Stability analysis of a closed thermosyphon

Abstract

Under Boussinesq and hydraulic engineering approximations, convection in a closed loop under a given external heat flux is governed by an initial-boundary value problem for a first-order nonlinear PDE and an integral equation in two unknown functions (one depending only on the space variable and the other on space and time). By a regularization method and using variation of constants formulas, under various constraints, the authors prove the existence and uniqueness of the solutions. They derive explicit expressions of the stationary solutions by direct integration and discuss their linear stability by analyzing the spectrum of an associated nonselfadjoint operator by means of a Fourier series technique. Small changes in the geometry of the loop or heating applied to it make the solutions linearly unstable.