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

Abstract

Abstract. 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.

Numerical Solution for Linear Parabolic Reaction-Double Diffusivity System using the Operational Matrices of the Haar Wavelets Method

“…Antic and Hill (2000) [2] are studied a mathematical model for heat transfer in grain store microclimates, this model is "double diffusivity" such that they are used the heat-balance integral method to transform the coupled partial differential equations to the coupled ordinary differential equations and solved it numerically by using the Fehlberg fourth-fifth order Rangekutta method. Antic and Hill (2003) [3] are studied a Two-stage heat transfer model for the peripheral layers of a grain store, they are observed that the predictions of the air and grain temperatures of the two-stage model lag behind those of the double-diffusivity heat transfer model, but this lag decreases as time increases.…”