Numerical study of magneto-nanolubricant transport through a porous wavy channel using three non-Newtonian rheological models

Synovial fluid dynamics in arthritic knees involve non-Newtonian rheology, porous cartilage, peristaltic motion, magnetic nanoparticles, and neural pain pathways, yet existing models rarely couple these phenomena. This study develops a finite-volume framework for magneto-nanolubricant flow through a wavy, porous channel representing the articular cartilage gap. Three non-Newtonian viscosity models, an exponential model, a variable shear-thinning-index model, and a Carreau–Yasuda model with combined temperature and concentration dependence, are integrated with an induced magnetic field, retaining the full induction equation, and a FitzHugh-Nagumo neural-activation model. A nested secant algorithm enforces pressure periodicity over one wavelength, and each governing block is verified against a closed-form limit. Of the three rheologies, only the Carreau–Yasuda formulation couples the viscosity to both the thermal and the nanoparticle field, yielding a tempered response that the exponential and variable-index models cannot reproduce. The induced magnetic field proves to be governed by the cartilage permeability, expressed through the Darcy number, together with the magnetic Reynolds number, and weakens as the permeability falls toward osteoarthritic values. Linking these transport fields, principally temperature and nanoparticle concentration, to the neural-activation variable furnishes a proof-of-concept mechanistic route to pain signaling, while raising the Reynolds number increases the pressure gradient required to sustain the flow and thereby shifts the lubrication regime. Taken together, the temperature-concentration Carreau–Yasuda rheology, the pressure-periodic formulation, the induced-field dynamics, and the fluid-neural coupling provide a framework for exploring how cartilage porosity, inflammation, and applied magnetic field influence synovial transport, with a view toward personalized osteoarthritis therapy.