Steady-state solutions in a nonlinear pool boiling model

We consider a relatively simple model for pool boiling processes. This model involves only the temperature distribution within the heater and desribes the heat exchange with the boiling fluid via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat equation with a nonlinear Neumann boundary condition on part of the boundary. In this paper we analyze the qualitative structure of stationary solutions of this heat equation. It turns out that depending the model allows both multiple homogeneous and multiple heterogeneous solutions in certain regimes of the parameter space. The latter solutions originate from bifurcations on a certain branch of homogeneous solutions. We present a bifurcation analysis that reveals the multiple solution structure in this mathematical model. In the numerical analysis a continuation algorithm is combined with the method of separation-of-variables and a Fourier collocation technique. For both, the continuous and discrete problem a fundamental symmetry property is derived that implies multiplicity of heterogeneous solutions. It will be shown that numerical simulations for this model problem predict phenomena that are consistent with laboratory observations for pool boiling processes. AMS subject classification. 35K55, 65P30, 80A20, 93A30