A mathematical model for heat transfer in grain store microclimates

Alexsandar Antic, James M. Hill


Australia's reputation as a supplier of insect-free grain is being threatened by Psocids ( Liposcelis spp.), an insect pest which is wreaking havoc within the Australian grain industry. These pests are very mobile and appear to move in and out of infested grain bulks in response to variations in temperature. This movement is the cause of much difficulty in controlling these insects so an understanding of what happens to the heat transfer at the surface of the grain bulk would allow a better understanding of the observed behaviour by these insects. Here we examine the heat transfer at the grain store surface and the grain bulk surface. A heat transfer variant of the theory of "double-diffusivity" is developed, which is a mathematical model that assumes two separate diffusion paths; one for high-diffusivity and one for regular-diffusivity. This approach takes into consideration the fact that the rate of heat transfer through the grain is different to that through the interstitial air surrounding the grain. Based on a heat-balance approach, approximate analytical results are obtained from which the overall variation in temperature close to the grain store wall may be calculated. The behaviour for typical parameter values is shown graphically.

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DOI: http://dx.doi.org/10.21914/anziamj.v42i0.592

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.