Identification of time-varying inaccessible thermal conductance from data at the boundary

ABSTRACT

A composite specimen, made of two slabs and an interface A is heated through one of its sides S, in order to evaluate the thermal conductance H of A. The direct model consists of a system of Initial Boundary Value Problems completed by suitable transmission conditions. Thanks to the properties of multilayer diffusion, we reduce the problem to the slab between A and S only. In this case evaluating the thermal resistance of A means to identify a coefficient in a Robin boundary condition. We evaluate H numerically by means of Thin Plate Approximation.

KEYWORDS:

• Inverse problems
• heat equation
• layered materials

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 80A23
• 74A45

Disclosure statement

No potential conflict of interest was reported by the authors.