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^{1}Federal University of Uberlândia, School of Mechanical Engineering, Brazil

**Keywords:** experimental technique, inverse problem, temperature measurement, thermal properties measurement**property:** thermal conductivity, thermal diffusivity**material:** polymers, copper

This study presents an experimental technique to obtain the thermal conductivity of conductor and non conductor materials of small dimensions [1]. As usual, the thermal conductivity estimation involves a thermal model with a known heat flux input. The main contribution of this study is the use of inverse techniques to estimate the heat flux input instead of measuring with heat transducers. It can be observed that the presence of transducers represents an additional experimental limitation for small samples. Besides the experimental difficulties, the smaller the transducer dimensions the more difficult it is to obtain the calibration curves due to the low sensitivity. The procedure proposed here is based on the following steps: i) development of experimental apparatus and thermal model considering a heat flux input in part of the sample surface while the remaining surfaces are kept isolated; ii) estimation of a dimensionless heat flux, Ф(t), proportional to the heat flux input using inverse techniques; iii) estimation of thermal diffusivity; iv) comparison between this heat flux, Ф(t), with the total heat flux supplied by the heating element P/S1 to estimate the thermal conductivity of the sample. The technique proposed here can be applied to a large range of materials as isolating materials with thermal conductivity of order of 0.07 W/mK (Skamol) and 401 W/mK (copper). Although different thermal model or experimental apparatus must be used depend on the sample the conception of the method is unique. The great advantage of the technique is the estimation of thermal diffusivity without knowing the heat flux imposed in the frequency domain. The basic idea here is the observation that the delay between the experimental temperature and the heat flux imposed is an exclusive function of thermal diffusivity. Therefore, the minimization of an objective function, Sp, based on the difference between experimental and calculated values of the phase is used to determine the thermal diffusivity. The procedure that eliminates the needs of heat flux sensor gives a great flexibility to the technique allowing the technique to deal with sample of small dimensions. An experimental apparatus must have enough sensitivity and reproduce the thermal conditions assumed in the thermal model. Therefore the boundary conditions present in the theoretical model must be guaranteed in the experimental apparatus. This means that the isolated condition at the reminiscent surface needs to be reached for the success of the estimation technique. An analysis demonstrates the validity of these hypotheses.

- V. L. Borges, P. F. B Sousa, G. Guimarães, Inverse Problems in Science & Engineering ( 2008) doi:10.1080/17415970802166659

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