Abstract
The effective thermal conductivity of composite materials can be calculated when the temperature distribution in the body is known.
The present paper deals with a numerical analysis on the effective thermal conductivity of filament assembly, where the filaments lie in parallel and at regular intervals with each other. In this case, a filament of circular cross section surrounded by matrix can be considered as a unit model of rectangular profile. Further, it is assumed that two surfaces of the model are isothermal and opposite to each other in parallel to the filament axis, and that residual others are insulated. Then a quarter of the model can be used as an element. The mumerical analysis is applied to this model as the two-dimentional steady state heat conduction problem, and the procedure is as follows:
(1) To replace the element under consideration by a various rectangular-grid network.
(2) Calculation of the temperature distribution in the element by means of the so-called iteration method.
(3) Calculation of the effective thermal conductivity using the rates of heat flow in and out across the isothermal surfaces of the element.
From the method described above, a new result is obtained. The value K/Km of the filament assembly composed of circular filaments lying in a line and in contact with two opposite isothermal surfaces may be expressed by the following equation:
K: Effective thermal conductivity of filament assembly Ks: Thermal conductivity of a filament Km: Thermal conductivity of matrix f: Filament volume fraction
This equation will be confirmed in the experiments in the succeeding paper.
