Rayleigh–Bénard magnetoconvection with asymmetric boundary condition and comparison of results with those of symmetric boundary condition

The paper concerns two Rayleigh–Bénard magnetoconvection problems, one in a mono-nanofluid (H 2 O–Cu) and the other in a hybrid nanofluid (H 2 O–Cu–Al 2 O 3 ) bounded by asymmetric boundaries. A minimal Fourier–Galerkin expansion is used to obtain the generalized Lorenz model (GLM) which is then reduced to an analytically solvable Ginzburg–Landau equation using the multiscale method. The results of asymmetric boundaries are extracted by using the Chandrasekhar function with appropriate scaling of the Rayleigh number and the wave number. The solution of the steady-state version of the GLM is used to estimate the Nusselt number analytically, and the unsteady version is solved numerically to estimate the time-dependent Nusselt number and also to study regular, chaotic, and periodic convection. Streamlines are plotted and analyzed in both steady and unsteady states. The analytical expression for the Hopf–Rayleigh number, r H , coincides with the value predicted using the bifurcation diagram. This number determines the onset of chaos. For r ∗ > r H , one observes chaotic motion with spells of periodic motion in between. For r ∗ < r H , one sees non-chaotic motion (regular motion). It is found that by increasing the strength of the magnetic field, we can prolong the existence of regular motion by suppressing the manifestation of chaos. The Lorenz attractor is a signature of chaos since it is found that the attractor appears only for r ∗ > r H . The magnitude of the influence of the asymmetric boundary on r H is between those of the two symmetric boundary conditions with the free–free isothermal boundary being the one that most favors chaotic motion: A result also seen in the context of regular convection.