Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model

We consider a relatively simple model for pool-boiling processes. This model involves only the temperature distribution within the heater and describes the heat exchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heater interface. This results in a standard heat-transfer problem with a nonlinear Neumann boundary condition on part of the boundary. In a recent paper [18] we analysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steadystate solutions. The study revealed that, depending on system parameters, the model allows both multiple homogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al. [18] can be generalised to the physically more realistic case of three space dimensions. A fundamental shift-invariance property is derived that implies multiplicity of heterogeneous solutions. We present a numerical bifurcation analysis that demonstrates the multiple solution structure in this mathematical model by way of a representative case study.