Unsteady double-diffusive Brinkman–Bénard convection in cylindrical enclosure saturated with hybrid bi-viscous Bingham nanoliquid

This paper aims to present an analytical as well as a comparative study to investigate the effect of the Brinkman porous medium on the onset of regular and chaotic motion in cylindrical enclosures of different heights. The hybrid bi-viscous Bingham nanoliquid is considered as the working fluid. Modified Brinkman–Buongiorno and bi-viscous Bingham fluid models are incorporated to obtain the flow governing dynamics. The thermophysical properties of the hybrid nanoliquid are calculated using phenomenological laws and the mixture theory. The study is carried out for the axisymmetric mode, and the Bessel functions are taken as the eigenfunctions of the problem. Double Fourier–Bessel series expansions are used for weakly non-linear stability analysis. The limiting cases of the study are obtained, and the results on the onset of convection, heat, and mass transport are discussed graphically. The behavior of the dynamical system is analyzed using the maximum Lyapunov exponent plot, the bifurcation diagram, and phase plots. Outcomes suggest that convection sets in earlier in the water-based hybrid nanoliquid than in the bi-viscous Bingham hybrid nanoliquid. The use of Single-walled carbon nanotubes enhances the heat transfer rate by approximately 17%. Further, it is concluded that a tall cylindrical enclosure is the most favorable geometry for achieving a higher heat transfer rate among the others.