Local mass and thermal equilibria in ventilated grain bulks. Part II: The development of constraints

In Part I of this paper it was pointed out that stored grains ecologists, toxicologists and engineers require simple, yet accurate models of the heat and mass transfer processes that occur in bulks of stored food grains. Detailed equations that govern the processes of heat and mass transfer in grains were developed, and expressed in terms of phase weighted variables, and macroscopic deviations from them. In this paper we carry out order of magnitude analyses aimed at determining when these deviations are negligible so that local mass or thermal equilibrium may be deemed to have been approached. Magnitudes of the rates of change in moisture concentrations and temperatures are estimated using established mathematical models of grain aeration in which there are no dispersive effects. The order of magnitude analysis is then used to determine the appropriateness of the underlying assumptions of the model. In the case of grain drying, the magnitudes are provided by a model in which the only dispersive effect arises from the finite resistance to mass transfer in the grains. The analysis shows that thermal equilibrium is always likely to exist in a bulk of aerated grain, but mass equilibrium is attained only as the elapsed time of the process increases or when the grain size is small. The analysis also suggests that thermal equilibrium is likely to be attained in grain dryers, regardless of the grain size. The nature of commerical dryer operation implies that mass equilibrium is not generally attained.