A variance propagation algorithm for stochastic heat and mass transfer problems in food processes

A variance propagation algorithm for stochastic coupled heat and mass transfer problems subjected to 7rst order autoregressive random process boundary conditions was developed. The algorithm is based on the 7nite element formulation of Luikov’s coupled heat and mass transfer equations and involves the numerical solution of coupled Lyapunov and Sylvester matrix di=erential equations. It o=ers a cheap alternative to the Monte Carlo method for the computation of the mean value and variance of the temperature and moisture content 7eld. The algorithm is generally applicable and can easily be inserted in any existing 7nite element code. Also, it can be extended to other types of random processes. The algorithm was applied to analyse the drying of a soybean kernel. Simulation results show that random >uctuations of the process conditions may cause considerable variability of the temperature and the moisture content within the drying soybean kernel. This is an important feature to take into account for the design of a drying process, and for thermal food processes in general.