The onset of convection instability in a differentially heated layer consisting of gray and non-gray gaseous mixtures is studied numerically. The conditions investigated cover a wide range of Planck number values (\(Pl = \dfrac{\kappa k_T}{4\sigma T_0^3}\)), from the conduction-dominated regime of \(Pl\gg 1\) to the radiation-dominated regime of \(Pl \ll 1\). The linear stability theory is applied to mass, momentum and energy balance equations and the resulting linear stability equations are solved by Chebyshev spectral collocation method. The divergence of radiative flux is solved by the finite-volume-based discrete ordinates method. The Spectral Line Weighted sum of gray gas (SLW) model is used to represent the fine spectral variation of absorption coefficient for a non-gray gas medium. The results indicate that the critical Rayleigh number (\(Ra_c\)) for the onset of convection increases with mean temperature (\(T_0\)) in the conduction-dominated regime at low values of \(T_0\). In the radiation-dominated regime (\(Pl\ll 1\)), \(Ra_c\) decreases with \(T_0\) for gray media. If the medium is non-gray, the critical \(Ra_c\) reduces to even lower values (as compared with those of gray gases) due to the dependence of gas absorptivity on temperature \(T_0\). A reduction in the wall emissivity value increases the stability of the fluid layer due to reflection of radiation from the wall, in the radiation-dominated regime. The reverse trend is seen for \(Pl\gg 1\). The critical parameters also significantly depend on the concentrations of radiatively participating gases in the mixture. The temperature profile in the fluid layer transforms from a linear profile in conduction regime to a stratified profile with steep gradients near the walls, in the presence of non-gray participating gases.

数值研究了由灰色和非灰色气体混合物组成的差热层中对流不稳定性的开始。所研究的条件从\（Pl \ gg 1 \）的传导占主导地位的范围涵盖了广泛的普朗克数值（\（Pl = \ dfrac {\ kappa k_T} {4 \ sigma T_0 ^ 3} \））。到辐射占主导的\（Pl \ ll 1 \）。将线性稳定性理论应用于质量，动量和能量平衡方程，并通过Chebyshev谱配点法求解线性稳定性方程。辐射通量的发散通过基于有限体积的离散纵坐标法求解。灰色气体的光谱线加权总和（SLW）模型用于表示非灰色气体介质的吸收系数的精细光谱变化。结果表明，在以传导为主导的状态下，对流开始时的临界瑞利数（\（Ra_c \））随着平均温度（\（T_0 \））的增加而在\（T_0 \）的值较低时增加。在辐射占主导的状态（\（Pl \ ll 1 \））中，\（Ra_c \）随\（T_0 \）用于灰色介质。如果介质是非灰色的，则由于气体吸收率对温度\（T_0 \）的依赖性，临界值\（Ra_c \）降低到更低的值（与灰色气体相比）。在辐射主导的状态下，壁的辐射率值的减小会由于来自壁的辐射反射而增加流体层的稳定性。对于\（Pl \ gg 1 \）可以看到相反的趋势。关键参数还显着取决于混合物中辐射参与气体的浓度。在存在非灰色参与气体的情况下，流体层中的温度曲线从传导状态的线性曲线转变为壁附近具有陡峭梯度的分层曲线。