Abstract The variations in the total effective thermal conductivity ( k eff , t ) of a tetrakaidecahedra unit cell structure as functions of porosity ( ϕ ), thermal conductivity of the solid phase ( k s ) and the average temperature of the medium ( T avg ), in the presence of combined conduction and radiation heat transfer, are presented in this article. For this purpose, the governing energy conservation equation is numerically solved using the blocked-off region approach based on the finite volume method. In addition, the variations in the radiative properties of the structure as functions of surface reflectivity ( ρ s ), pore density ( PPC ) and ϕ are investigated, for which, a pure radiation heat transfer based numerical model is developed and used. From the detailed numerical simulations, three different correlations for k eff , t are proposed. Correlation 1 is developed by fitting the raw simulated data, although its form does not respect some of the limiting conditions. Particularly for k s 5 W / mK and in the absence of thermal radiation, it under-predicts the effective thermal conductivity due to pure heat conduction ( k eff , PC ). Correlation 2, on the other hand, satisfies all possible limiting conditions, although it requires one additional simulation or correlation for k eff , PC . Finally, correlation 3 is obtained by superposing the effective thermal conductivities due to pure radiation ( k eff , R ) and k eff , PC , while introducing an adjustable coefficient in order to account for the coupling between them. From the investigation on radiative properties, it is observed that the extinction coefficient increases with the decrease in ϕ and with the increase in PPC as well as ρ s and hence k eff , t as well as k eff , R is expected to decrease for these conditions.

中文翻译：

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存在联合传导和辐射传热的情况下，开发四面体结构有效热导率的相关性

摘要 四面体晶胞结构的总有效热导率 (k eff , t ) 作为孔隙率 ( ϕ )、固相热导率 ( ks ) 和介质平均温度 ( T avg ) 的函数的变化，在存在组合传导和辐射传热的情况下，在本文中进行了介绍。为此，使用基于有限体积方法的封闭区域方法对控制能量守恒方程进行数值求解。此外，研究了作为表面反射率 ( ρ s )、孔隙密度 ( PPC ) 和 ϕ 函数的结构辐射特性的变化，为此，开发并使用了基于纯辐射传热的数值模型。根据详细的数值模拟，k eff 的三种不同相关性，t 被提议。相关性 1 是通过拟合原始模拟数据得出的，尽管其形式不符合某些限制条件。特别是对于 ks 5 W / mK 并且在没有热辐射的情况下，由于纯热传导 (k eff , PC )，它低估了有效热导率。另一方面，相关性 2 满足所有可能的限制条件，尽管它需要对 k eff , PC 进行一次额外的模拟或相关性。最后，通过叠加由纯辐射 (k eff , R ) 和 k eff , PC 引起的有效热导率，同时引入可调节系数以解决它们之间的耦合，从而获得相关性 3。从辐射特性的调查来看，