AN ALGORITHM FOR SOLVING INVERSE PROBLEMS OF HEAT AND MASS TRANSPORT IN AGRICULTURAL PRODUCTS

Abstract

An algorithm was developed for solving transient, three-dimension al, quasi-linear, inverse problems of heat and mass transport in nonhomogeneous agricultural products of irregular geometry. A numerical approach consisted of an optimization technique and a generalized finite element method, with the use of isoparametric, curvilinear, 3D-space elements, and a three-point recurrence scheme in time, absolutely stable, with iterative procedure to deal with the quasi-linearity of equations. A computer pro- gram was developed and the method was applied to estimate the moisture diffusion coefficient, and then to predict heat and moisture transport in individual corn kernels during drying. Proper understanding of heat and mass transport in complex agricultural products is an essential ingredient in the advancement of food processing systems. Therefore, fast and reliable computer methods for predicting such processes as heating, drying, and cooling of biomaterials are of particular importance. Accuracy of predictions depends on adequate representation of the process parame- ters in the mathematical model. In case of heat and mass transport in agricultural pro- ducts, it has not been fully determined which of the factors responsible for the process should be considered in the model. It has generally been accepted that the effective mois- ture transport coefficient is the most critical quantity affecting accuracy of predictions in case of drying agricultural products (4, 5, 6, 9), Its value is highly dependent on the product moisture content, changes during drying, and also manifests significant differ- ences for the product components. Such nonhomogeneity is the most significant factor in the first and middle periods of dry ing, whereas the geometric irregularity of the product is the most pronounced factor in the final period (9, 11), Due to the complexity of biomaterials and the interactions which occur between the product and the surrounding fluid, direct determination of some coefficients is cumberso- me and often leads to erroneous results. Thus, an indirect approach was examined in this study to estimate unknown coefficient values, based on the inverse heat and mass trans- port concept (1, 2, 3, 8, 10), optimization techniques (7), and the structural mathemati- cal model for the corresponding direct problems of heat and mass transport (9, 11), The objectives of this study were to develop a numerical algorithm for solving tran- sient, three-dimensional, quasi-linear, inverse problems of heat and mass transport in nonhomogeneous agricultural products of irregular geometry, and to estimate, using measured and predicted moisture content values, the moisture diffusion coefficient in the thin-layer drying of corn.