B-SPLINE COLLOCATION SIMULATION OF NON-LINEAR TRANSIENT MAGNETIC NANOBIO-TRIBOLOGICAL SQUEEZE-FILM FLOW

Abstract

A mathematical model is presented for magnetized nanofluid bio-tribological squeeze-film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nanosuspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nanoparticle) conservation equations are normalized with appropriate transformations which renders the original coupled, non-linear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in non-linear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular, smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems.