A generalized model for the effective thermal conductivity of porous media is derived based on the fact that statistical self-similarity exists in porous media. The proposed model assumes that porous media consist of two portions: randomly distributed non-touching particles and self-similarly distributed particles contacting each other with resistance. The latter are simulated by Sierpinski carpets with side length L = 13 and cutout size C = 3, 5, 7 and 9, respectively, depending upon the porosity concerned. Recursive formulae are presented and expressed as a function of porosity, ratio of areas, ratio of component thermal conductivities and contact resistance, and there is no empirical constant and every parameter has a clear physical meaning. The model predictions are compared with the existing experimental data, and good agreement is found in a wide range of porosity of 0.14-0.80, and this verifies the validity of the proposed model.
A new model, the self-similarity model, for effective thermal conductivity of porous media is proposed based on the thermal–electrical analogy technique and on statistical self-similarity of porous media. The proposed thermal conductivity model is expressed as a function of porosity (related to stage n of Sierpinski carpet), ratio of areas, ratio of component thermal conductivities, and contact resistance. A recursive algorithm for the thermal conductivity is obtained using the proposed model and is found to be quite simple. The predictions of the model are compared with those of other models and with existing measurements and good agreement was found. This proves that the proposed model is a valid one.
In this paper, an analytical expression for transverse thermal
conductivities of unidirectional fibre
composites with thermal barrier is derived based on the
electrical analogy technique and on the
cylindrical filament-square packing array
unit cell model (C-S model). The
present analytical expressions both with and without thermal barrier between
fibre and matrix are presented. The present theoretical predictions without
thermal barrier are found to be in excellent agreement with the existing
analytical model and nomogram from the
finite difference method (FDM), and
in good agreement with existing experimental data.
Furthermore, the present
analytical predictions with thermal barrier
can best fit the experimental data and can provide a
higher accuracy than the finite element method (FEM). The validity of the
present analytical solution is thus verified for transverse thermal
conductivities of unidirectional fibre
composites with thermal barrier.
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