Сумісне використання R-функцій і проекційного методу в задачах теорії сушіння

Abstract

Запропоновано метод дослідження процесів тепломасообміну в капілярно-пористих тілах складної форми, який базується на застосуванні проекційного методу у формі Бубнова–Гальоркіна та конструктивних засобів теорії R-функцій. Побудована структура розв’язку дозволяє точно враховувати геометричну форму тіла та межові умови. Запропонована структурна модель дозволяє проводити числові експерименти з метою підвищення ефективності інтенсифікації процесів сушіння харчової сировини.

To increase the efficiency intensification of drying of food raw materials the mathematical model of the process in the form of non-stationary partial differential equations with given initial and boundary conditions were proposed. Presence of the time component and the tendency to take into account the real spatial geometric form of capillary-porous bodies complicate the mathematical model of the problem. These difficulties overcome by the application of R-functions and projection Bubnov – Galerkin methods. The proposed form of solution of initial value problem precisely takes into account the body shape and geometric boundary conditions. The stage of obtaining numerical solutions solving the systems of ordinary differential equations with initial conditions which shaped by projection method came to an end. The literature review under that topic shows that the solutions of only the bodies which use integral transformations (infinite plane, cylinder, sphere, rectangle) were researched in detail. The article is dedicated to the establishment of a rational modes of drying capillary-porous bodies through the construction physical and mathematical model using the projection method in Bubnov-Galerkin form and design tools of the theory of R-functions. Thus the development of R-functions method with the use of projection BubnovGalerkin method was proposed. An approximate solution of the problem of distributing the temperature and moisture in a spatial capillary-porous body with boundary conditions of the third kind was obtained. The proposed algorithm can be used for the elucidation of the mechanism of heat transfer process during the dehydration of food raw materials.