Hydrodynamic and thermosolutal analysis of MHD ternary hybrid nanofluids in BFS configuration: high-order FEM for drag reduction and thermal enhancement

Purpose This study aims to numerically investigate the combined effects of thermosolutal convection, magnetohydrodynamics (MHD) and radiative heat transfer in a backward-facing step (BFS) channel filled with a ternary hybrid ferrofluid suspension (Cu–Fe 3 O 4 –CoFe 2 O 4 /water) modeled as a Casson fluid. The primary objective is to analyze how key parameters, such as the Reynolds number ( Re ), Hartmann number ( Ha ), Lewis number ( Le ) and obstacle positioning, influence hydrodynamic forces (drag and lift coefficients), heat and mass transfer and flow stability. The study aims to provide actionable insights for optimizing thermal management systems, enhancing microfluidic device performance and advancing biomedical applications involving hybrid nanofluids and non-Newtonian fluids. Design/methodology/approach The governing equations for mass, momentum, energy and solute transport are solved using a high-order finite element method (FEM), with nonlinearities addressed via Newton’s method. Time integration is carried out using a nonstationary scheme based on the backward differentiation formula (BDF). The model accounts for magnetohydrodynamic (MHD) effects, thermal radiation and the rheological behavior of Casson fluid. The numerical implementation is validated against experimental data and benchmark solutions prior to performing the simulations. Findings Key results show that the ternary hybrid nanofluid enhances heat transfer, with a 1.03% increase in the Nusselt number, while the Casson fluid reduces drag and stabilizes flow reattachment. Increasing Re enlarges recirculation zones but decreases the drag coefficient ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>C</m:mi></m:mrow><m:mi>D</m:mi></m:msub></m:mrow></m:math> ) by 95%. In contrast, higher Ha increases <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>C</m:mi></m:mrow><m:mi>D</m:mi></m:msub></m:mrow></m:math> by 92% due to Lorentz forces. Obstacle positioning significantly alters hydrodynamic forces, with minimal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>C</m:mi></m:mrow><m:mi>D</m:mi></m:msub></m:mrow></m:math> at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>y</m:mi></m:mrow><m:mn>0</m:mn></m:msub><m:mo>=</m:mo><m:mn>0.7</m:mn><m:mi>H</m:mi></m:mrow></m:math> and maximum shear-induced drag at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>y</m:mi></m:mrow><m:mn>0</m:mn></m:msub><m:mo>=</m:mo><m:mn>1.3</m:mn><m:mi>H</m:mi></m:mrow></m:math> . The lift coefficient ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>C</m:mi></m:mrow><m:mi>L</m:mi></m:msub></m:mrow></m:math> ) transitions nonmonotonically with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>x</m:mi></m:mrow><m:mn>0</m:mn></m:msub></m:mrow></m:math> , and magnetic fields redistribute pressure, amplifying <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi>C</m:mi></m:mrow><m:mi>L</m:mi></m:msub></m:mrow></m:math> . Originality/value This work’s novelty lies in its holistic analysis of ternary hybrid ferrofluids with Casson fluid behavior in an MHD-driven BFS flow, a configuration unexplored in prior studies. The integration of radiative heat transfer, thermosolutal convection and non-Newtonian effects under transient conditions offers new insights into flow-thermal-stability tradeoffs. Practical value emerges from parametric optimizations (e.g. obstacle positioning for minimal drag, Ha -dependent vortex control) applicable to microfluidic cooling, targeted drug delivery and energy systems. The validated high-order FEM framework also advances computational methods for complex multiphysics flows.