Thermoelastic mechanical and heat conduction study through inverse method and transfer functions

• Published in: International journal of heat and mass transfer 2019-06, Vol.135, p.1260-1268
• Main Authors: Bauzin, Jean-Gabriel, Nguyen, Minh-Nhat, Laraqi, Najib, Vaca Hernández, Andrea, Dehmani, Anas
• Format: Article
• Language: English
• Subjects: Analytical thermoelastic resolution; Conduction heating; Conductive heat transfer; Cylinders; Displacement; Engineering Sciences; Inverse method; Inverse thermoelastic problem; Laser surface treatment; Regularization; Regularization methods; Stretching; Temperature distribution; Thermal displacement; Transfer functions
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2019.02.049

•An original analytical transfer function is established for a thermoelastic problem.•An inverse thermoelastic method is proposed to study the effect of a laser treatment.•The method is validated by comparison to available theoretical and experimental data.•The proposed method is generalized to noised measurements by regularization. This study proposes an inverse thermoelastic methodology, to study the effect of a laser treatment being applied to the surface of a thin cylinder bonded to a displacement sensor. By means of an analytical approach, we establish the thermoelastic transfer function between the temperature of the heated surface, and the mechanical dilatation of the cylinder. Subsequently we measure, at discrete time intervals, the displacement of an internal point of the cylinder; we then apply a deconvolution product to those measurements, in order to identify the temperature of the heated surface. In this way, it is no longer necessary to know the temperature field to solve the thermoelastic problem of our experimental device. Then, two examples drawn from previous works, one theoretical, the other experimental, are used to demonstrate the accuracy and efficiency of our approach based on the measurement of thermal displacements. Lastly, we demonstrate that our inversion procedure can be applied successfully even for situations where the measurement signal is affected by noise, through using the Tikhonov regularization method.