An analytical method to estimate spatially-varying thermal contact conductances using the reciprocity functional and the integral transform methods: Theory and experimental validation Ricardo S. Padilha a , Marcelo J. Colaço a,⇑ , Helcio R.B. Orlande a , Luiz A.S. Abreu b a Department of Mechanical Engineering (PEM/COPPE), Federal University of Rio de Janeiro (UFRJ), Cx. Postal 68503, Rio de Janeiro, RJ 21941-972, Brazil b Department of Mechanical Engineering and Energy, Rio de Janeiro State University (UERJ/IPRJ), Rua Bonfim, 25, Vila Amélia, Nova Friburgo, RJ 28625-570, Brazil article info Article history: Received 8 December 2015 Received in revised form 1 April 2016 Accepted 16 April 2016 Available online 13 May 2016 Keywords: Inverse heat transfer problem (IHTP) Reciprocity functional Classical integral transform technique (CITT) Thermal contact conductance abstract The increasingly interest in using composite materials in engineering application requires the proper knowledge of the interaction that occurs between their layers. One of these interactions is related to the temperature jump and heat flux through the interface of different materials, known as thermal contact resistance, or its reciprocal, the thermal contact conductance. Methods to estimate thermal contact resistance usually require temperature measurements taken inside the sample (test body) and complicated experimental arrangements. In this work we propose an analytical, non-iterative and non-intrusive method to solve an inverse heat transfer problem in order to estimate a one- dimensional steady-state distribution of the thermal contact conductance, combining the reciprocity functional and the Classical Integral Transform Technique (CITT). This paper is an extension of our pre- vious works, where the solution procedure was developed numerically and required the solution of two linear systems. In this paper, the estimate is reduced to a single algebraic equation. The method was applied to some test cases using simulated measurements and results were compared with the exact solution showing a good agreement between them. A validation involving a double-layered material was also conducted, where an infrared camera was used to measure the temperature non-intrusively. A micromachinery produced flaw was created in the contact between the two materials and, once the temperature measurements were available, the method was able to identify the flaw location in 0.2 s using an Intel Atom(TM) CPU N450 1.66 GHz. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Many processes in engineering and related sciences require the complete knowledge of the interaction that occurs in the interface of materials or living bodies, or even in mixed boundaries, such as a material body and a living organism that are placed in contact. These interfaces usually present some gaps between the materials. One of these interactions is related to the heat transfer process in the contacting interface of two bodies where a temperature dis- continuity exists. This temperature jump is the result of a thermal resistance to the heat flux in the interface, been called thermal con- tact resistance, or its reciprocal, thermal contact conductance-TCC. In many industrial applications the previous knowledge of the TCC is essential for the design and proper operation of systems and equipment, such as in aerospace [1], electronic [2], nanoparti- cles [3], refrigeration [4], heat exchangers [5] and aviation engines [6]. Most of existing procedures to estimate TCC are experimental and require very complex techniques and complicated arrange- ments. In addition, many of these techniques also require the knowledge of the surface profiles of the materials in contact, such as their roughness, and temperature measurements taken inside the materials, close to the contact interface. Physically, the interface of two materials is characterized by an irregular distribution of micro regions. Only in some parts of these micro regions the materials are in perfect contact. When the mate- rials are submitted to a heat flux, in micro regions where the mate- rials are in contact the temperature across the interface presents continuity, while in micro regions without contact a temperature discontinuity between the contacting surfaces is observed. Consid- ering this, TCC (h C ) is defined as the ratio of the heat flux (q C ) to the temperature jump (DT C ) at the interface C between the materials: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.04.052 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: rspadilha@hotmail.com (R.S. Padilha), colaco@ufrj.br (M.J. Colaço), helcio@mecanica.ufrj.br (H.R.B. Orlande), abreu.l@gmail.com (L.A.S. Abreu). International Journal of Heat and Mass Transfer 100 (2016) 599–607 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt