A SOLUTION PROCEDURE FOR THE EQUATIONS THAT GOVERN 3-DIMENSIONAL FREE-CONVECTION IN BULK STORED GRAINS

This article presents a mathematical formulation of the physical laws that govern the behavior of free convection and diffusion processes th at occur in grain bulks. The analysis applies to the transient behavio r of three-dimensional systems, and this represents a significant impr ovement on previous analyses. The momentum equation is based on Darcy' s law, and a one concentration equation is proffered to describe the c onvection and diffusion of fumigants through the interstitial air and grain kernels. The momentum equation is expressed in terms of a vector potential that ensures mass is conserved. The governing equations are discretised on both uniform and non-uniform grids and solved using an alternating direction implicit method. During each real-time step, th e components of the vector potential are evaluated by solving a parabo lic equation by means of a false transient method. The walls and roof of the grain store have been taken as being isothermal, while the floo r is assumed to be adiabatic. Numerical experiments have been performe d to investigate the effects of the false transient parameter, the gri d size, and non-uniformity. It is shown that a 31 x 31 x 31 non-unifor m grid yields accurate solutions to the partial differential equations . Graphical results are presented for the temperature, vector potentia l, grain moisture content, dry matter loss, and pesticide decay and fu migant concentration at selected cross-sections of a grain store with a simple geometry.