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Asymptotic Analysis of a Multiphase Drying Model Motivated by Coffee Bean Roasting

Title: Asymptotic Analysis of a Multiphase Drying Model Motivated by Coffee Bean Roasting

Abstract:  Asymptotic Analysis of a Multiphase Drying Model Motivated by Coffee Bean Roasting Recent modelling of coffee bean roasting suggests that in the early stages of roasting, within each coffee bean, there are two emergent regions: a dried outer region and a saturated interior region. The two regions are separated by a transition layer (or drying front). In this talk, we consider the asymptotic analysis of a multiphase model of this roasting process which was recently put forth and studied numerically, in order to gain a better understanding of its salient features. The model consists of a PDE system governing the thermal, moisture, and gas pressure profiles throughout the interior of the bean. Obtaining asymptotic expansions for these quantities in relevant limits of the physical parameters, we are able to determine the qualitative behaviour of the outer and interior regions, as well as the dynamics of the drying front. Although a number of simplifications and scaling are used, we take care not to discard aspects of the model which are fundamental to the roasting process. Indeed, we find that for all of the asymptotic limits considered, our approximate solutions faithfully reproduce the qualitative features evident from numerical simulations of the full model. From these asymptotic results, we have a better qualitative understanding of the drying front (which is hard to resolve precisely in numerical simulations) and hence, of the various mechanisms at play as heating, evaporation, and pressure changes result in a roasted bean. This qualitative understanding of solutions to the multiphase model is essential if one is to create more involved models that incorporate chemical reactions and solid mechanics effects.

This seminar will take place on Friday 10th November, at 4 p.m, in  Room A2-002.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726, iain.moyles@ul.ie).

A full list of upcoming seminars can be found at http://www.ulsites.ul.ie/macsi/node/48011

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.

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