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A variance propagation algorithm for stochastic heat and mass transfer problems in food processes
Author(s) -
Scheerlinck Nico,
Verboven Pieter,
Stigter Johannes D.,
De Baerdemaeker Josse,
Van Impe Jan F.,
Nicolai Bart M.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.202
Subject(s) - monte carlo method , algorithm , mathematics , kernel (algebra) , finite element method , mathematical optimization , statistical physics , statistics , physics , thermodynamics , combinatorics
A variance propagation algorithm for stochastic coupled heat and mass transfer problems subjected to first order autoregressive random process boundary conditions was developed. The algorithm is based on the finite element formulation of Luikov's coupled heat and mass transfer equations and involves the numerical solution of coupled Lyapunov and Sylvester matrix differential equations. It offers a cheap alternative to the Monte Carlo method for the computation of the mean value and variance of the temperature and moisture content field. The algorithm is generally applicable and can easily be inserted in any existing finite 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 fluctuations 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. Copyright © 2001 John Wiley & Sons, Ltd.