The diffusion of moisture in food grains—II. Estimation of the effective diffusivity

Abstract

In Part I Thorpe et al. ( J. stored Prod. Res., 27, pp. 1–9, 1991) developed an equation that describes mass transfer by diffusion in bulk stored food grains. The equation is expressed in terms of an equilibrium weighted spatial average concentration and a volume averaged temperature, along with local spatial deviations from the average concentration. In this paper we formulate and solve the boundary value problems that govern the spatial deviations, and subsequently estimate the effective diffusivity of moisture in stored grains. In this paper we take particular care to establish the length scale constraints that must be satisfied for the boundary value problems to be a true reflection of reality. In keeping with this approach, we also establish the constraints that must be satisfied if we are to treat a bulk of grain as if it is a spatially periodic porous medium. A closed form expression for the effective diffusivity of moisture in a bulk of grain is obtained by exploiting the properties of the Chang ( Chem. Engng Commun. 15, 83–91, 1986) unit cell. Results from the analysis are compared with published experimental data and it is found that agreement between the two is excellent.