This paper focuses on a numerical investigation of steady two-dimensional natural convection and volumetric radiation interactions in a concentric annulus between two square isothermal cylinders. The annulus is filled with a gray absorbing–emitting and non-scattering medium. All the walls are assumed to be gray, diffuse, and opaque. The dynamic and thermal interactions are studied through a finite volume method combined with an immersed boundary technique to handle the square-shaped cylinder, whereas the discrete ordinates method is used to solve the radiative transfer equation. The present study is performed to investigate the effect of volumetric radiation on the flow for a variety of Rayleigh numbers ${10}^3–{10}^6$, three different optical thicknesses $\tau =0.2–1–5$, a variety of Planck numbers 0.01–1, and three different aspect ratios $A=0.2–0.4–0.6$. The analysis is based on the dynamic and thermal fields in addition to the heat transfer rate. Results show that radiation affects significantly the flow and temperature distributions for a higher Rayleigh number $Ra>{10}^4$, depending on the Planck number. The optical thickness and the aspect ratio has an important impact on the Nusselt number and percentage of radiation in heat transfer.

本文着重于两个方形等温圆柱体之间的同心环空中，稳定的二维自然对流和体积辐射相互作用的数值研究。环空填充有灰色的吸收性和非散射性介质。假定所有墙都是灰色的，散布的和不透明的。通过有限体积法与沉浸边界技术相结合来研究方形圆柱体的动力和热相互作用，而离散坐标法则用于求解辐射传递方程。进行本研究是为了研究体积射线对各种瑞利数的影响${10}^3–{10}^6$，三种不同的光学厚度 $\tau =0.2–\mathrm{1个}–5$，各种普朗克数0.01–1和三种不同的长宽比 $\mathrm{一种}=0.2–0.4–0.6$。除传热速率外，分析还基于动态和热场。结果表明，对于较高的瑞利数，辐射会显着影响流量和温度分布$\mathrm{[R}\mathrm{一种}>{10}^4$，具体取决于普朗克编号。光学厚度和纵横比对热传递中的努塞尔数和辐射百分比有重要影响。