Unveiling transient heat transfer and irreversibility in magnetohydrodynamic natural convection of ternary hybrid nanofluids within novel cross-shaped cavities featuring three internal geometries

Purpose The purpose of this study is to investigate the transient behaviour of magnetohydrodynamic (MHD) natural convection and entropy generation in a cross-shaped cavity filled with a ternary hybrid nanofluid. This research aims to assess how time-dependent flow development, magnetic field strength and internal heated-body geometry influence thermal performance and irreversibility. Design/methodology/approach A comprehensive numerical analysis is performed using a finite-volume formulation to solve the governing equations of laminar incompressible MHD convection and entropy generation. Three internal heating geometries – a flower-shaped body, a horizontally oriented ellipse and a vertically oriented ellipse – are embedded within the cavity. Transient behaviour is analysed through time series, phase portraits, Fourier spectra and root-mean-square velocities across various Rayleigh and Hartmann numbers. The model is validated against established benchmark solutions to ensure accuracy. Findings Results show that the flower-shaped body provides the highest heat transfer enhancement but produces the greatest entropy generation. The horizontally oriented ellipse yields the lowest irreversibility but exhibits weak thermal performance. The vertically oriented ellipse maintains oscillatory convection and offers a balanced compromise with effective heat removal under moderate magnetic fields. The transient analysis highlights the role of magnetic damping in suppressing fluctuations and shaping flow stability. Originality/value This paper presents the first combined examination of transient convection, ternary hybrid nanofluids and variable novel heated-body geometries within a cross-shaped cavity. The findings deliver new physical insights and design guidelines relevant to advanced thermal management applications such as electronic cooling, solar collectors and energy-storage systems.