Abstract Natural convection in an inclined cavity filled with saturated porous media has been investigated. A time-dependent solution using a spectral weighted residual method is determined. Preparing the governing equations by the substitution of the stream functions, we obtained a system of nonlinear ordinary differential equations. Integrating in time using the Runge-Kutta method of variable order the final system is determined. The study consisted of the investigation of the problem in the transient and unsteady modes. For each configuration, the solution is developed for different values of Rayleigh numbers and different inclination levels of the cavity. The high accuracy of the results with the reduced computational cost is well proved by the comparison with results determined using a finite element method that has shown an excellent agreement with our developed solution. This work is very efficient to understand from a physical insight the effect of the inclination parameters on the unsteady and transient mode of changes in the mechanisms of natural convection. The results provide a set of high-accurate data that can be used as a benchmark case for the time-dependent natural convection problems. As a result, the inclination effect of the cavity has clearly influenced the heat transfer process and the fluid flow. Therefore, the inclination can be considered as a control parameter for heat and fluid flow effectively.

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倾斜多孔腔中自然对流随时间解的全局方法

摘要 研究了充满饱和多孔介质的倾斜空腔中的自然对流。确定使用频谱加权残差方法的时间相关解。通过对流函数的代换来准备控制方程，我们得到了一个非线性常微分方程组。使用可变阶次的 Runge-Kutta 方法及时积分，确定最终系统。该研究包括对瞬态和非稳态模式中的问题的调查。对于每种配置，针对不同的瑞利数值和不同的腔倾角水平开发了解决方案。通过与使用有限元方法确定的结果进行比较，很好地证明了结果的高精度和降低的计算成本，该方法与我们开发的解决方案非常吻合。这项工作非常有效地从物理角度理解倾角参数对自然对流机制中不稳定和瞬态变化模式的影响。结果提供了一组高精度数据，可用作瞬态自然对流问题的基准案例。因此，腔体的倾斜效应明显影响了传热过程和流体流动。因此，倾角可以被认为是有效的热量和流体流动的控制参数。这项工作非常有效地从物理角度理解倾角参数对自然对流机制中不稳定和瞬态变化模式的影响。结果提供了一组高精度数据，可用作瞬态自然对流问题的基准案例。因此，腔体的倾斜效应明显影响了传热过程和流体流动。因此，倾角可以被认为是有效的热量和流体流动的控制参数。这项工作非常有效地从物理角度理解倾角参数对自然对流机制中不稳定和瞬态变化模式的影响。结果提供了一组高精度数据，可用作瞬态自然对流问题的基准案例。因此，腔体的倾斜效应明显影响了传热过程和流体流动。因此，倾角可以被认为是有效的热量和流体流动的控制参数。腔体的倾斜效应明显影响了传热过程和流体流动。因此，倾角可以被认为是有效的热量和流体流动的控制参数。腔体的倾斜效应明显影响了传热过程和流体流动。因此，倾角可以被认为是有效的热量和流体流动的控制参数。