ANALYSIS OF A SQUARE NATURAL CONVECTIVE LOOP

Abstract

The dynamic behaviour of a one-dimensional model of a natural convective loop of square geometry is studied. Steady states are obtained, and linear stability analysed. Two specific heat flux cases are studied, one with sinusoidal and the other with a piecewise uniform distribution of heating. In the first case, three ordinary differential equations decouple from an infinite set. Transition to chaos is similar to that for a toroidal geometry, that is through subharmonic cascade. In the second case a coupled infinite set of differential equations governs the systems. The stability region in parametric space decreases continuously as the number of modes considered is increased, showing that the system in this case is intrinsically unstable. Onset of chaos is through quasi-periodicity.