Determination of the Temperature of the Components of a Raw Cotton

Khonimkul Normamatovich Pardaev
Alisher Zununovich Mamatov
Obid Kosimov

Budapest International Research in Exact Sciences (BirEx Journal)
Vol 5, No 3 (2023): Budapest International Research in Exact Sciences, July

The article considers one boundary value problem for systems of parabolic type, consisting of two differential equations for determining the temperature and moisture content of a lump of raw cotton during drying in dryers. Based on the laws of thermodynamics (the laws of thermal conductivity of Fourier, Newton, conservation of energy, etc.), this problem is formulated as a system of differential equations of parabolic type An approximate solution of the problem under consideration was constructed using the variational-grid method, and a comparative analysis with experimental data was carried out. To solve this problem, was used the Galerkin variational method, i.e. introduce the basis function ji(x) satisfying the conjugacy condition ji(0)=0. A comparative analysis shows that the error in the calculated and experimental data is no more than 4-5%. And this makes it possible to analyze the heating rate in the form of a lump.