Unsteady magneto-hydrodynamic behavior of TiO2-kerosene nanofluid flow in wavy octagonal cavity

The aim of this study is to mathematically model the behavior of magneto-hydrodynamics (MHD) in a two-dimensional unsteady flow, specifically focusing on natural convection (NC) and heat transfer (HT) within a wavy octagonal cavity. The study investigates how heat is transferred and fluid flows within this cavity under specific conditions. In particular, it examines the impact of various parameters, such as the Hartmann number (Ha), Rayleigh number (Ra), and the volume fraction of nanoparticles (ϕ) on the flow and heat transfer patterns. This cavity includes a rectangular vertical wall (RVW) at the center of its bottom wall, filled with kerosene-TiO2 nanofluid of spherical shape. Within this setup, the RVW is maintained at a high temperature (T = Th), while the wavy wall is kept at a lower temperature (T = Tc, where Tc