## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2012-08-26

PAPER REVISED: 2013-05-20

PAPER ACCEPTED: 2013-05-20

PUBLISHED ONLINE: 2013-06-16

**THERMAL SCIENCE** YEAR

**2013**, VOLUME

**17**, ISSUE

**3**, PAGES [665 - 672]

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