Mathematical model of thermal process in an infinite cylinder heated by a moving heat source

• Published in: AIP Conference Proceedings 2022-09, Vol.2522 (1)
• Main Authors: Lyashenko, V., Kobilskaya, E., Zagirnyak, M., Demyanchenko, O.
• Format: Article
• Language: English
• Subjects: Boundary value problems; Conjugation; Cylinders; Differential equations; Domains; Exact solutions; Heat; Heat sources; Mathematical analysis; Mathematical models; Ordinary differential equations; Temperature distribution; Thermodynamics; Three dimensional printing
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0100782

The paper presents a mathematical model of the temperature field of an infinite cylinder, heated by a moving, dispersed, on a finite segment (in an extruder), a heat source. Heating of the cylinder by both internal and external heat sources is considered. The mathematical model is constructed in the form of a nonlinear boundary value problem for the heat equation with conjugation conditions in three combined domains. A method for solving the problem is proposed. It consists in introducing a moving system of dimensionless coordinates. Further, the solution of the problem is reduced to the solution of a system of one-dimensional boundary value problems for ordinary differential equations of the second order with conjugation conditions on the boundaries of the domains of definition of the equations and a regularity condition at infinity. The function of a heat source, internal or external, is written using the Heaviside unit function. In the linear case, an analytical solution is obtained and a graph of the temperature distribution is constructed. The mathematical model, which is built in this work, allows us to describe the temperature distribution in a filament during 3D printing. The temperature distributions of a filament both in the extruder and outside of it have been constructed for various conditions for controlling the process of additive manufacturing of parts.