263 IGPM.pdf        August 2006
TITLE Steady-State Solutions in a Three-Dimensional Nonlinear Pool-Boiling Heat-Transfer Model
AUTHORS Michel Speetjens, Arnold Reusken, Wolfgang Marquardt
ABSTRACT 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 steady-state 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.
KEYWORDS pool boiling, nonlinear heat transfer, bifurcations, numerical simulation
DOI 10.1016/j.cnsns.2006.11.002
PUBLICATION Communications in nonlinear science & numerical simulation
13(8), 1518-1537 (2008)