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Role of heat source/sink in transient free convective flow through a vertical cylinder filled with a permeable medium: An analytical approach

机译：热源/水槽在瞬态自由流流动中的作用通过填充有渗透介质的垂直圆筒：分析方法

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摘要

In this study, an investigation is performed to analyze the impact of the heat source/sink parameter on the laminar transient free convective flow through a vertical cylinder filled with a permeable medium. The governing nondimensional PDEs of the mathematical model along with their appropriate initial and boundary conditions are solved analytically by incorporating the Laplace transform scheme. Moreover, we explored the impact of emerging physical parameters of the considering model in the presence of the source/sink on the velocity profiles by graphs and tables. It is found that the velocity profile has a increasing tendency with enhancement in the numerical values of the time, which finally attains its steady-state solution in the presence of heat source/ sink. Moreover, the Prandtl number, sink parameter, and viscosity ratio parameter lead to a decrease in the velocity profiles, whereas the reverse phenomenon occurs with the Darcy number and source parameter. Finally, the numerical values of the Nusselt number, skin friction, and mass flux are given in the tabular forms. The main result obtained in this paper is that the velocity is higher in the case of the source parameter, whereas an opposite behavior is observed in the case of the sink parameter.
机译：在该研究中，进行调查以分析通过填充有可渗变介质的垂直圆筒的层状瞬态自由对流流动的热源/水槽参数的影响。通过结合拉普拉斯变换方案，分析了数学模型的管理非潜能PDE以及它们适当的初始和边界条件。此外，我们探讨了考虑模型在源/下沉在速度范围内的速度范围的影响的影响。结果发现，速度曲线具有增加的趋势，其时间值的增强趋势，最终在热源/水槽存在下实现其稳态解决方案。此外，PRANDTL数，沉积参数和粘度比参数导致速度剖面的减小，而反向现象发生在达西数和源参数中。最后，以表格形式给出了豆浆数，皮肤摩擦和质量磁通的数值。本文获得的主要结果是在源参数的情况下，速度较高，而在水槽参数的情况下观察到相反的行为。

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