Mathematical and Physical Foundations of Drying Theories

Abstract

In this paper a survey is given concerning to the stochastic modelling approaches in vansport processes with a special emphasis on application possibilities for simultaneous heat and mass transfer in drying. First, the mostly used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (stateindependent) conductivity coefficients. Powerful discretisation methods are shown for their solution. Basic principles of variational calculus are discussed then with an attention on direct methods. As a simple application a first-order approximation example is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivity coelficients has a crucial influence on the flow pattern of the coupled heat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefkients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statistical properties of percolative

Mathematical Modeling of Drying Processes Using Methods of the Nonequilibrium Thermodynamics and Percolation Theory

“…[3,29] Within framework of the approximation leading to (24), the solution of the system of (17)- (18) is…”

“…Although the relaxation time constants are in general built up from conductivity and coupling coefficients as thermodynamically state-dependent quantities, [7] their statedependence will not be discussed here, because it would lead to research topics belonging to dynamic scaling theory. [24] According to descriptions of coupled transport processes taking place in porous media, the coefficients have the following meaning: [3] D a m ; K a m d;…”

“…[8,24,25] The reason is, that this well-developed branch of probability theory [26] and statistical physics [27] has shown its efficiency at solving many practical problems. This theory is particularly important to describe the phase transition phenomena in complex systems of very different character.…”

Effect of Dielectric Material on Microwave Freeze Drying of Skim Milk

“…Based on the Luikov's system [20] within a framework of the irreversible thermodynamics, [21] the mathematical model of coupled heat and mass transfer for a one-dimensional frozen porous sphere with a dielectric material core is derived as follows. Solid matrix is rigid, homogeneous, and isotropic.…”