The nonlinear stability of a rotating Rayleigh–Bénard system with internal heat generation is analyzed through a generalized five-dimensional Lorenz model formulated for a bi-viscous Bingham fluid (BVBF) layer. The governing equations are nondimensionalized using a stream function formulation, and a five-mode Fourier expansion is employed to derive a reduced autonomous system that captures the essential nonlinear dynamics. The inclusion of Coriolis effects and rheological nonlinearity introduces new dynamical regimes beyond those of the classical Lorenz system. The BVBF parameter strongly influences the system's behavior. As the yield stress increases, convective motion becomes weaker or may even cease altogether. In contrast, when the fluid behaves more like a Newtonian fluid, the system reduces to the classical Lorenz system. Nonlinear analyses using bifurcation diagrams and largest Lyapunov exponents confirm a sequence of transitions from steady convection to periodic and chaotic states. Numerical simulations show a transition from steady convection through periodic to chaotic regimes. The findings suggest that rotation reduces the Nusselt number, whereas enhanced internal heating improves convective heat transfer. The results demonstrate that the model provides a comprehensive low-dimensional framework for understanding the emergence of chaos and heat transport in rotating non-Newtonian systems applicable to geophysical and industrial scenarios.
Lodwal et al. (Sun,) studied this question.