Heat Conduction in Heterogeneous Solid Mixtures : 1st Report, The Apparent Thermal Conductivity of a Mixture Containing Parallel Fiber Elements of Random Distribution

Abstract

In this report, apparent thermal conductivity perpendicular to the fiber of compound material, which contains parallel fiber elements of irregular distribution, is discussed. (1) Concerning many compound materials which are taken at random using random numbers, the values λ/λ (the ratios of apparent thermal conductivities λ and conductivities P of models of parallel arrangement λ_P) are shown to be approximated by a linear function of η (the volume ratio of discontinuous phase), for η = 0∼0.2. (2) Defining ξ=λ_P/λ_h, where λ_h is the value for uniform fiber distribution, the value of ξ is discussed statistically. (3) Considering (1) and (2), the approximate equation of apparent thermal conductivity is derived as, λ/λ_c = [(1+Fη)ξ]/[(λ_c/λ_d)η+1-η], F=1.08-6.8/[(λ_d/λ_c)+5.3], (η=00.2, λ_d≥λ_c, l/d≥10) which is shown to agree within an error of 8% with the experimental data of electrolytic bath.