This work presents a hybrid approach to solve the unsteady one-dimensional coupled heat conduction-radiation problem in a non-gray semitransparent planar medium. The diffusely absorbing/emitting medium scatters radiation anisotropically and is bounded by two gray or non-gray parallel planar surfaces that are diffuse in emission and diffuse or specular in reflection. A combination of the Discrete Ordinate Method (DOM) to discretize the angular coordinate of the Radiative Transfer Equation (RTE) and the Generalized Integral Transform Technique (GITT) to solve the energy equation is proposed as a solution approach. To account for the spectrally varying nature of the radiative properties, the entire wavelength spectrum is discretized into bands in which the radiative properties are assumed to be constant. The versatility and accuracy of the proposed methodology are verified against data from the literature for different spectrally varying radiative parameters (extinction coefficient, absorption coefficient, albedo), scattering phase functions, and emissivity/reflectivity boundaries. The results obtained for the temperature field, incident radiation, and heat fluxes showed that the GITT/DOM combination is suitable for solving coupled conduction-radiation problems for gray or non-gray media and, due to its hybrid numerical-analytical nature, can be used as a benchmarking tool.

中文翻译：

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非灰色半透明平面介质中的传导-辐射传热：积分变换与离散坐标法相结合


这项工作提出了一种混合方法来解决非灰色半透明平面介质中的不稳定一维耦合热传导辐射问题。漫吸收/发射介质各向异性地散射辐射，并由两个灰色或非灰色平行平面表面界定，这两个平面在发射中是漫射的并且在反射中是漫射或镜面反射的。提出了一种结合离散坐标法（DOM）来离散化辐射传递方程（RTE）的角坐标和广义积分变换技术（GITT）来求解能量方程的方法。为了考虑辐射特性的光谱变化性质，整个波长谱被离散成多个频带，其中假设辐射特性是恒定的。所提出方法的多功能性和准确性根据不同光谱变化辐射参数（消光系数、吸收系数、反照率）、散射相函数和发射率/反射率边界的文献数据进行了验证。温度场、入射辐射和热通量的结果表明，GITT/DOM 组合适合解决灰色或非灰色介质的耦合传导辐射问题，并且由于其混合数值分析性质，可以用作基准测试工具。