Analytical Study on Effective Thermal Conductivity of Three-Phase Composites

Abstract

Effective thermal conductivity of three-phase composites, consisting of matrix and two kinds of spherical inclusions, has been derived as an explicit form by extending modified Eshelby model (MEM) for two-phase composites. The present results are compared with those by differential effective medium model (DEMM), which are also compared with the experimental results of two-and three-phase composites in the literatures to be validated. For two-phase composites, the results by MEM are better than those by DEMM for the inclusion volume fraction smaller than 0.5. Comparisons between the results by two models and experimental results have been made for three-phase composite, resulting in that MEM predicts better than DEMM for smaller volume fraction of the inclusion having larger inclusion-to-matrix thermal conductivity ratio, but DEMM predicts better as its volume fraction increases. It has been observed through parametric study that its volume fraction is the critical factor affecting the deviation of predictions by the two models. The results by them show a good agreement with the three-phase composite proposed by Molina et al..

Effects of Magnetite Aggregate and Steel Powder on Thermal Conductivity and Porosity in Concrete for Nuclear Power Plant

“…(1) DEMM (Differential Effective Medium Model) [21][22][23]. The generalized DEMM with different components can be written as (3) with 1st differential equation form:…”

“…(2) MEM (Modified Eshelby Model) [22][23][24]. In the MEM, 2 spherical components with different thermal conductivity are irregularly arranged in concrete with constant thermal conductivity and it is subject to constant thermal velocity of 0 ( 3 direction).…”

“…In Figure 2, constant thermal velocity ( 0 ) can be written as (7) in which and 0 are equivalent thermal conductivity matrix and constant thermal gradient without components. When the fluctuating temperature in the composite is integrated, the result is zero so that the condition of (8) can be assumed [22,23]: The intrinsic temperature gradient can be obtained as (9a) and (9b) through matrix transformation:…”

Study on Analysis Technique Comparison and Evaluation of High Thermal Conductivity Concrete with Magnetite Aggregates and Steel Powder

“…15) 이 연구에서는 DEMM 을 연속하여 2회 적용하는 기법을 사용하였다. 일반화된 DEMM을 여러 종류의 구형 입자가 포함된 복합재에 적 용하면 등가열전도계수는 다음과 같은 일차 비선형 미분 방정식으로 표현된다 10,15).…”

“…3개의 재료가 복합적으로 들어있는 경우에는 먼저 모 재에 포함되는 2가지 종류의 구형 입자중 한 종류만 모 재에 포함된 복합재의 열전도계수로 가정하여 계산한 뒤, 이를 새로운 모재로 간주한다. 이 모재의 열전도계수 (  )와 원모재의 열전도계수(  )의 관계는 비선형 3차 방정식으로 식4(a)와 4(b)와 같이 표현할 수 있다 10).…”