Michel Speetjens, Arnold Reusken, Wolfgang Marquardt:
Steady-state solutions in a three-dimensional nonlinear pool-boiling heat-transfer model
Communications in Nonlinear
Science and Numerical Simulation, 2008, 13(8), 1518-1537
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  we anal- ysed this nonlinear heat-transfer problem for the case of two space dimensions and in particular studied the qualitative structure of steady-state solutions. The study revealed that, depending on system parameters, the model allows both multiple ho- mogeneous and multiple heterogeneous temperature distributions on the fluid-heater interface. In the present paper we show that the analysis from Speetjens et al.  can be generalised to the physically more realistic case of three space dimensions. A funda- mental 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.
pool boiling; nonlinear heat transfer; bifurcation analysis; numerical simulation