The Mathcad system usage in finding normal equations in the description of food extraction processes

Abstract

The article describes using electronic computer systems, particularly Mathcad when finding standard equations for building mathematical models of technological processes in the chemical and food industries. Classical mathematical models of the extraction process are usually based on analyzing the differential equation of diffusion under appropriate boundary and initial conditions. Also, when describing mathematical models, Fick's equation, the equation of the adsorption pore model of molecular-statistical studies, models that take into account the physics of the process of substance transfer in a capillary-porous medium, etc., are used. Modeling of mass transfer processes under the influence of the intensifying action of the microwave field is described in the studies for the systems “coffee – water” and “oak wood – water-alcohol solution”, “coffee grounds – alcohol,” “amorant – hexane,” a mechanism of the combined process of mass transfer of extractive substances from a porous structure is proposed into solution The description of mass transfer processes under the influence of microwave field intensification is rather complicated. The mass transfer of extractive substances from porous structures to the solution occurs through the distribution of concentrations at the “solid–solvent” interface. However, it passes from the inner part through the outer part, through the capillaries into the border diffusion layer. Complex mathematical models for mass transfer processes do not have analytical solutions. When using the Mathcad system to solve nonlinear systems of equations, it is recommended to use the built-in find function in the calculated Given block. Also, the universal function genfit is quite adequate, which makes it possible to determine unknown parameters for nonlinear combinations of functions by the method of least squares. This system was used in describing extraction processes in the structure of interaction “oil – containing raw materials – solvent” with the intensifying effect of the microwave field. Such simplified analytical description systems are recommended to be used along with experimental modeling with the classic use of similarity theory and the “dimensional analysis” method. The final result of these directions is the construction of sound engineering methods for the design of extractors for industrial purposes.