Numerical study of the effect of the environmental temperature in the natural two-dimensional convection of heat in grain stored at cylindrical silos

A numerical study on the dynamics of grain storage in cylindrical silos was performed based on transport equations of momentum and energy for multiphase media. The purpose of this study is to analyze simultaneously the effect of the heat of respiration and three types of boundary conditions; two of them constants (Case I, θ = 1 and Case II, θ = 0) and a time-dependent (Case III, simulating the change of temperature along the day-night cycle) on the flow patterns, the isotherms and heat transfer to the environment. The governing equations were solved via spatial discretization using second order finite differences and time discretization using an implicit scheme. The set of algebraic equations generated was solved using Nonlinear Relaxation. In this simulation, the thermodynamic properties of sorghum grain stored in a silo of 44 m³ grain capacity were used. Stability for Case I and II, were reached in a dimensionless time (Fo) equals 0.3 (that is equivalent a real time of 3.01 h), while for Case III was for Fo = 20 (equivalent to 200.88 h) because the periodicity of the boundary condition. For cases II and III, the boundary conditions induce the formation of multicellular flow.