Inverse Approaches to Drying of Thin Bodies With Significant Shrinkage Effects

Abstract

This paper deals with the application of inverse concepts to the drying of bodies that undergo changes in their dimensions. Simultaneous estimation is performed of moisture diffusivity, together with the thermal conductivity, heat capacity, density, and phase conversion factor of a drying body, as well as the heat and mass transfer coefficients and the relative humidity of drying air. This was accomplished by using only temperature measurements. A mathematical model of the drying process of shrinking bodies has been developed where the moisture content and temperature fields in the drying body are expressed by a system of two coupled partial differential equations. The shrinkage effect was incorporated through the experimentally obtained changes of the specific volume of the drying body in an experimental convective dryer. The proposed method was applied to the process of drying potatoes. For the estimation of the unknown parameters, the transient readings of a single temperature sensor located in the midplane of the potato slice, exposed to convective drying, have been used. The Levenberg–Marquardt method and a hybrid optimization method of minimization of the least-squares norm are used to solve the present parameter estimation problem. Analyses of the sensitivity coefficients and of the determinant of the information matrix are presented as well.

Determination of the diffusion coefficient of dry mushrooms using the inverse method

“…Among the deterministic methods, the Levenberg-Marquardt method has been used successfully in several areas (Kanevce et al, 2005;Mendonça et al, 2005;Mejias et al, 1999). Among the stochastic methods, the Differential Evolution method has been less applied to inverse problems, which include the works of Kanevce et al (2003), and Mariani et al (2008).…”

CITT and inverse analyses applied to the study of the mushroom drying process

“…Among the deterministic methods, the Levenberg-Marquardt method has been used successfully in several areas (Silva et al, 2009a;Kanevce et al, 2005;Mendonça et al, 2005;Mejias et al, 1999).…”

Mathematical modelling of far-infrared vacuum drying processes

“…In the case of an infinite flat plate when the influence of thermodiffusion is small, δ = 0, the the unsteady temperature, t(x, τ), and moisture content, u(x, τ), fields in the drying body are expressed by the following system of coupled nonlinear partial differential equations for energy and moisture transport (Kanevce et al, 2006) …”

“…Then, the equation of second Fick's law can be solved analytically (Karathanos et al, 1990;da Silva et al, 2009) or numerically (Daud et al, 1997;Park et al, 2007) depending on whether the diffusivity is taken as a constant or variable value, -in the third group are categorized models which are based on the numerical solution of the equation of second Fick's law with constant or variable value of diffusivity, whereby in the calculation are taken outside the mass transport and shrinkage of materials (Zogzas et al, 1996;Park et al, 2007), -the fourth group consists of models that are based on the simultaneous processes of heat and mass transfer. The modelling of drying process is defined by a system of two coupled partial differential equations of second order with appropriate initial and boundary conditions, and the model take into account or not the shrinkage of the dry material (Kanevce et al, 2004;Kanevce et al, 2006;Kanevce et al, 2007;Мitrevski et al, 2009;Afolabi and Agarry, 2014), -in the fifth group are classified models that are based on the theory of porous media, and when it is applied equilibrium approach (Yamsaengsung and Moreira, 2002;Dinčov et al, 2004), and -the sixth group consists of models based on the theory of non-equilibrium approach (Ousegui et al, 2010;Halder et al, 2011).…”