Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Australia's reputation is well established in the international marketplace as a producer of high-quality grain. We remain competitive by exporting grain in accor dance with a 'nil tolerance' for live insects. Protecting the grain while in storage means maintaining such a reputation is difficult and costly as one must deal with such factors as varying climatic conditions, particularly temperature, which can have an adverse affect on grain quality and insect infestation. An understanding of the flow of heat in grain store structures is very important from many industrial perspec tives, and the heat transfer within the peripheral layer is of particular importance. To analyse the heat-transfer within such regions, we develop two mathematical models known as the double-diffusivity heat transfer model and the two-stage heat transfer model, and since the grain bulk is composed of predominantly air and grain, we make this distinction in our models. Semi-analytical and numerical approximations are obtained for both models from which the overall variation in temperature close to the grain store wall may be predicted. Very good agreement is obtained between the two solutions for both models. Good agreement is also obtained between the double-diffusivity heat transfer and two-stage heat transfer models.

Currently, there is an ongoing reduction in the number of chemicals permitted for pest control, as insects have developed resistance to some chemicals and others are currently being phased out due to safety and environmental reasons. As a result, the grain storage industry is moving towards physical methods as opposed to chemical methods, as a safer and potentially better alternative. One well studied area is known as thermal disinfestation, with one of the potentially best forms being heat disinfestation via microwave radiation. The mathematical modelling of microwave heating processes in general requires the solution of a complex system of equations, which can be very difficult to obtain. In this work we illustrate the possibility of reducing the problem to one which involves extending the double-diffusivity heat transfer model which we develop to include a non-linear body heating source term to account for the heating due to microwave radiation. This model is known as the double-diffusivity heat transfer model incorporating microwave heating. Very good agreement is found between the semi-analytical and numerical approximations obtained.

These models are of practical importance because at present there is no experi mental data available due to the difficulty involved in measuring air and grain tem peratures separately, particularly within the peripheral layer. The proposed mod elling by either linear or relatively simple non-linear models, allows semi-analytical approximations to be obtained in order to provide important insight into the poten tial difference that exists between the air and grain temperatures, in particular, for small time and spatial scales. We comment that this work forms the foundations for subsequent work to what is a very complex practical problem, which we believe will ultimately lead to a better understanding of the microclimate within the peripheral layer of a grain bulk.