A new analysis of the closed loop thermosyphon

Abstract This theoretical study addresses the nature of motions in a toroidal fluid loop oriented in the vertical plane and subject to rather general internal heating and/or thermal wall conditions. It is shown that previous one-dimensional models of flow in the loop can be transformed, without further approximation, to a ‘master’ problem of three non-linear ordinary differential equations, along with an infinite set of linear ‘slaved’ problems. The mass flux is determined solely by the master problem. The question of existence and stability of steady flows reduces to a study of cubic algebraic equations. In the strongly non-linear regime, it is argued that only steady or chaotic flows, not periodic ones, are possible. The sensitivity of the one-dimensional model predictions to various wall-stress parameterizations is described.