Finite Amplitude Thermal Convection in Porous Media with Uniform Heat Source

摘要

An unbounded horizontal fluid layer in a porous medium with an internal heat source and uniformly heated from below was studied. The layer is in the gravitational field. Linear theory predicts that the disturbances of infinitesimal amplitude will start to grow when the Rayleigh number exceeds its critical value. These disturbances do not grow without limit; but by advecting heat and momentum, the distrurbances alter their forms to achieve a finite amplitude. Just like infinitesimal amplitude disturbances the degenercies of possible solutions persist for finite amplitude solutions. This study evaluates the stability of these various forms of solutions. The small parameter method of Poincare is used to treat the problem in successive order. (ERA citation 02:027583)