The Mathematical Modelling of Stored Grain Microclimates
by
Alex Antic
School of Mathematics and Applied Statistics, University of Wollongong
Coauthors: Jim Hill (School of Mathematics and Applied Statistics, University of Wollongong), James Darby (Stored Grain Research Laboratory, CSIRO Division of Entomology)

Australia is a major grain exporter and its reputation relies upon its ability to supply clean, high-quality, and insect-free grain. The control of insect pests is made difficult due to the fact that pest species change over time in response to certain factors. In recent years, increasing problems have occurred with psocids (Liposcelis spp.). These pests are very mobile and appear to move in and out of infested grain bulks in response to environmental factors. This movement is the cause of much difficulty in controlling these insects under industrial conditions. An understanding of what happens from a heat transfer viewpoint at the surface of the grain bulk will allow a better understanding of the observed behaviour by these insects. It will allow predictions to be made of insect activity, which might lead to application of pest control methods to be timed to periods of high insect activity. The surface of the grain bulk which comes into contact with the vertical grain store wall is of particular interest as this is where considerable diurnal temperature fluctuations occur and where psocids have been observed.

In this study, we examine the heat transfer on the microscopic scale at the grain store surface and the grain bulk surface. Our aim is to understand the micro-environment which the insect experiences in such regions, and to determine how ambient temperatures effect the temperature at the surface. We examine this 'micro-surface' by developing a mathematical model to obtain a temperature profile of this region. This model is based on a heat conduction variant of the theory of 'double-diffusivity', which is a mathematical model that assumes two separate diffusion paths; one for high-diffusivity and one for regular-diffusivity. This approach allows us to determine a more realistic temperature profile as it takes into consideration the fact that the rate of heat conductivity through the grain is different from that through the interstitial air surrounding the grain. Based on a heat-balance approach, analytical and numerical results are presented showing the overall variation in temperature in a region close to the grain store wall.

Date received: August 3, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadr-00.