Stability and computational assessment of fractional Maxwell–Casson fluid in a Darcy-Brinkman model with variable porosity

Purpose Motivated by diverse industrial applications involving viscoelastic fluids in porous media, the current study aims to investigate the buoyancy-driven flow and heat transfer of Maxwell–Casson fluid over a vertical flat plate embedded with porous structures. Design/methodology/approach To account for flow resistance and permeability effects, the Darcy–Brinkman model with spatially varying porosity is adopted to characterize the transport within the porous medium. The fluid formulation enables accurate representation of non-Newtonian effects, where yield stress significantly influences both velocity and temperature profiles. Temporal linear stability analysis of the proposed model is conducted to investigate the dynamic response of the system under small perturbations. The governing fractional equations are discretized using a finite difference scheme in conjunction with the L1 algorithm, while the stability of the numerical procedure is validated through von Neumann analysis to ensure robustness of the computed results. The resulting flow and thermal fields are analyzed graphically, with comprehensive discussion provided to interpret the impact of key parameters. Findings Stability analysis of the system reveals that increasing the value of Casson fluid parameter (γ) enhances the stability of the convective flow, whereas higher fractional order parameters (α, β) reduce stability by weakening memory-induced damping effects. Moreover, higher fractional orders lead to thicker velocity and thermal boundary layers accompanied by reduced heat diffusion. Collectively, these findings provide valuable insights for the design and optimization of porous media systems involving complex non-Newtonian fluids, offering practical guidance for effectively controlling heat and fluid transport in engineering applications. Originality/value The present work represents a novel contribution by developing a comprehensive framework for analyzing buoyancy-driven flow of viscoelastic fluids in porous media under a fractional-order framework. A key feature of this approach is its robustness and generality, achieved through the integration of the Maxwell–Casson fluid model with the Darcy–Brinkman model and variable porosity. The formulation effectively captures memory effects and yield stress behavior without requiring restrictive assumptions, while the adopted numerical scheme ensures stable and accurate solutions across varying physical parameters, making the model adaptable to a wide range of engineering thermal systems.