The influence of heat transfer on the stability of parallel flow between concentric cylinders
Abstract
The stability of parallel flow between concentric cylinders at different temperatures is investigated for infinitesimal velocity and pressure disturbances. Primary interest is in the effect of heat transfer and the radius ratio of the inner to outer cylinder on the critical point of the neutral stability curve. The modified OrrSommerfeld equation includes perturbations for the velocity and viscosity as well as its gradient terms, and results in a fourth order ordinary differential equation. This equation and boundary conditions represent an eigenvalue problem that is transformed to an equivalent initial value problem and solved numerically using a fourth order RungeKutta integration scheme. The results indicate a strong dependence of the critical eigenvalues on both the heat transfer and the radius ratio a/b of inner to outer cylinder. Heating the inner cylinder destabilizes the flow.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1975
 Bibcode:
 1975PhDT........74C
 Keywords:

 Concentric Cylinders;
 Flow Stability;
 Heat Transfer;
 Parallel Flow;
 OrrSommerfeld Equations;
 Pressure Distribution;
 RungeKutta Method;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer