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

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.