A proposal of analysis of the drying phenomena by means of fractal theory

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

© 2002 by CRC Press LLC. A proposal for studying the kinetic aspects of convective drying is presented herein, based on the fractal evaluation of the drying curve, taking slabs and spheres as working geometric systems. Drying kinetics of these models were determined and the fractal dimensions of the surface temperature distribution (STD) of the slabs and of the mass and size of spheres were obtained. It was possible to correlate the different stages of the drying curve with the fractal dimension of the STD of the slabs along this curve. The STD presents a Sierpinski carpet pattern suggesting the absence of a constant rate period of drying. Based on the determinations of the STD and of the range of invariance of the fractal dimensions found, a falling rate period of drying governed by randomness was identified. Euclidian (linear) behavior was observed toward the end of this period and, along the period of adjustment of conditions, a chaotic region characterized by the presence of a strange attractor was found. When comparing surface temperature kinetics at different operating conditions, self-similarity behavior is presented within the points of measurement, which could make possible the prediction of the surface temperature of these systems. Also, fractal dimensions of mass and fractal dimensions of the drying process for the dehydration of spheres were evaluated, and correlations between the rate of drying and the homogeneity of the process were found. This study may constitute a proposal toward the systematic study of drying kinetics with the aid of the fractal theory and can be applied to predict the degree of homogeneity of the process and its consequence in product quality.
Original languageAmerican English
Title of host publicationEngineering and Food for the 21st Century
Number of pages19
ISBN (Electronic)9781420010169
StatePublished - 1 Jan 2002

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Fractals
Drying
Fractal dimension
Temperature distribution
Kinetics
Invariance
Dehydration
Temperature

Cite this

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title = "A proposal of analysis of the drying phenomena by means of fractal theory",
abstract = "{\circledC} 2002 by CRC Press LLC. A proposal for studying the kinetic aspects of convective drying is presented herein, based on the fractal evaluation of the drying curve, taking slabs and spheres as working geometric systems. Drying kinetics of these models were determined and the fractal dimensions of the surface temperature distribution (STD) of the slabs and of the mass and size of spheres were obtained. It was possible to correlate the different stages of the drying curve with the fractal dimension of the STD of the slabs along this curve. The STD presents a Sierpinski carpet pattern suggesting the absence of a constant rate period of drying. Based on the determinations of the STD and of the range of invariance of the fractal dimensions found, a falling rate period of drying governed by randomness was identified. Euclidian (linear) behavior was observed toward the end of this period and, along the period of adjustment of conditions, a chaotic region characterized by the presence of a strange attractor was found. When comparing surface temperature kinetics at different operating conditions, self-similarity behavior is presented within the points of measurement, which could make possible the prediction of the surface temperature of these systems. Also, fractal dimensions of mass and fractal dimensions of the drying process for the dehydration of spheres were evaluated, and correlations between the rate of drying and the homogeneity of the process were found. This study may constitute a proposal toward the systematic study of drying kinetics with the aid of the fractal theory and can be applied to predict the degree of homogeneity of the process and its consequence in product quality.",
author = "Guti{\'e}rrez-L{\'o}pez, {G. F.} and J. Chanona-P{\'e}rez and L. Alamilla-Beltr{\'a}n and A. Hern{\'a}ndez-Parada and A. Jim{\'e}nez-Aparicio and R. Farrera-Rebollo and C. Ordorica-Vargas",
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language = "American English",
isbn = "9781420010169",
booktitle = "Engineering and Food for the 21st Century",

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A proposal of analysis of the drying phenomena by means of fractal theory. / Gutiérrez-López, G. F.; Chanona-Pérez, J.; Alamilla-Beltrán, L.; Hernández-Parada, A.; Jiménez-Aparicio, A.; Farrera-Rebollo, R.; Ordorica-Vargas, C.

Engineering and Food for the 21st Century. 2002.

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - A proposal of analysis of the drying phenomena by means of fractal theory

AU - Gutiérrez-López, G. F.

AU - Chanona-Pérez, J.

AU - Alamilla-Beltrán, L.

AU - Hernández-Parada, A.

AU - Jiménez-Aparicio, A.

AU - Farrera-Rebollo, R.

AU - Ordorica-Vargas, C.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - © 2002 by CRC Press LLC. A proposal for studying the kinetic aspects of convective drying is presented herein, based on the fractal evaluation of the drying curve, taking slabs and spheres as working geometric systems. Drying kinetics of these models were determined and the fractal dimensions of the surface temperature distribution (STD) of the slabs and of the mass and size of spheres were obtained. It was possible to correlate the different stages of the drying curve with the fractal dimension of the STD of the slabs along this curve. The STD presents a Sierpinski carpet pattern suggesting the absence of a constant rate period of drying. Based on the determinations of the STD and of the range of invariance of the fractal dimensions found, a falling rate period of drying governed by randomness was identified. Euclidian (linear) behavior was observed toward the end of this period and, along the period of adjustment of conditions, a chaotic region characterized by the presence of a strange attractor was found. When comparing surface temperature kinetics at different operating conditions, self-similarity behavior is presented within the points of measurement, which could make possible the prediction of the surface temperature of these systems. Also, fractal dimensions of mass and fractal dimensions of the drying process for the dehydration of spheres were evaluated, and correlations between the rate of drying and the homogeneity of the process were found. This study may constitute a proposal toward the systematic study of drying kinetics with the aid of the fractal theory and can be applied to predict the degree of homogeneity of the process and its consequence in product quality.

AB - © 2002 by CRC Press LLC. A proposal for studying the kinetic aspects of convective drying is presented herein, based on the fractal evaluation of the drying curve, taking slabs and spheres as working geometric systems. Drying kinetics of these models were determined and the fractal dimensions of the surface temperature distribution (STD) of the slabs and of the mass and size of spheres were obtained. It was possible to correlate the different stages of the drying curve with the fractal dimension of the STD of the slabs along this curve. The STD presents a Sierpinski carpet pattern suggesting the absence of a constant rate period of drying. Based on the determinations of the STD and of the range of invariance of the fractal dimensions found, a falling rate period of drying governed by randomness was identified. Euclidian (linear) behavior was observed toward the end of this period and, along the period of adjustment of conditions, a chaotic region characterized by the presence of a strange attractor was found. When comparing surface temperature kinetics at different operating conditions, self-similarity behavior is presented within the points of measurement, which could make possible the prediction of the surface temperature of these systems. Also, fractal dimensions of mass and fractal dimensions of the drying process for the dehydration of spheres were evaluated, and correlations between the rate of drying and the homogeneity of the process were found. This study may constitute a proposal toward the systematic study of drying kinetics with the aid of the fractal theory and can be applied to predict the degree of homogeneity of the process and its consequence in product quality.

M3 - Chapter

SN - 9781420010169

BT - Engineering and Food for the 21st Century

ER -