Abstract
In this paper we study multiphase models for simultaneous heat and mass transfer processes during bread baking. Our main objective is to provide an explanation and a remedy to the observed erroneous and/or divergent results associated with an instantaneous phase change model used in the literature. We propose a reaction-diffusion model based on the Hertz–Knudsen equation, where phase change is not instantaneous but determined by an evaporation/condensation rate. A splitting scheme is designed for the reaction-diffusion model so that a link between these two models can be established and the nonintuitive numerical instability associated with the instantaneous phase change model can be identified and eliminated. The evaporation/condensation rate is estimated by comparing results of the reaction-diffusion model with experimental observations reported in the literature. For evaporation/condensation rate beyond the estimated value, oscillatory solution with multiple regions of dry and two-phase zones is observed. We show that these are caused by an instability intrinsic to the model (which we call diffusive instability) using linear stability analysis and numerical tests.
| Original language | English |
|---|---|
| Pages (from-to) | 222-238 |
| Number of pages | 17 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 68 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2007 |
Keywords
- Diffusive instability
- Finite difference methods
- Heat
- Linear stability analysis
- Multiphase modelling
- Phase change
- Reaction-diffusion equations
- Mass transfer