Thermal conductivity of graded spherical composites with contact resistance

The effective thermal conductivity of graded composites with contact resistance on the inclusion surface is investigated. As an example, we have considered the graded composite media with a spherical particle embedded in a homogeneous matrix, where the thermal conductivity of spherical inclusion is an exponential function k(i) = c exp(betar) (where r is the inside distance of a point in particle from the center of the spherical particle in a spherical coordinate). For both heat contact resistance and perfect contact cases, we have given a reasonable effective medium approximation to calculate the effective conductivity. (C) 2003 Elsevier B.V. All rights reserved.

Effective thermal conductivity of graded nonlinear composites with heat contact resistance

The perturbation expansion method is used to find the effective thermal conductivity of graded nonlinear composites having thermal contact resistance on the inclusion surface. As an example, we have studied the graded composites with cylindrical inclusions immersed in a homogeneous matrix. The thermal conductivity of the cylindrical inclusion is assumed to have a power-law profile of the radial distance r measured from its origin. For weakly nonlinear constitutive relations between the heat flow density q and the temperature field T, namely, q = -mu del T - chi vertical bar del T vertical bar(2) del T, in both the inclusion and the matrix regions, we have derived the temperature distributions using the perturbation expansion method. A nonlinear effective medium approximation of graded composites is proposed to estimate the effective linear and nonlinear thermal conductivities. by considering the temperature singularity on the inclusion surface due to the heat contact resistance. (c) 2006 Elsevier B.V. All rights reserved.