On Theth Linear Instabilty Analysis of The Thermal Instability Brobem

Abstract

The linear stability analysis of a Newtonian incompressible fluid in a vertical curved channel formed by two coaxial cylindrical surfaces with a radial temperature gradient and an azimuthal pressure gradient shows that the critical modes are oscillatory and non-ax symmetric. A generalized Ray leight dicriminant which includes both the curvature and buoyancy effect is derived. Centrifugal buoyancy induces week asymmetry of the dependence of the control parameter critical values on the sign of the temperature gradient . The critical parameters depend on the temperature gradient, the radius ratio and the nature of the fluid . For a wide curvature channel flow ,there are two critical modes : oscillatory Dean modes for small temperature gradients and oscillatory centrifugal — thermal modes for relatively large temperature gradients .