradient on the stability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure gradient is studied when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number beta based on the radial velocity at the inner cylinder and the inner radius R (1) is varied from -130 to 30 and both positive and negative values of the parameter N are taken, where N depends on the temperature difference T (2) - T (1) between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem, which are solved by using a classical Runge-Kutta scheme combined with a shooting method, termed unit disturbance method. It is found that for a given value of N the radially outward flow (beta > 0) has a stabilizing effect and the stabilization is more as the gap between the cylinders increases. But the inward throughflow (beta < 0) has a destabilizing influence when |beta| increases up to a certain critical value and thereafter the throughflow is stabilizing with further increase in |beta|. When the outer cylinder is kept at a lower temperature than the inner one (N < 0), the flow becomes more and more stable with an increase in |N|. On the other hand, for N > 0, the flow becomes more and more unstable with an increase in N.