A heat and mass transfer study of carbon paste baking

Roberts, Lindon; Nordgård-Hansen, Ellen; Mikkelsen, Øyvind; Halvorsen, Svenn Anton; Gorder, Robert A. Van

doi:10.1016/j.icheatmasstransfer.2017.07.025

Cited by 6 publications

(5 citation statements)

References 13 publications

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“…However, for other particles, such as large briquettes of compressed agglomerates, where diffusivity in the binder is important, the simple shrinking core approach is not a good representation, and our model is preferred. The role of binder during heat treatment of carbon has been studied in [23]. Since our model allows both sharp interface behavior and a diffuse reaction front, it is an ideal means of comparing the reactivity of different raw materials.…”

Section: 1mentioning

confidence: 99%

“…In practice, the conversion of one solid to another through reaction with gas can lead to volumetric increase or decrease of grains within the particle, with the stresses caused by the solid expansion or contraction possibly causing cracks and fracturing of the solid (again see [23]). Such mechanical effects have not been considered in this paper, due to the difficulty in considering how displacements at the microscale grain level would influence neighboring grains inside a spherical particle.…”

Section: 1mentioning

confidence: 99%

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php depend on the specific reaction of interest. We allow for different limits of D S /D V to be considered by writing (23) D S D V = \delta n \nu for \nu an \scrO (1) parameter and n \in \BbbR . Typically, we would physically expect n > 0, that is, D S < D V , since it is harder for gas to diffuse through the porous matrix than through the void space.…”

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confidence: 99%

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Homogenization of a Shrinking Core Model for Gas–Solid Reactions in Granular Particles

Sloman¹,

Please²,

Gorder³

2019

SIAM J. Appl. Math.

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\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft . Reactions between gases and solid particles are commonly modeled using a shrinking core framework, where a sharp interface between an inner unreacted core and an outer product shell moves inward until the reaction is complete. However, for some physical systems this sharp divide is not present, and so a better model is needed to capture a transition region for the reaction. We are interested in large particles made of many small grains where there are strong interactions between microscale granular and macroscale particulate effects, and where a shrinking core model represents behavior at the microscale level. We obtain homogenized equations for macroscale behavior by exploiting the small ratio of granular to particle lengthscales. These macroscale equations allow for a diffuse reaction front, as well as a sharp interface between reacted and unreacted solid material. We analyze the resulting model asymptotically in the limits where the reaction time is rate-limited by chemical kinetics, and separately by diffusion, determining the thickness of the reaction front. Numerical simulations support the law of additive reaction times, which states that the total reaction time is given as the sum of the conversion times under these limits. We further show how the model results can be extended to incorporate the transport of the product gas out of the solid particle, using a binary Fickian diffusion model. In metallurgical production the particle size and porosity are known to influence reaction times. Our results help quantify these effects and may be an aid in raw material selection.\bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . homogenization, gas-solid reactions, porous media, shrinking core model, diffusion, asymptotics \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs . 35B27, 35C20, 80A30, 92E20 \bfD \bfO \bfI .

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Section: 1mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

mentioning

confidence: 99%

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Homogenization of a Shrinking Core Model for Gas–Solid Reactions in Granular Particles

Sloman¹,

Please²,

Gorder³

2019

SIAM J. Appl. Math.

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“…We should finally note that similar modeling efforts to those applied to the roasting of a single coffee bean have been directed at understanding applications such as bread baking [66], carbon paste baking [57], wood drying [51], and popcorn popping [32]. While our motivating application has been to coffee bean roasting, the approach that we have taken may be adapted to the study of the roasting, baking, or drying of periodic arrays of material arising in these and other applications.…”

Section: Sensitivity Analysismentioning

confidence: 99%

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

Sachak-Patwa¹,

Fadai²,

Gorder³

2019

SIAM J. Appl. Math.

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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.

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“…Incorporating these elements into such models should provide additional insight into macroscopic phenomena that are observed during the roasting process. While the focus of this paper will be on macroscopic deformations in a roasting coffee bean, it is important to note that this phenomena is seen in a variety of applications, including the thermal cracking of baking carbon paste [24], wood drying [20], and popcorn popping [14].…”

Section: Introductionmentioning

confidence: 99%

Modelling structural deformations in a roasting coffee bean

Fadai

Please

Gorder

2019

International Journal of Non-Linear Mechanics

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Macroscale deformations in a roasting coffee bean are important mechanisms in determining flavour development, moisture loss, and consistency of the bean. In this paper, we model the stresses and strains in the cellulose structure of a roasting coffee bean via temperature-dependent poroviscoelastic constitutive equations. This model accounts for the deformations that are created and controlled by the moisture content, temperature, and gas pressure inside of the roasting coffee bean. The model combines previously derived multiphase heat and mass transfer models for roasting coffee beans with these poroviscoeleastic equations, to determine when and where macroscale deformations of the cellular matrix are likely to occur. By exploiting reasonable asymptotic reductions of the poroviscoelastic equations, we find that a large surge of stress is produced in the interior of a coffee bean. We determine that this build-up of stress is due to the viscoelastic interior of the bean being contained by a rigid elastic exterior and unable to expand. Our theoretical results suggest directions for possible improvement in standard industrial coffee roasting techniques, which may allow the macroscale deformations of the cellular matrix to be controlled and thereby improve properties such as flavour, moisture loss, and consistency of the final product.

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A heat and mass transfer study of carbon paste baking

Cited by 6 publications

References 13 publications

Homogenization of a Shrinking Core Model for Gas–Solid Reactions in Granular Particles

Homogenization of a Shrinking Core Model for Gas–Solid Reactions in Granular Particles

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

Modelling structural deformations in a roasting coffee bean

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