In a layered thermal conductor, the inaccessible interface could be dam- aged by mechanical solicitation, chemical infiltration, aging. In this case, the original thermal properties of the specimen are modified. The defect occurs typically in form of delamination. The present paper deals with nondestructive evaluation of interface ther- mal conductance h from the knowledge of the surface temperature when the specimen is heated in some controlled way. The goal is achieved by expanding h in powers of the thickness of the upper layer. The mathematical analysis of the model produces exact formulas for the first coefficients of h which are tested on simulated and real data. The evaluation of interface flaws comes from reliable approximation of h.

A hidden defect D affecting the interface in a layered specimen is evaluated from temperature maps collected on its top side. An explicit formula that approximates thermal conductance of the damaged interface is derived by means of first order Thin Plate Approximation. This formula is used to obtain a geometrical description of D from experimental data.

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical solution of the underlying direct mathematical model. Usually, this step requires specific techniques in order to limit an abnormal use of memory resources and computing time due to excessively fine meshes necessary to follow a very thin fracture in the domain. Our contribution to this problem consists in decomposing the temperature of the damaged specimen as a sum of a term (with known analytical form) due to an infinite virtual fracture and the solution of an initial boundary value problem for the heat equation on one side of the fracture (i.e. on a rectangular domain). The depth of the fracture is a variable parameter in the boundary conditions that must be estimated from additional data (usually, measurements of the surface temperature). We apply our method to the detection of simulated cracks in concrete and steel specimens.

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.

Longitudinal defects of the internal coated surface of a metal pipe can be evaluated in a fast, precise and cheap way from thermal measurements on the external surface. In this paper, we study two classes of real situations in which the thickness of the coating is much smaller than the thickness of the metal tube: the transportation of potable water and crude oil. A very precise and stable reconstruction of damages is obtained by means of perturbation methods. To do this, first we translate a composite (coating-plus-tube) boundary value problem in a virtual one on the metallic part only. The information about possible damages is now included in the deviations delta h of the effective heat transfer coefficient from a known background value. Finally, we determine delta h by means of Thin Plate Approximation. (C) 2017 Elsevier Ltd. All rights reserved.

Viene studiata l'evoluzione nel tempo del degrado del rivestimento interno di un tubo metallico al cui interno scorre un fluido. Il degrado si manifesta in tagli longitudinali del rivestimento. Per questo motivo il problema puo' essere posto e risolto (per mezzo di Thin Plate Approximation) in due dimensioni. We deal with the mathematical model of the incremental degradation of the internal coating (e.g. a polymeric material) of a metallic pipe in which a fluid flows relatively fast. The fluid drags solid impurities so that longitudinal scratches, inaccessible to any direct inspection procedure, are produced on the coating. Time evolution of this kind of defects can be reconstructed from the knowledge of a sequence of temperature maps of the external surface. The time-varying orthogonal section of this damaged interface is determined as a function of time and polar angle through the identification of a suitable effective heat transfer coefficient by means of Thin Plate Approximation.

We derive a rule for the reconstruction of the internal heat transfer coefficient hint of a pipe, from temperature maps collected on the external face. The pipe is subjected to internal heating by connecting two electrodes to the external surface. To estimate hint we apply the perturbation theory to a thin plate approximation of a boundary value problem for the stationary heat equation.[object Object]

Infrared thermography is widely used in non-destructive testing and in the non-destructive evaluation of subsurface defects in several materials. The detection and reconstruction (location and shape) of a defect inside a material from thermal data requires the solution of an inverse heat conduction problem. Here the problem is tackled by the thin-plate approximation of the investigated domain. A number of physical quantities must be known for the reconstruction procedure to be successful: some relating to the material (thermal conductivity, heat capacity, density), usually known, and others relating to the heating process. This paper proposes procedures for accurately measuring the latter, whose importance is often not given due consideration. Those procedures allow us to accurately measure the heat flux distribution produced by the sources on the heated surface, and the heat exchange coefficient at the remaining surfaces, and are easily applicable in 'on field' situations.

We derive and test a formal explicit approximated rule for the reconstruction of a damaged inaccessible portion of the boundary of a thin conductor from thermal data collected on the opposite accessible face.