Mathematical Modeling of the Coupled Transport Phenomena and Color Development: Finish Drying of Trellis-Dried Sultanas

Abstract

A mathematical model for simulation of simultaneous heat and mass transport was developed to describe the drying kinetics during finish drying of trellis-dried sultanas. In this model, the governing partial differential equations for heat and mass transfer for a solid spherical body were numerically solved using a finite difference technique. In addition, a kinetic model was coupled to the heat and mass transfer calculations to simultaneously predict the evolution of product color during the drying process. This allows predictions of moisture content, temperature, and color profiles of the product in a space–time domain during the drying process as a function of various operating conditions.

Predictions compared well with the experimental values, implying that the proposed numerical model can be used with confidence for the simulation of the important transport phenomena in optimizing the design and operation of a drying system for sultanas that maximizes the retention of the desired product color. The work has demonstrated the importance of establishing optimal and closely controlled drying conditions because significant effects of the key operational parameters on drying kinetics and the associated changes of product color were found. The modeling approach proposed here can be extended to other products and for incorporation of other product quality indices.

Keywords:

• Dried grapes
• Finish drying
• Mathematical modeling
• Sultanas
• Trellis-dried

ACKNOWLEDGMENTS

The author thanks David Raynor (formerly from CSIRO) for helping in setting up the experimental test drying rig, Ewa Orszulok (formerly from CSIRO) for her assistance in carrying out the laboratory drying experiments, and Caroline Tarr (CSIRO Plant Industry) for undertaking the damage index tests. The author also thanks Dr. Raymond Mawson and Peerasak Sanguansri for reviewing the article and Dr. Roman Buckow for his helpful comments.

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ldrt.