Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt

Abstract

The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.