辐射下加热腔内自然对流传热特性研究

Characterization of Natural Convection Heat Transfer in a Heated Cavity under Radiation

摘要: 辐射吸收引发的自然对流现象广泛存在于自然界以及工业领域，为了探究辐射引发的自然对流传热特性，采用理论分析与数值模拟相结合，对由下方入射辐射加热二维方腔内半透明流体所引发的自然对流进行研究。结果表明：同一瑞利数下，流体失稳时间随光学厚度τ 的增加而减小，当τ=20 时，流体失稳时间最短；通过尺度分析推导出当光学厚度τ → 0 时，热边界层厚度与瑞利数及光学厚度之间满足标度率： ，并将数值模拟结果与之对比， Ra_I数的标度指数基本吻合；同时发现，不同光学厚度下， Nu数随着Ra_I 数的增加而逐渐增大，随着光学厚度的增加， 中的标度指数β 反而减小；最后采用数值模拟方法，得到了Nu 数与光学厚度及Ra_I 数之间的标度关系： ，并利用尺度分析方法推导出光学厚度τ → 0 时， Nu数与光学厚度τ 满足： 。

Abstract: The phenomenon of natural convection induced by radiation absorption exists widely in nature as well as in industry. In order to investigate the heat transfer characteristics of radiation-induced natural convection, a combination of theoretical analyses and numerical simulations is used to in-vestigate the natural convection induced by incident radiation from below heating a two-di- men-sional square cavity with a semi-transparent fluid. The results show that at a constant Rayleigh number, the fluid destabilization time decreases with the increase of the optical thickness, when τ=20, with a large fluctuation of the temperature at the lower wall surface; through the scale analysis, it is deduced that when the optical thickness τ → 0 , the scale rate is satisfied between the temperature boundary layer thickness and the Rayleigh number and the optical thickness: , and the numerical simulation results are compared with it, and the scale exponent of the Rayleigh number Ra_I is basically coincident. It is also found that the Nu num-ber gradually increases with increasing Ra_I number for different optical thicknesses, and the scaling index β in decreases instead with increasing optical thickness. By using the numerical simulation method, the scaling relationship between the Nu  number and the optical thickness and Ra_I number is obtained: , and the scaling analysis method is used to deduce that the Nu number and the optical thickness τ satisfy: when the optical thickness τ → 0.