Weighted Residual-Self Consistent Method For Effective Thermal Conductivity Of Particulate Composites

A new micromechanical method, the Weighted Residual Self-Consistent Scheme (WRSCS) is developed to study the thermal conduction of two-phase composite with arbitrary geometry of particulates.The micromechanics model of Self-Consistent Scheme is that a particle is embedded in a homogeneous and isotropic medium whose conductivity is the unknown. At infinite distance from the particle a homogeneous boundary condition is prescribed. For some typical configurations of the inclusions, for example, for spherical or ellipsoidal inclusions, the thermal conduction problem of the composite can be solved without much difficulty using self-consistent method. But for arbitrary geometry of particulates, such as polygon or other irregular configurations, the analytical solution is impossible or hard to obtain. In the WRSCS, the self-consistent model is used to describe the complex configurations of the particulate composite and the temperature field is solved by weighted residual collocation method with some proper simplifications. This method provides a more efficient way of setting up the algebraic equations corresponding to the governing differential equations. The prediction formula for the effective thermal conductivity of the composite is obtained.The average thermal intensity inside the particle is obtained based on the solution of the temperature field inside the particle. The effective thermal conductivities for composites with different particulate geometry are calculated by using the prediction formula. For the case of circular and elliptical inclusion, the result from the WRSCS is almost the same with the one from standard self-consistent method. Examining results corresponding to different particulate geometry, it shows that the effective thermal conductivity not only depends upon the volume fractions and the properties of components, but also depends on the particulate geometry.