ESTIMATION OF THERMAL CONDUCTIVITY OF POROUS MATERIAL WITH FEM AND FRACTAL GEOMETRY

The relationship between thermal conductivity of porous material and fractal dimension is numerically simulated by using the finite element method. The solid matrix and pore space are generated randomly according to material porosity. Material parameters and element properties are changed by using ANSYS parameter design language. The effective thermal conductivity is derived according to thermal flux through some sections computed by FEM and Fourier heat transform law. The investigation shows that the effective thermal conductivity decreases with increasing porosity. The effective thermal conductivity will decrease exponentially with increasing fractal dimension of porosity space and increase exponentially with increasing fractal dimension of solid matrix.

On generalized heat polynomials

We consider the generalized heat equation ofnthorder∂2u∂r2+n−1r∂u∂r−α2r2u=∂u∂t. If the initial temperature is an even power function, then the heat transform with the source solution as the kernel gives the heat polynomial. We discuss various properties of the heat polynomial and its Appell transform. Also, we give series representation of the heat transform when the initial temperature is a power function.