Local mass and thermal equilibria in ventilated grain bulks. Part I: The development of heat and mass coservation equations

Abstract

Stored grains ecologists, toxicologists and engineers require simple, yet accurate, mathematical models of the stored grains ecosystem. Existing mathematical models of the heat and mass transfer processes that occur in ventilated food grains cover a wide range of complexity. The simplest models assume local mass and thermal equilibrium at each point in the grain bulk, and the resulting hyperbolic partial differential equations may be solved by the method of characteristics. By making use of the thermodynamic properties of the air/grain/water mixture the system is therefore completely specified by only one temperature and one moisture content at each point. More detailed models take into account finite resistances to interphase heat and mass transfer, but such models are often numerically intensive. The choice of models has been somewhat subjective. One reason for this is that models of heat and mass transfer phenomena in bulks of grain are traditionally written in terms of implicitly averaged variables such as grain and air moisture contents and temperatures. As a result, details of phenomena that occur on length scales associated with those of grain kernels and intergrannular air spaces are lost. In Part I of this paper we establish heat and mass transfer equations expressed in terms of volume averaged quantities. The analysis is based on differential equations that govern heat and mass transfer in each phase, and this allows considerable detail to be retained in the equations that are developed to describe macroscopic phenomena. In Part II of the paper we make use of the new, more detailed equations to develop constraints that indicate a priori the level of detail that is required to accurately simulate a ventilated bed of food grains.