Stability Analysis of Two-Dimensional Pool-Boiling Systems

In this paper we consider a model for pool-boiling systems known from the literature. This model involves only the temperature distribution within the heater and models the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. The model allows multiple homogeneous (i.e. spatially constant) and multiple heterogeneous steady-state solutions. The structure of this family of steady-state solutions has been studied by means of a bifurcation analysis in two recent papers (Speetjens et al. (2006a), Speetjens et al. (2006b)). The present study concentrates on stability properties of these steady-state solutions. To this end, a generic linear and a case-specific nonlinear stability analysis are performed which show that only the homogeneous steady-states of complete nucleate or complete film boiling are linearly stable. All heterogeneous steady-state solutions appear linearly unstable. These stability results are consistent with laboratory observations. PACS 44.35.+c, 44.05.+e, 02.60.Cb, 02.70.Jn