Electromagnetic effects on membrane–driven Ree–Eyring fluid with slip conditions

Significance: Valveless membrane contractions-driven pumping has emerged as a promising mechanism for efficient fluid transport in microfluidic and biomedical systems. Particularly when handling electrically conducting and shear-dependent biological fluids. Understanding the significance of nonlinear rheology, slip effects, and magnetic fields together influencing such transport is essential for designing next-generation microscale pumping devices. Problem statement: Existing studies on membrane contraction-driven flows rarely integrate Ree-Eyring shear-thinning behaviour, multi-slip boundary effects, magnetohydrodynamic forcing, and coupled with heat-mass transport effects. As a result, the collective influence of these mechanisms on membrane-driven micro-pumping remains unexplored. Aim of the study: A comprehensive mathematical framework is developed to analyse MHD flow of a Ree-Eyring fluid in a deformable membrane microchannel, incorporating velocity, thermal, and concentration slip, along with heat and mass transfer effetcs. Methodology: The governing equations are formulated from the Navier–Stokes, energy, and species transport laws and reduced to dimensionless form using long-wavelength and low-Reynolds-number approximations. The analytical solutions are derived for velocity, temperature, concentration, shear stress, stream function, and volumetric flow. A parametric analysis is conducted using MATLAB R2024b to quantify the influences of the Ree-Eyring parameter, Hartmann number, and multi-slip conditions. Conclusions: This study demonstrates that shear-thinning rheology, magnetic damping, and interfacial slip provide effective control over pumping performance, thermal regulation, and solute transport in membrane-driven microchannels. These insights provide useful strategies for optimising such microfluidic pumping, thermal management, and biomedical transport processes in electrically conducting non-Newtonian fluids.