Open AccessStudy on heat transfer between the rod and the environment under conditions of forced convection
Author(s) -
А. В. Еремин
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/791/1/012008
Subject(s) - separation of variables , mathematics , thermal conduction , eigenvalues and eigenvectors , transcendental equation , heat equation , simple (philosophy) , boundary value problem , differential equation , partial differential equation , mathematical analysis , work (physics) , convergence (economics) , heat transfer , fourier series , transfer problem , series (stratigraphy) , parametric statistics , thermodynamics , physics , paleontology , philosophy , statistics , business , epistemology , quantum mechanics , biology , economic growth , international trade , economics
Obtaining analytical solutions to unsteady heat conduction problems is of great scientific and practical interest. Such solutions make it possible to do an in-depth analysis of thermal processes, such as isotherm fields analysis, study of the thermally stressed states of structures, parametric identification, etc. This article deals with a simple method for obtaining approximate analytical solutions of one-dimensional heat conduction problems. In particular, an algorithm for solving the problem for a rod (plate) with a given boundary condition of the third kind on one of the surfaces is presented. It is shown that solving the equation at isolated points of the spatial variable allows obtaining the high-precision solutions to this problem with a minimum amount of computational work. The relations for determining the temperature have a simple form and do not contain special functions and parameters. It should be noted that the exact solution to a similar problem based on the Fourier separation method is an infinite series containing eigenvalues (roots of the transcendental equation).The practical application of such solutions is very limited. The paper also contains the convergence analysis of the method, the residuals of the initial differential equation for various approximations. The method developed can be used to solve more complex problems that allow separation of variables in the initial l differential equation.