Many Materials which consist of substances having different thermal conductivities have been used in various engineering fields. It is necessary to obtain the thermal property of these materials in order to study the heat transfer problems concerned with these materials. The effective thermal conductivity of dispersed materials such as suspensions and emulsions, which are considered as homogeneous and isotropic in macroscopic view have been investigated theoretically and experimentally by Maxwell, Fricke, Hamilton et al., and predicting formulae have been proposed. However, there are other materials containing armature (steel frame, etc.) in matrix (concrete, insulation materials, etc.), and they are used in many fields such as architecture. The composite materials described above which are heterogeneous in macroscopic view are also dipersed materials in wider difinition. But, on the thermal conductivity of the composite materials, a few examples are written as the values of over-all coefficient of heat transmission, and there are little investigations. From this standpoint, in this paper, the thermal conductivity of composite materials are studied by numerical method, and the factors which affect thermal conductivity are analyzed, and the predicting formula containing several factors is proposed. Main results obtained are as follows: 1) The effect of armature on the temperature field is not proportional to its width but is arithmetically. 2) The over-all coefficients of heat transmission increase with increasing Biot modulus, but increasing rate becomes gradually small and the coefficients reach each values asymptoticaly. 3) The predicting formula of composite materials proposed in the present paper is λ_e^*=(λ_d^*+K-Kφ(1-λ_d^*))/(λ_d^*+K+φ(1-λ_d^*)) where, K=2.0D_d^<*n_1>L_d^<*n_2> This equation is able to estimate the thermal conductivity of composite materials to within ±3% in the range of the thermal conductivity ratio λ_d^*≦10^3, of L_d^*≦0.2, of D_d^*≦1.0 and of L_o^*≦5.0, and has wider range applicability than previous equations.
View full abstract