Analytical solution for the heat and mass transfer of spherical grains during drying

Abstract

Analytical solutions play a role in predicting the moisture content of grains in agricultural engineering applications due to their convenience and accuracy. However, most of them ignore evaporation from internal or surface moisture which is not reasonable in real drying. Therefore, this investigation aims to analyse the drying behaviour of a single barley grain analytically. Analytical solutions to the coupled heat and mass transfer equations for spherical particle drying are presented by introducing an auxiliary function through the variable separation approach. Both internal and surface moisture evaporations in barley are fully considered in the equations, which are generally solved with numerical methods. The results reveal that the analytical solution predicted accurately the temperature and moisture content of the barley drying, and the predicted temperatures were lower than that without internal moisture evaporation. The non-linear relationship between the safe storage time ( τ ) with a moisture content of 0.13 kg kg −1 d.b. and vapour pressure ( P v ) can be best described by the fitted quadratic polynomial of τ = 3.768 × 10 − 6 P v 2 + 1.943 × 10 − 2 P v + 1.444 × 10 3 ( R 2 = 0.99849) at an air temperature of 348.15 K. The analytical solution deduced in this work is able to describe the drying behaviour of different of grains if they are simplified to spherical geometry under given drying conditions. • Grain drying model considering evaporation throught kernal was analytically solved. • Variable diffusivity allocated by time period was considered in the solution. • Time required to dry to an arbitrary moisture content can be easily obtained.