The mathematical modelling of coffee bean roasting is important in the production of high-quality coffee. In the present article, the authors use asymptotic methods to investigate the model of bean drying that was described in [N. T. Fadai et al., “A heat and mass transfer study of coffee bean roasting”, Int. J. Heat Mass Transf. 104, 787–799 (2017; doi:10.1016/j.ijheatmasstransfer.2016.08.083)]. It is supposed that beans have a simple geometry (a slab or a sphere).
The equations that describe drying processes are non-dimensionalized and two main parameters are found that influence the process. The first is the ratio of the vapor Darcy transport rate to the rate of evaporation; it is supposed to be small. The second is the density ratio of water vapor to water. It is of order unity, but to simplify governing equations sometimes it is supposed to be small, too. Three values of interest in the problem are the water saturation \(W\), the partial pressure of vapor \(P\) and the temperature \(T\).
The entire bean volume is divided into three regions: region \(i\) with equilibrium vapor pressure; the dryed region \(ii\) that contains no vapor; a thin transition layer that separates the first two regions.
The estimation of the moment \(t^{*}\) when region \(ii\) appears in the bean is obtained. Asymptotic expansions for the values of interest are found and matched on the region boundaries; the existence of the transition layer is crucial for that purpose. The time dependence of the dryed region thickness is determined, too.
The obtained asymptotic results are in qualitative agreement with the results of numerical simulation.