On stability of a nonlinear distributed model of natural circulation

The nonlinear distributed model of natural circulation of the paper is shown to be reducible, without any simplifying assumptions to a system of ordinary differentia! equations whose order is equal to the number of harmonics in the Fourier expansion of the function describing the shape of the circulation loop. Sufficient conditions are obtained for stability of natural circulation «in the large» for a loop of an arbitrary shape and qualitative analysis is applied to a second-order system to which the model discussed is reducible in the case of a circular, eight-shaped and other loops.