Solving Nonlinear Thermal Problems of Friction by Using Method of Lines

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 boundary-value heat conduction problem was obtained in three stages. At the first stage a partial linearization of the problem was performed by...

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Main Author: Och Ewa
Format: Article
Language:English
Published: Sciendo 2015-03-01
Series:Acta Mechanica et Automatica
Subjects:
method of lines
thermal problems of friction
thermosensitive materials
Online Access:https://doi.org/10.1515/ama-2015-0007
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spelling doaj-ded9c5681dd34cf4aedeef0e6c97bf082021-09-06T19:39:46ZengSciendoActa Mechanica et Automatica 2300-53192015-03-0191333710.1515/ama-2015-0007Solving Nonlinear Thermal Problems of Friction by Using Method of LinesOch Ewa0Faculty of Mechanical Engineering, Bialystok University of Technology, 45C Wiejska Street, Bialystok, 15-351, PolandOne-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.https://doi.org/10.1515/ama-2015-0007method of linesthermal problems of frictionthermosensitive materials
collection DOAJ
language English
format Article
sources DOAJ
author Och Ewa
spellingShingle Och Ewa
Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
Acta Mechanica et Automatica
method of lines
thermal problems of friction
thermosensitive materials
author_facet Och Ewa
author_sort Och Ewa
title Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
title_short Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
title_full Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
title_fullStr Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
title_full_unstemmed Solving Nonlinear Thermal Problems of Friction by Using Method of Lines
title_sort solving nonlinear thermal problems of friction by using method of lines
publisher Sciendo
series Acta Mechanica et Automatica
issn 2300-5319
publishDate 2015-03-01
description 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.
topic method of lines
thermal problems of friction
thermosensitive materials
url https://doi.org/10.1515/ama-2015-0007
work_keys_str_mv AT ochewa solvingnonlinearthermalproblemsoffrictionbyusingmethodoflines
_version_ 1717770137975652352

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