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

Abstract 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.