Purpose This study aims to investigate transient thermo-bioconvection with solid-particle diffusion in a porous noncanonical Z-shaped cavity containing internal solid inclusions, and to clarify how thermal buoyancy, microorganism-induced buoyancy, porous resistance, magnetic damping and memory effects interact to control heat and oxygen transport. A further objective is to develop a rapid surrogate framework for predicting the global transport characteristics of this strongly coupled enclosure system. Design/methodology/approach A two-dimensional, unsteady, incompressible bioconvection model is formulated for a porous Z-shaped cavity filled with a nano-encapsulated phase change material–based suspension containing oxytactic microorganisms. The governing equations for momentum, temperature, oxygen concentration, microorganism density and solid-particle transport are solved using a meshfree incompressible smoothed particle hydrodynamics (ISPH) method in a Lagrangian framework. The formulation incorporates Darcy–Brinkman–Forchheimer porous resistance, microorganism-induced buoyancy, an optional inclined magnetic field and a fractional-time operator to represent temporal memory effects. The numerical model is benchmarked against appropriate limiting cases, and a multilayer perceptron surrogate is trained on the ISPH-generated database to predict the averaged Nusselt and Sherwood numbers efficiently. Findings The numerical results indicate that increasing the Darcy number from Da = 10−5 to 10−2 significantly enhances the circulation intensity and increases the averaged Nusselt and Sherwood numbers by approximately 30%–60%, and increases peak velocity magnitude by approximately 25%–40%, reflecting enhanced convective heat and oxygen transport. In contrast, increasing the Hartmann number from Ha = 0 to 80 suppresses fluid motion due to Lorentz-force damping and reduces the global transport rates by up to about 40%. Increasing the thermal Rayleigh number from Ra = 103 to 106 markedly strengthens buoyancy-driven circulation and leads to a pronounced increase in heat and mass transfer. The Lewis number primarily controls oxygen diffusion and microorganism clustering, while decreasing the fractional order α from 1 to 0.85 introduces memory-induced retardation that delays particle redistribution during early transient stages. The Z-shaped configuration promotes asymmetric circulation cells and turning-induced recirculation, which intensifies plume interaction compared with canonical cavity geometries. Research limitations/implications The analysis is limited to a two-dimensional laminar formulation, a homogeneous porous-medium assumption and an effective-mixture treatment of the suspension. Even with these assumptions, this study provides useful physical insight into coupled thermo-bioconvective transport in irregular porous enclosures and establishes a computational basis for future three-dimensional, locally nonequilibrium and experimentally validated extensions. Practical implications The proposed ISPH–ANN (artificial neural network) framework enables rapid estimation of global transport indicators for complex porous enclosures without repeated high-cost simulations. Such capability can assist in the design and optimization of compact bio-thermal systems, including microfluidic reactors, porous bioreactors and serpentine cooling passages, where controlling buoyancy-driven circulation and oxygen transport is critical for system performance. Social implications Improved predictive understanding of coupled heat, oxygen, particle and microorganism transport can contribute to the development of more efficient bioinspired thermal systems, biomedical microdevices and sustainable energy-related processes involving porous transport and biological activity. Originality/value This study offers a unified numerical data–driven analysis of thermo-bioconvection with oxytactic microorganisms, solid-particle diffusion, porous resistance, magnetic control and fractional-time effects inside a noncanonical Z-shaped cavity. Its originality lies in combining a validated meshfree ISPH formulation with ANN-based surrogate prediction for a geometrically complex porous enclosure, thereby extending existing SPH/ISPH bioconvection studies beyond conventional cavity configurations while providing both deeper physical interpretation and computational efficiency. This study also provides quantitative characterization of how permeability, magnetic damping, buoyancy forcing and fractional temporal dynamics influence the global heat and mass transfer performance in irregular porous enclosures.
Aly et al. (Thu,) studied this question.