Steady-state solutions in a nonlinear pool boiling model

We consider a relatively simple model for pool boiling processes. This model involves only the temperaturedistribution within the heater and describes the heat exchange with the boiling fluid via a nonlinearboundary condition imposed on the fluid-heater interface. This results in a standard heat equation with anonlinear Neumann boundary condition on part of the boundary. In this paper we analyse the qualitativestructure of steady-state solutions of this heat equation. It turns out that the model allows bothmultiple homogeneous and multiple heterogeneous solutions in certain regimes of theparameter 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-variablesand a Fourier collocation technique. For both the continuous and discrete problem a fundamental symmetryproperty is derived that implies multiplicity of heterogeneous solutions. Numerical simulations of thismodel problem predict phenomena that are consistent with laboratory observations forpool boiling processes.