Calculation of Biot Numbers in Food Drying

LEIVA DÍAZ, EVANGELINA; GINER, SERGIO ADRIÁN

ACTA HORTICULTURAE

ISHS

Lugar: Leuven; Año: 2008 p. 41 - 52

0567-7572

This paper describes the calculation of mass and heat transfer Biot number for food drying processes, dimensionless numbers relating internal to external resistances to either mass or heat fluxes. Four case studies are covered: wheat drying kinetics, solving the unsteady state diffusion equation by implicit finite differences for this low-moisture product, and three types of fruit pectic gels a high moisture product: sucrose-added, apple pectic gel, tomato pectic gel and low-calorie, apple pectic gel (LCAPG). In wheat drying, the mass transfer Biot number varied from low  to high values during the process if the grain started drying at high moistures, but only showed high values if starting drying at practical, lower moisture contents. For the first two gels, an analytical solution considering internal-external control was fitted to the drying curves in order to optimize mass transfer Biot numbers and diffusion coefficient, for an average thickness calculated by a shrinkage relationship. Mass transfer Biot values ranged from 1 for tomato pectic gel, to 2 for sucrose-added, apple pectic gel, showing that, on average, both internal and external resistances are important and that internal control could not be assumed from the beginning of drying. The LCAPG was solved with the most complex model: finite differences for the unsteady state diffusion equation considering shrinkage, and simultaneous solution of the macroscopic energy balance to predict the temperature curve. Mass transfer Biot numbers varied from almost zero at the start of drying to some 2000 at the end, while the heat transfer Biot number only varied from 0.25 to 0.5. Prediction of heat and mass transport in solids are quite different phenomena, so the heat transfer results should not be translated to predict the mass transfer behavior.