Development of a general numerical approach for transient natural convection of viscoplastic fluids

Purpose This study aims to perform the first comprehensive numerical investigation of transient natural convection in viscoplastic fluids. This study elucidates the temporal evolution of flow, temperature and yield surfaces from an initial quiescent state to the final steady-state in a square cavity. Design/methodology/approach The transient governing equations for the Bingham model are solved using a Galerkin Finite Element Method in a differentially heated square cavity. A systematic parametric study investigates the influence of the Rayleigh (Ra), Bingham (Bn) and Prandtl (Pr) numbers on the system’s transient dynamics. Findings The time required to reach steady-state paradoxically increases with a higher Bingham number, despite weaker convection. Higher Rayleigh numbers also prolong the transient period and can, at a given instant, result in larger unyielded regions due to a more concentrated flow. Critically, contrary to its negligible effect on the final steady-state, increasing the Prandtl number dramatically extends the transient duration. The evolution of yielded zones is shown to be a complex, multi-stage process. Originality/value This paper presents the first complete transient analysis of this problem, providing fundamental insights into the time-dependent behavior of viscoplastic natural convection. The findings are crucial for applications with time-dependent boundary conditions and establish a benchmark for future research into complex rheological models and flow instabilities.