Journal of Applied Mathematics and Decision Sciences
Volume 7 (2003), Issue 3, Pages 147-164

A two-stage heat transfer model for the peripheral layers of a grain store

Alexsandar Antic and James M. Hill

School of Mathematics & Applied Statistics, University of Wollongong, Wollongong, NSW, Australia

Copyright © 2003 Alexsandar Antic and James M. Hill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An understanding of the flow of heat in grain store structures, in particular, within the peripheral layer, is important from many industrial perspectives. To analyse the heat transfer within such regions a mathematical model known as the two-stage heat transfer model is proposed. This model makes a distinction between the air and grain within the grain bulk, and thus 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. Such a model lends itself to a solution via Laplace transforms and approximate analytical results are obtained for small and large times. In addition, the Stehfest numerical algorithm is used for the inversions and very good agreement is obtained between the two approaches. The present model is compared to a previously developed double-diffusivity heat transfer model by the authors, and good agreement is obtained. At present, no experimental data is available to validate the model as it is very difficult to measure the air and grain temperatures separately, particularly in the peripheral layer. The proposed model provides insight into the potential difference existing between the air and grain temperatures.