A Homogenization Approach for the Roasting of an Array of Coffee Beans

Sachak-Patwa, Rahil; Fadai, Nabil T.; Van Gorder, Robert A.

Abstract

While the processes underlying the roasting of a single coffee bean have been the focus of a number of recent studies, the more industrially relevant problem of roasting an array of coffee beans has not been well studied from a modeling standpoint. Starting with a microscale model for the heat and mass transfer processes within a single bean during roasting, we apply homogenization theory to upscale this model to an effective macroscale model for the roasting of an array of coffee beans. We then numerically simulate this effective model for two caricatures of roasting configurations which are of great importance to industrial scale coffee bean roasting: namely, drum roasters (where the beans are placed in a rotating drum) and fluidized bed roasters (where hot air is blown through the beans). The derivation of the homogenization problem has been carried out in a three-dimensional rectangular geometry. Simulations are presented both for simplified one-dimensional arrays of three-dimensional beans (as these are easier to visualize), as well as cross sections of full three-dimensional arrays of beans (for the sake of verification). We also verify our simulation results against experimental data from the literature. Among the findings is that increasing the air-to-bean volume fraction ratio decreases the drying time for the array of beans in a linear manner. We also find that, in the case of a fluidized bed, an increase in the hot air inflow velocity will decrease the drying time in a nonlinear manner, with diminishing returns observed beyond some point for large enough air inflow velocities.

Citation

Sachak-Patwa, R., Fadai, N. T., & Van Gorder, R. A. (2019). A Homogenization Approach for the Roasting of an Array of Coffee Beans. SIAM Journal on Applied Mathematics, 79(4), 1550-1580. https://doi.org/10.1137/18m1221904

• Journal Article Type: Article
• Acceptance Date: Jun 14, 2019
• Online Publication Date: Aug 22, 2019
• Publication Date: 2019-01
• Deposit Date: May 29, 2020
• Publicly Available Date: Jun 9, 2020
• Journal: SIAM Journal on Applied Mathematics
• Print ISSN: 0036-1399
• Electronic ISSN: 1095-712X
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 79
• Issue: 4
• Pages: 1550-1580
• DOI: https://doi.org/10.1137/18m1221904
• Keywords: Applied Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/4531433
• Publisher URL: https://epubs.siam.org/doi/10.1137/18M1221904