<abstract xmlns="http://www.w3.org/1999/xhtml"><p>One-dimensional heat conduction problem of friction for two bodies (half spaces) made of thermosensitive materials was considered. Solution to the nonlinear boundary-value heat conduction problem was obtained in three stages. At the first stage a partial linearization of the problem was performed by using Kirchhoff transform. Next, the obtained boundary-values problem by using the method of lines was brought to a system of nonlinear ordinary differential equations, relatively to Kirchhoff’s function values in the nodes of the grid on the spatial variable, where time is an independent variable. At the third stage, by using the Adams's method from DIFSUB package, a numerical solution was found to the above-mentioned differential equations. A comparative analysis was conducted (Och, 2014) using the results obtained with the proposed method and the method of successive approximations.</p></abstract>

One-dimensional heat conduction problem of friction for two bodies (half spaces) made of thermosensitive materials was considered. Solution to the nonlinear boundary-value heat conduction problem was obtained in three stages. At the first stage a partial linearization of the problem was performed by using Kirchhoff transform. Next, the obtained boundary-values problem by using the method of lines was brought to a system of nonlinear ordinary differential equations, relatively to Kirchhoff’s function values in the nodes of the grid on the spatial variable, where time is an independent variable. At the third stage, by using the Adams's method from DIFSUB package, a numerical solution was found to the above-mentioned differential equations. A comparative analysis was conducted (Och, 2014) using the results obtained with the proposed method and the method of successive approximations.

Solving Nonlinear Thermal Problems of Friction by Using Method of Lines

Faculty of Mechanical Engineering, Bialystok University of Technology, 45C Wiejska Street, Bialystok, 15-351, Poland

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Solving Nonlinear Thermal Problems of Friction by Using Method of Lines"}

One-dimensional heat conduction problem of friction for two bodies (half spaces) made of thermosensitive materials was considered. Solution to the nonlinear...

Solving Nonlinear Thermal Problems of Friction by Using Method of Lines

Published Online: May 15, 2015

Page range: 33 - 37

DOI: https://doi.org/10.1515/ama-2015-0007

© Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.