The linear and non-linear study of effect of rotation and internal heat source/sink on Bénard convection

Abstract

The primary objective of this study is to investigate non-linear Bénard convection in a single-walled carbon nanotube suspension saturated in a rotating porous medium with an internal heat sink/source. The modified Buongiorno model is utilized to formulate the governing equations for the flow. Both linear and weak non-linear stability analyses are conducted in this investigation. The linear stability analysis employs the truncated Fourier series transformation, while the weakly non-linear stability analysis utilizes the Lorenz model, assuming weak thermophoresis, porous friction, and small-scale convective motion. The cubic Ginzburg–Landau equation is formulated and subsequently solved to derive the expression for the amplitude. The influence of various parameters, such as the Taylor number, heat sink/source parameter, and viscosity parameter, is discussed in relation to the threshold criteria of convection, as well as heat and mass transport rates. Based on the linear stability analysis, it is determined that the introduction of a rotating frame of reference delays the initiation of convection, whereas the energy supplied to the system accelerates the onset of convection. The heat transfer rate increases by when the nanofluidic system is placed in the rotating frame of reference under the presence of an internal heat source.