Characterization of isotherms and thin-layer drying of red kidney beans, Part II: Three-dimensional finite element models to estimate transient mass and heat transfer coefficients and water diffusivity

ABSTRACT

Three-dimensional finite element models with consideration of shrinkage and irregular shape were developed to estimate the relationships among the transient heat and mass transfer coefficients, the transient water diffusivity, and the temperature and moisture content of the red kidney beans being dried under different drying conditions. An equation was developed to calculate the transient mass transfer coefficient using the measured time–moisture content data. This calculated transient mass transfer coefficient was further used to calculate the transient heat transfer coefficient. To verify the predicted temperature on the surface of the red kidney beans, surface temperature was measured using a handhold infrared thermometer. These measured temperature and time–moisture content data were used to determine the transient water diffusivity using the least square method when the red kidney bean kernel experienced a shrinkage during drying. Strong relationship among the transient heat and mass transfer coefficients, the water diffusivity, and the ratio of the transient heat and mass transfer coefficients was revealed. This relationship could be used to predict temperature and moisture content of the red kidney beans during the entire drying period. The Lewis number = 27, and the ratio of the transient heat over mass transfer coefficients was 10765 J m⁻³ k⁻¹ at 30 and 40°C, and 10729 J m⁻³ k⁻¹ at 50°C. Shrinkage did not significantly influence the value of the estimated transient water diffusivity.

KEYWORDS:

• Lewis number
• shrinkage
• three-dimensional finite element model
• transient mass and heat transfer coefficients
• transient water diffusivity

Additional information

Funding

The authors thank the Natural Sciences and Engineering Research Council of Canada for partial funding of this study as well as the Canada Foundation for Innovation, the Manitoba Research Innovation Fund, and several other partners for creating the research infrastructure. The authors are grateful to Darsana Divagar for technical assistance.