a b s t r a c tInverse problems can be found in many areas of science and engineering and can be applied in different ways. Two examples can be cited: thermal properties estimation or heat flux function estimation in some engineering thermal process. Different techniques for the solution of inverse heat conduction problem (IHCP) can be found in literature. However, any inverse or optimization technique has a basic and common characteristic: the need to solve the direct problem solution several times. This characteristic is the cause of the great computational time consumed. In heat conduction problem, the time consumed is, usually, due to the use of numerical solutions of multidimensional models with refined mesh. In this case, if analytical solutions are available the computational time can be reduced drastically. This study presents the development and application of a 3D-transient analytical solution based on Green's function. The inverse problem is due to the thermal properties estimation of conductors. The method is based on experimental determination of thermal conductivity and diffusivity using partially heated surface method without heat flux transducer. Originally developed to use numerical solution, this technique can, using analytical solution, estimate thermal properties faster and with better accuracy.
This study presents a new experimental technique to obtain the thermal conductivity of conductor and non-conductor materials of small dimensions. 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, T(t), proportional to the heat flux input using inverse techniques; (iii) estimation of thermal diffusivity; (iv) comparison between this heat flux, T(t), with the total heat flux supplied by the heating element P/S 1 to estimate the thermal conductivity of the sample.
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