Moisture Transport and Diffusive Instability During Bread Baking

Abstract

In this paper we study multiphase models for simultaneous heat and mass transfer process during bread baking. Our main objective is to provide an explanation and a remedy to the observed erroneous and/or divergent results associated with the instantaneous phase change model used in the literature. We propose a reaction-diffusion model based on the Hertz-Knudsen equation, where the 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 non-intuitive numerical instability associated to the instantaneous phase change model can be identified and eliminated. The evaporation/condensation rate is estimated by comparing the results of the reaction-diffusion model with the experimental observations in the literature. For the 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.

Modelling of coupled heat and mass transfer during a contact baking process

“…The heat transfer causes a rapid raise of the temperature within the pancake batter, which induces water migration by diffusion and evaporation. Heat and mass transfer interact via evaporation (Huang et al, 2007). The most important phenomena influencing key process variables are temperature, concentration of liquid water and concentration of water vapour within the pancake batter.…”

Quasi-steady-state and steady-state models for heat and moisture transport in textile assemblies

“…Moreover, we have presented a theoretical analysis for the corresponding steady-state model and showed the existence of a classical positive solution. Multi-component flow models can also be found in many other areas, such as the oil industry (Chen et al 2000) and food industry (Huang et al 2007). Numerical studies in these areas have been done extensively (Douglas et al 1997;Wang et al 2002Wang et al , 2006Wang 2008).…”

“…Simultaneous heat and moisture transfer in porous media attracts considerable attention as it can be found in a wide range of industrial and engineering domains, such as food industry (Huang et al 2007), building materials (Ogniewicz & Tien 1981;Choudhary et al 2004) and more recently, textile materials (Smith & Twizell 1985;Fan et al 2000;Li & Zhu 2003;Cheng & Wang 2008;Huang et al 2008). Here we focus our attention on clothing assemblies.…”

Porous multiphase approach for baking process – Explicit formulation of evaporation rate

“…However, further investigations using the initial form of the model report serious numerical difficulties related to the type of numerical schemes, time step size, and meshes methods used (uniform, non-uniform) in converging to a solution (Zhou, 2005), and also an inadequacy in satisfying the mass conservation (Zhang and Datta, 2004). Thus, an improved model was suggested by replacing the instantaneous phase change of liquid to vapour and by introducing an evaporation rate term (Huang et al, 2007). Other improvements were also made (Zhang et al, 2005(Zhang et al, , 2007Zhang and Datta, 2006;Hadiyanto et al, 2007Hadiyanto et al, , 2008 which could be categorized as equilibrium approach and include:…”