Steady states and stability of nonlinear pool-boiling systems

The steady-state behaviour and corresponding stability properties of pool-boiling systems are studied in terms of arepresentative model problem. This model problem involves only the temperature distribution within the heater andmodels the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the heater-mediuminterface. The steady-state behaviour is investigated via a bifurcation analysis in terms of the system parameters ofthe model problem. To this end a compact numerical continuation algorithm has been developed that facilitatesinvestigation of the behaviour of the system with changing parameters. This algorithm is based uponanalytical reduction of the original problem to a boundary problem for the state on the interface with the method ofseparation-of-variables and numerical treatment of this boundary problem with a Fourier collocation method.The bifurcation analysis revealed that steady-state solutions with homogeneous interface temperatures in specificparameter ranges undergo pitchfork bifurcations that result in multiple solutions with essentially heterogeneous interfaceprofiles. These heterogeneous states are found in both the 2D and 3D model problems and qualitatively correspond withthe arrangements of dry spots and wet regions on the interface that typically occur during transition boiling. The stability analysis revealed that all steady-statesolutions, except one homogeneous solution in the nucleate-boiling regime and one homogeneous solution in thefilm-boiling regime, are inherently unstable. This implies the investigated model problem is essentiallya bi-stable system. The findings on the model problem are consistent with laboratory experiments and thus strongly suggest thatit provides an (at least qualitatively) adequate description of the global behaviour of pool-boiling systems.