Heat transfer with magnetic force and slip velocity on non-Newtonian fluid flow through a porous medium

This study investigates the combined effects of heat and mass transfer on free convection flow of Brinkman fluid over a plate embedded in porous media, focusing on applications in engineering and environmental science where efficient thermal and mass transport are essential. This research addresses the complexity of controlling fluid behavior in porous structures, where factors like heat, mass, and momentum fluxes play a critical role. The Atangana–Baleanu fractional derivative is employed to model the flow, integrating Fourier’s and Fick’s laws to handle heat and mass transfer, with added effects from slip conditions and chemical reactions to capture a more realistic flow scenario. The governing partial differential equations are transformed into dimensionless form and solved semi-analytically using the Laplace transform method. Model validation is achieved by comparing results obtained through algorithmic solutions, confirming the robustness of the fractional approach by taking the values of fractional parameter γ in the range 0 . 2 ≤ γ ≤ 1 , whereas the values of slip parameter λ lies in the range 0 ≤ λ ≤ 0 . 8 . The model also discussed the effect of magnetic lines of force relative to fluid as well as relative to plate by taking values of ϵ is equal to 0 and 1. Key findings reveal that increasing thermal and mass Grashof numbers by 10% results in a 12% rise in fluid velocity, emphasizing the positive impact of buoyancy forces on flow acceleration. Conversely, stronger magnetic fields, chemical reactions, and the Brinkman parameter exhibit a damping effect, reducing velocity by up to 8% when these parameters increase. Additionally, heat sink intensification further slows down fluid motion. A comparative analysis between fractionalized and classical models highlights that fractional techniques capture flow behaviors more precisely, revealing a more flexible and accurate description of convection phenomena. This model advances previous studies by demonstrating that fractional derivatives significantly enhance the prediction of fluid behavior in porous media, underscoring the effectiveness of fractional modeling for complex convection processes. These insights position the fractional approach as a preferred alternative to classical methods for simulating real-world convection flows, offering greater applicability to porous media transport phenomena in engineering and environmental systems.