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

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

Modelling the Kinetics, Thermodynamic and Physical Properties of Coconut (Cocos nucifera L.) during Convective Drying

The drying kinetics, thermodynamic properties, and energy consumption of five potential coconut cultivars identified by Ghana's CSIR-Oil Palm Research Institute were studied. Drying was carried out in a convectional dryer using four temperatures (70, 80, 90 and 100oC) and 2.0 m/s air velocity. The asymptotic model was adjudged the best fit model in predicting moisture content based on the highest coefficient of determination (0.9589-0.9998) and lowest residual sum of squares (8.427-252.61), chi-square (0.52671-16.8409) and root mean square error (2.8744-3.4421). Temperature caused between 66.8-96.5% variations in moisture diffusivity. Thermodynamic study revealed endothermic and non-spontaneous reactions in the drying system resulting from enthalpy change and Gibbs free energy change. Meanwhile, a direct relation was established among higher spontaneity and higher temperature. Despite the high drying temperatures used for the experiment, internal cellular composition was not affected as a result of excellent rehydration capacity. In effect, the Vanuatu TThe drying kinetics, thermodynamic properties, and energy consumption of five potential coconut cultivars identified by Ghana's CSIR-Oil Palm Research Institute were studied. Drying was carried out in a convectional dryer using four temperatures (70, 80, 90 and 100oC) and 2.0 m/s air velocity. The asymptotic model was adjudged the best fit model in predicting moisture content based on the highest coefficient of determination (0.9589-0.9998) and lowest residual sum of squares (8.427-252.61), chi-square (0.52671-16.8409) and root mean square error (2.8744-3.4421). Temperature caused between 66.8-96.5% variations in moisture diffusivity. Thermodynamic study revealed endothermic and non-spontaneous reaction in the drying system resulting from enthalpy change and Gibbs free energy change. Meanwhile, a direct relation was established among higher spontaneity and higher temperature. Despite the high drying temperatures used for the experiment, internal cellular composition was not affected as a result of excellent rehydration capacity. In effect, the Vanuatu Tall was adjudged as the best coconut variety based on its lower energy consumption and activation energy, shorter drying time and higher moisture diffusivity. All was adjudged as the best coconut variety based on its lower energy consumption and activation energy, shorter drying time and higher moisture diffusivity

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

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 paper, we consider the asymptotic analysis of a recent multiphase model 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. By 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 scalings 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 including heating, evaporation, and pressure changes. This qualitative understanding of solutions to the multiphase model is essential when creating more involved models that incorporate chemical reactions and solid mechanics effects

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 paper, we consider the asymptotic analysis of a recent multiphase model 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. By 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 scalings 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 including heating, evaporation, and pressure changes. This qualitative understanding of solutions to the multiphase model is essential when creating more involved models that incorporate chemical reactions and solid mechanics effects

African Handbook of Climate Change Adaptation

This open access book discusses current thinking and presents the main issues and challenges associated with climate change in Africa. It introduces evidences from studies and projects which show how climate change adaptation is being - and may continue to be successfully implemented in African countries. Thanks to its scope and wide range of themes surrounding climate change, the ambition is that this book will be a lead publication on the topic, which may be regularly updated and hence capture further works. Climate change is a major global challenge. However, some geographical regions are more severly affected than others. One of these regions is the African continent. Due to a combination of unfavourable socio-economic and meteorological conditions, African countries are particularly vulnerable to climate change and its impacts. The recently released IPCC special report "Global Warming of 1.5º C" outlines the fact that keeping global warming by the level of 1.5º C is possible, but also suggested that an increase by 2º C could lead to crises with crops (agriculture fed by rain could drop by 50% in some African countries by 2020) and livestock production, could damage water supplies and pose an additonal threat to coastal areas. The 5th Assessment Report produced by IPCC predicts that wheat may disappear from Africa by 2080, and that maize— a staple—will fall significantly in southern Africa. Also, arid and semi-arid lands are likely to increase by up to 8%, with severe ramifications for livelihoods, poverty eradication and meeting the SDGs. Pursuing appropriate adaptation strategies is thus vital, in order to address the current and future challenges posed by a changing climate. It is against this background that the "African Handbook of Climate Change Adaptation" is being published. It contains papers prepared by scholars, representatives from social movements, practitioners and members of governmental agencies, undertaking research and/or executing climate change projects in Africa, and working with communities across the African continent. Encompassing over 100 contribtions from across Africa, it is the most comprehensive publication on climate change adaptation in Africa ever produced

Plants and Plant Products in Local Markets Within Benin City and Environs

AbstractThe vulnerability of agriculture systems in Africa to climate change is directly and indirectly affecting the availability and diversity of plants and plant products available in local markets. In this chapter, markets in Benin City and environs were assessed to document the availability of plants and plant products. Markets were grouped into urban, suburban, and rural with each group having four markets. Majority of the plant and plant product vendors were women and 88 plant species belonging to 42 families were found. Their scientific and common names were documented as well as the parts of the plant and associated products available in the markets. Most of the plant and plant products found in local markets belong to major plant families. Urban markets had the highest diversity of plants and plant products. Three categories of plants and plant products were documented. Around 67% of the plants and plant products were categorized as whole plant/plant parts, 28% as processed plant parts, while 5% as reprocessed plant/plant parts. It was revealed that 86% of these plants are used as foods, 11% are for medicinal purposes, while 3% is used for other purposes. About 35% of plants and plant products across the markets were fruits, which is an indication that city and environs are a rich source of fruits. The local knowledge and practices associated with the plants and plant products can contribute towards formulating a strategic response for climate change impacts on agriculture, gender, poverty, food security, and plant diversity