29E-3 |
Analysis of the shrinkage during drying through the fractal dimensión |
V. SANTACRUZ-VÁZQUEZ, Facultad de Ingeniería Química, Benemérita Universidad Autónoma de Puebla, Av 18 sur y Av. San Claudio, Ciudad Universitaria, Puebla, 72570, Mexico, G. F. Gutiérrez, Departamento de Graduados en Alimentos, Escuela Nacional de Ciencias Biológicas, Instituto Politécnico Nacional, Prol. Carpio y Plan de Ayala, Mexico D.F., Mexico, H. Hernández-Sanchez, Escuela Nacional de Ciencias Biológicas-IPN Departamento de Graduados en Alimentos, Insituto0 Politécnico Nacional, Carpio y Plan de Ayala, México, D.F, 11340, Mexico, and C. Santacruz-Vázquez, Facultad de Ingeniería Química, Benmérita Universidad Autónoma de Puebla, av. 18 sur y Av. San Claudio, Puebla, 72570, Mexico. A proposal for studying the shrinkage of apple slabs is presented here, based on the fractal evaluation of the shrinking profiles, taking the infinite slabs as geometric system, diameter 5cm and thickness 0.2cm. The drying kinetic of the slabs were obtained 70°C and air speed in the dryer of 2 m/s. The diffusion coefficients were determined according to the Second Law of Fick, reporting that the coefficients varies during the process time and the falling rate period has three stages. During the first and second stages the shrinkage is a linear function of loss of water in presence of high moisture content (0.42 kg moisture/kg dry solid). During the third stage a non-linear relationship between the loss of water and the shrinkage is reported. The volume and area (V/Vo, A/Ao) were obtained finding a power function with the moisture content with a exponent of 0.4402 and 0.1652 for V/Vo and A/Ao respectively. The fractal dimension of the shrinkage of the slabs was determined through Richardson’s plot founding that shrinkage is a non-linear process, that it can be described with the fractal dimension. Based on the determination of the surface temperatures and the moisture content in different points of the apple slabs, we reported gradients of this parameters in the slabs, showing that mass and heat transfer rate are different in each point. The shrinkage kinetic and its fractal dimension was correlate with the surface temperature and moisture content showing during the falling rate period the shrinkage is non linear phenomenon and its affected by the non-linear mass and heat transfer rate. This study may constitute a proposal toward the understanding the drying process and the shrinkage like a non-lineal process using the new concept of fractal theory.
Session 29E, Food Engineering: Transport processes and kinetics
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