THERMAL SCIENCE

International Scientific Journal

SIMPLE AND ACCURATE CORRELATIONS FOR SOME PROBLEMS OF HEAT CONDUCTION WITH NONHOMOGENEOUS BOUNDARY CONDITIONS

ABSTRACT
Heat conduction in solids subjected to non-homogenous boundary conditions leads to singularities in terms of heat flux density. That kind of issues can be also encountered in various scientists’ fields as electromagnetism, electrostatic, electrochemistry and mechanics. These problems are difficult to solve by using the classical methods such as integral transforms or separation of variables. These methods lead to solving of dual integral equations or Fredholm integral equations, which are not easy to use. The present work addresses the calculation of thermal resistance of a finite medium submitted to conjugate surface Neumann and Dirichlet conditions, which are defined by a band-shape heat source and a uniform temperature. The opposite surface is subjected to a homogeneous boundary condition such uniform temperature, or insulation. The proposed solving process is based on simple and accurate correlations that provide the thermal resistance as a function of the ratio of the size of heat source and the depth of the medium. A judicious scale analysis is performed in order to fix the asymptotic behaviour at the limits of the value of the geometric parameter. The developed correlations are very simple to use and are valid regardless of the values of the defined geometrical parameter. The performed validations by comparison with numerical modelling demonstrate the relevant agreement of the solutions to address singularity calculation issues.
KEYWORDS
PAPER SUBMITTED: 2016-04-11
PAPER REVISED: 2016-05-10
PAPER ACCEPTED: 2016-06-25
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160411243L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 1, PAGES [125 - 132]
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© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence