Non-Destructive Testing of Thermal Resistances for a Single Inclusion in a 2-Dimensional Domain

Abstract

The ability to determine whether there are any defects in the interior of an object without destroying it is an invaluable tool in today’s industries. One popular method for doing this is steady state thermal imaging. This paper outlines a process where steady state heat flow is used to determine the con- stitutive law governing how a single inclusion in an object resists the flow of heat. In particular, we will be concerned with circular domain D encapsulated inside an outer region Ω. Our goal is to produce a function which quantifies the behavior of the heat flow across the interface between Ω and D. That is, as we move along the inclusions boundary, we want to know at any particular point how much heat flow is being impeded. From this, we can make inferences as to how much disbanding or corrosion has occurred on the interface between Ω and D.