Osteoarthritis affects more than 500 million people worldwide, yet existing viscosupplements suffer from rapid clearance and poor cartilage penetration. This study investigates how the coupled effects of viscous dissipation, thermophoretic migration, magnetic induction, and porous absorption govern the spatial distribution of gold nanoparticles injected into the osteoarthritic knee joint. A finite volume solver is developed for flow through a wavy, porous channel with a second-order velocity slip condition at the cartilage surface, incorporating a temperature and concentration-dependent Carreau-Yasuda viscosity, an absorption term in the concentration equation, and the full magnetic induction equation. The results reveal that each transport process is governed by a distinct mechanism: thermal buoyancy and surface slip shape the velocity field, viscous dissipation controls the temperature distribution, and thermophoresis provides a means of actively guiding nanoparticles. Most significantly, cartilage absorption emerges as the dominant barrier to effective drug delivery, while the axial pressure gradient is governed by cartilage permeability and fluid rheology, with second-order slip exerting a strong, previously neglected influence on the pressure distribution. These findings establish that nanoparticle absorption and second-order surface slip cannot be neglected in predictive models of synovial joint biomechanics and intra-articular drug delivery.