Abstract Natural convection of a fluid inside a closed square porous enclosure with inhomogeneous porosity distribution was studied numerically. The right and left walls of the cavity were cold and hot, respectively, provided the upper and lower walls were well insulated. The fluid and solid portions are in thermal equilibrium within the porous medium. Boundary conditions were considered based on the assumptions and were nondimensionalized using suitable dimensionless parameters. The non-uniform distribution of porosity was assumed as linear and quadratic functions with positive and negative gradients along the horizontal (x) and vertical (y) axes. To ensure the accuracy of results, several simulations in the literature performed by the same solution method were replicated, and the results were compared with those reported in these studies. Porosity could be an increasing or a decreasing function of x or y. A total of eight porosity distribution functions were used in this study. The results showed drastic changes in the flow and temperature fields with linear porosity distribution at ϵavg = 0.3 compare to uniform porosity distribution. Furthermore, inhomogeneous porosity caused a decrease in the Nusselt number. The observed reduction in the Nusselt number was maximum for linear porosity distribution along the x-axis and minimum for the Quadratic Porosity distribution along the y-axis.

中文翻译：

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使用线性和二次孔隙率分布的非均质多孔介质中的自然热交换

摘要 数值研究了孔隙度分布不均匀的封闭方形多孔外壳内流体的自然对流。如果上壁和下壁隔热良好，则腔体的左右壁分别是冷的和热的。流体和固体部分在多孔介质内处于热平衡状态。基于假设考虑边界条件，并使用合适的无量纲参数进行无量纲化。孔隙度的非均匀分布被假定为线性和二次函数，沿水平 (x) 和垂直 (y) 轴具有正梯度和负梯度。为确保结果的准确性，重复了文献中采用相同求解方法进行的多次模拟，并将结果与​​这些研究中报告的结果进行了比较。孔隙率可以是 x 或 y 的递增或递减函数。本研究共使用了八个孔隙度分布函数。结果表明，与均匀孔隙度分布相比，线性孔隙度分布在 ϵavg = 0.3 时流场和温度场发生了剧烈变化。此外，不均匀的孔隙率导致努塞尔数的减少。观察到的努塞尔数减少对于沿 x 轴的线性孔隙度分布最大，对于沿 y 轴的二次孔隙度分布最小。此外，不均匀的孔隙率导致努塞尔数的减少。观察到的努塞尔数减少对于沿 x 轴的线性孔隙度分布最大，对于沿 y 轴的二次孔隙度分布最小。此外，不均匀的孔隙率导致努塞尔数的减少。观察到的努塞尔数减少对于沿 x 轴的线性孔隙度分布最大，对于沿 y 轴的二次孔隙度分布最小。