CONVECTIVE INSTABILITIES IN FULLY DEVELOPED FLOWS
RAND CORP SANTA MONICA CA
Pagination or Media Count:
This paper considers the possibility of inducing a convective secondary flow in the fully developed channel flow of a quasi-incompressible Boussinesq fluid. Instabilities of this type can only occur when the temperature gradient in the direction of the body force exceeds a certain critical value. This temperature gradient is proportional to the Rayleigh number of the fluid. For channels of arbitrary cross section, the critical Rayleigh number is found to be R sub c or 1360 hd to the 4th power where h is the arbitrary channels maximum dimension in the body force direction and d is the diameter of an equal area circular channel. For two special geometries it is possible to improve the above lower bound estimate to the critical Rayleigh number. In a circular channel R sub c or 3450 and in a square channel R sub c or 2480.
- Fluid Mechanics