An inverse problem of parameter estimation for heat and mass transfer in capillary porous media

Abstract This work deals with the solution of an inverse problem of parameter estimation involving heat and mass transfer in capillary porous media, as described by the dimensionless linear Luikov’s equations. The physical problem under picture involves the drying of a moist porous one-dimensional medium. The main objective of this paper is to simultaneously estimate the dimensionless parameters appearing in the formulation of the physical problem by using transient temperature and moisture content measurements taken inside the medium. The inverse problem is solved by using the Levenberg–Marquardt method of minimization of the least-squares norm with simulated measurements.

[1]  M. D. Mikhailov,et al.  Integral transform solution of Luikov's equations for heat and mass transfer in capillary porous media , 1993 .

[2]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[3]  R. M. Cotta,et al.  On the solution of non‐linear drying problems in capillary porous media through integral transformation of Luikov equations , 1995 .

[4]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[5]  O. Alifanov,et al.  Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems , 1995 .

[6]  Helcio R. B. Orlande,et al.  Estimation of dimensionless parameters of Luikov's system for heat and mass transfer in capillary porous media , 2002 .

[7]  C. Weng,et al.  Inverse problem of coupled heat and moisture transport for prediction of moisture distributions in anannular cylinder , 1999 .

[8]  M. N. Özişik,et al.  Inverse Heat Transfer: Fundamentals and Applications , 2000 .

[9]  M. N. Özişik,et al.  Unified Analysis and Solutions of Heat and Mass Diffusion , 1984 .

[10]  Ephraim M Sparrow,et al.  Advances in Numerical Heat Transfer , 1996 .

[11]  Roland W. Lewis,et al.  A numerical solution of two-dimensional problems involving heat and mass transfer , 1976 .

[12]  Renato Machado Cotta,et al.  Integral Transforms in Computational Heat and Fluid Flow , 1993 .

[13]  K. Morgan,et al.  An application of the finite element method to the drying of timber. , 2007 .

[14]  Cheng-Hung Huang,et al.  An inverse problem in simultaneous estimating the Biot numbers of heat and moisture transfer for a porous material , 2002 .

[15]  O. Alifanov.  Inverse heat transfer problems , 1994 .

[16]  Hubert Maigre,et al.  Inverse Problems in Engineering Mechanics , 1994 .

[17]  Jorge C. Oliveira,et al.  Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven , 2001 .

[18]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[19]  M. N. Özişik,et al.  ON THE COMPLEX EIGEN-VALUES OF LUIKOV SYSTEM OF EQUATIONS , 1987 .

[20]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[21]  Parameter estimation in moist capillary porous media by using temperature measurements , 2000 .