THERMAL SCIENCE

International Scientific Journal

Najib LaraqiORCID

,

E Monier-VinardORCID

NEW ANALYTICAL SOLUTION FOR SOLVING STEADY-STATE HEAT CONDUCTION PROBLEMS WITH SINGULARITIES

ABSTRACT
A problem of steady-state heat conduction which presents singularities is solved in this paper by using the conformal mapping method. The principle of this method is based on the Schwarz-Christoffel transformation. The considered problem is a semi-infinite medium with two different isothermal surfaces separated by an adiabatic annular disc. We show that the thermal resistance can be determined without solving the governing equations. We determine a simple and exact expression that provides the thermal resistance as a function of the ratio of annular disc radii.
KEYWORDS
thermal resistance, heat sources, conformal mappings, Dirichlet problem
PAPER SUBMITTED: 2012-08-26
PAPER REVISED: 2013-05-20
PAPER ACCEPTED: 2013-05-20
PUBLISHED ONLINE: 2013-06-16
DOI REFERENCE: https://doi.org/10.2298/TSCI120826070L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE No. 3, PAGES [665 - 672]
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New analytical solution for solving steady-state heat conduction problems with singularities

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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