The Inverse Problems in Determining the Optimal Filler Shape of Composite Materials for Maximum Effective Thermal Conductivity

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The inverse problems in determining the optimal geometry of filler shape between two conductive bodies in a two-dimensional and three-dimensional multiple region domains, based on the desired thermal conductivity ratio and content of filler, are examined in the present study. The Levenberg-Marquardt method (LMM), B-Spline curve generation technique and commercial software CFD-ACE+ are utilized in this inverse design algorithm. In chapter two, the validity of this two-dimensional shape design analysis is examined using the numerical experiments. Different filler content and conductivity are considered in the numerical test cases to justify the validity of this study. The estimated results in the present work are then compared with the existing filler shapes designed by Zhang et al. [1] and it is found that (i) by fixing the filler conductivity, the effective thermal conductivity can be increased from 36.4% to 50.5% depending on different content of filler and (ii) by fixing the filler content, the effective thermal conductivity can be increased from 35.3% to 63.4% depending on different filler conductivity. Moreover, it is also concluded that the optimal fillers are not of “I” shape, which was suggested by Zhang et al. [1], instead, they are in a family of “T-like” shape. In chapter three, a three-dimensional filler shape is generated by a B-spline surface and different filler content and conductivity are also considered in the numerical experiments. It is found that (i) by fixing the filler conductivity, the effective thermal conductivity can be increased from 3.29% to 30.7% depending on different volume of filler and (ii) by fixing the filler volume, the effective thermal conductivity can be increased from 5.89% to 15.2% depending on different filler conductivity, it is also conclude that they are in the family of “Tee” shape.