Steady temperature fields associated with a moving rod in a medium with nonlinear thermal conductivity
type: Item
instance of: scholarly article
title: Steady temperature fields associated with a moving rod in a medium with nonlinear thermal conductivity
zbMATH Open document ID: 0657.73059
DOI: 10.1016/0020-7225(88)90066-3
published in: International Journal of Engineering Science
publication date: 1988-01-01T00:00:00Z
review text: The two-dimensional problem is considered of determining the temperature field when a rectangular rod of width h and at constant temperature moves at constant speed V in a medium with a temperature dependent thermal diffusivity D(T). It is assumed that \(Vh/D(T)\ll 1\) and the solution is first considered in the far field (``the outer solution'') where the problem is reduced to a nonlinear ordinary differential equation. Properties of this ``outer solution'' are then used to set a boundary condition at infinity for the ``inner problem'' of determining the temperature close to the rod. Finally, this inner problem is solved by using the Kirchhoff transformation to reduce the nonlinear equation to the Laplace equation valid close to the rod.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4074644
zbMATH Keywords: Schwarz-Christoffel transformation
zbMATH Keywords: matched asymptotic expansions
zbMATH Keywords: inner limit of outer solution
zbMATH Keywords: two-dimensional problem
zbMATH Keywords: rectangular rod
zbMATH Keywords: constant temperature
zbMATH Keywords: constant speed
zbMATH Keywords: medium with a temperature dependent thermal diffusivity
zbMATH Keywords: far field
zbMATH Keywords: nonlinear ordinary differential equation
zbMATH Keywords: inner problem
zbMATH Keywords: Kirchhoff transformation
zbMATH Keywords: Laplace equation
Wikidata QID: Q60171557
author: C. Atkinson
MaRDI profile type: Publication
full work available at URL: 0020-7225(88)90066-3
OpenAlex ID: W1977785078
cites work: Steady pore pressure profiles associated with a moving trench
cites work: Some qualitative properties of solutions of a generalised diffusion equation
cites work: SOME ASYMPTOTIC RESULTS FOR THE EFFECT OF COMPOSITION-DEPENDENT DIFFUSION ON THE GROWTH RATES OF PRECIPITATE PARTICLES
cites work: Q5509552
description: scientific article; zbMATH DE number 4074644