Using integral transform method to solve the problem
Authors: Plotnikov I.S., Puchkov V.M.
Published in issue: #2(74)/2018
DOI: 10.18698/2308-6033-2018-2-1729
Category: Power, Metallurgic and Chemical Engineering | Chapter: Nuclear Reactor Engineering, Machines, Assemblies, and Nuclear Materials Technology
The article presents an analytical solution to the problem of determining temperature field distribution in a system of coaxial cylinders as it cools. We developed a mathematical model for non-steady state thermal conductivity processes, which considers perfect contact between interacting bodies. We investigated the matter of simplifying the model by replacing thin cylindrical walls with flat infinite plates of the same thickness. We obtained a solution by means of integral transforms in Cartesian and cylindrical coordinates. The study deals with a mathematical problem of describing the interface between an internal bar of the system, defined in a cylindrical coordinate system, and an adjacent flat infinite plate, defined in Cartesian coordinates in the simplified model. We plotted the results on temperature field curves in the system of coaxial cylinders for various moments in the evolution of the cooling process. This solution is valid under the following conditions: a low ratio of cylindrical layer thickness to the radius of curvature of the actual cylinder axis, optical opacity of all layers and axial symmetry of the model geometry and boundary conditions.
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