A general mathematical model to determine temperature and moisture distributions in drying of spherical products: case studies of green peas, barley, and cranberry

Abstract

Forced convection drying is a simple and effective dehydration method widely applied in post-harvest technology. Sphere-shaped materials account for a large proportion compared to other shapes. Therefore, this study forms a general mathematical model and resolution method to predict the temperature and moisture content of spherical drying materials with time. Three representative spheres of green peas, cranberries, and barley were used as case studies to validate the simulation results with experimental results. All three crops are widely used in cooking. Green peas are often used in stews, salads or processed into soybeans. Cranberries are frequently employed in desserts, juices or processed into jam. Barley is often used to make bread and beer and is also an important grain source in human nutrition. The Arrhenius model predicts the moisture diffusion coefficient with temperature to link the temperature and moisture equations, and they are solved simultaneously. In drying applications, the Arrhenius model is often utilized to describe the temperature dependence of moisture diffusion coefficients or drying rates. By applying the Arrhenius equation to drying kinetics, the relationship between drying rate and temperature can be quantified, allowing for the prediction and optimization of drying processes under different temperature conditions. These three objects have very different input parameters to illustrate the wide applicability of the proposed solution method. The results show that there is a large difference in moisture content at the center and surface of a crop. On the contrary, the temperature is evenly distributed, and the dried object quickly reaches the drying air temperature. The laws of heat transfer and moisture transfer are analogy. However, the moisture diffusion coefficient and moisture transfer coefficient are much smaller than the thermal diffusion coefficient and heat transfer coefficient.