The current article investigates the effects of nonlinear mixed convection flow in an upright channel with asymmetric or symmetric heating and cooling conditions, considering the influence of temperature-dependent thermal conductivity. The momentum equation is approximated using the nonlinear Boussinesq approximation in the buoyancy force term. Computational solutions for the dimensionless partial differential equations are obtained through the use of an unconditionally stable and convergent implicit finite difference technique. A regular perturbation series approach is employed to ascertain steady-state solutions, facilitating the assessment of the correctness of the numerical approach. During the numerical computing process, it is observed that the nonlinearity in density variation with temperature, along with the mixed convection parameter and the symmetric or asymmetric heating and cooling of the plates, significantly influences flow generation. It is also noted that in the scenario of asymmetric heating, fluid motion is stronger at the bottom plate, whereas in the case of symmetric heating/cooling settings, the highest velocity is observed in the center of the channel.

本文研究了具有不对称或对称加热和冷却条件的直立通道中非线性混合对流的影响，并考虑了与温度相关的导热系数的影响。动量方程在浮力项中使用非线性 Boussinesq 近似来近似。无量纲偏微分方程的计算解是通过使用无条件稳定且收敛的隐式有限差分技术获得的。采用常规扰动级数方法来确定稳态解，有利于评估数值方法的正确性。在数值计算过程中，我们观察到密度随温度变化的非线性，以及混合对流参数和板的对称或不对称加热和冷却，显着影响流动的产生。还值得注意的是，在不对称加热的情况下，底板处的流体运动更强，而在对称加热/冷却设置的情况下，在通道中心观察到最高速度。