The main objective of this study is to examine 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 derived and further solved to obtain the amplitude expression. 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 concluded that the rotating frame of reference delays the onset of convection, while the energy supply to the system advances the onset of convection. The heat transfer rate increases by $22\%$ when the nanofluidic system is placed in the rotating frame of reference under the presence of an internal heat source.

The present study aims at discussing the onset of convection and heat transfer rate in a Casson nanofluid saturated in anisotropic porous enclosures of three types: shallow, square, and tall. The effects of Brownian motion and thermophoresis are included in the model. Normal modes are used to obtain the expression of stationary thermal Rayleigh number. Further, nonlinear stability analysis is performed using the truncated Fourier series expansion. The Nusselt number is calculated from the Lorentz model. The effects of pertinent flow governing parameters such as Casson parameter, thermal anisotropic parameter, mechanical anisotropic parameter, and nanoparticle concentration Rayleigh number are shown graphically on the onset of convection, Nusselt number, streamlines, isotherms, and isohalines. It is observed that shallow enclosure allows quick heat transfer by setting the convection earlier. Furthermore, it is concluded that the use of Casson-based single-walled carbon nanotube suspension (SWCNTS) enhances heat transportation and strengthens the magnitude of streamlines.