Induced magnetic field and thermal regulation of synovial fluid flow through irregular surfaces with first-order slip and gold nanoparticles

Abstract

ABSTRACT The current computational exploration develops a poroelastic model of the knee cartilage to elevate its temperature under cyclic sinusoidal loading. A contributing factor to the rise in temperature is this tissue’s viscous dissipation, which converts some of the mechanical energy supplied into heat. The manipulation of cartilage temperature is mostly reliant on the movement of synovial fluid inside the space between joints and within the permeable cartilage. We developed the region flow model in the presence of induced magnetic fields and gold nanoparticles, which enhanced the efficiency of joint lubrication by boosting the load-carrying capacity. We dealt with the problem for two different models. Model 1 assumes that viscosity is exponentially dependent on concentration. The shear thinning index in Model 2 is regarded as a concentration-dependent variable. We introduce these models for a complex wavy surface, where the first-order slip effect occurs. We modified the governing problem by assuming a long wavelength and a low Reynolds number. We followed up with a computational analysis utilizing the Rung–Kutta–Merson approach with Newton iteration in a shooting and matching strategy. We have conducted detailed comparisons between Model 1 and Model 2. The graphical findings have been shown for the distributions of velocity, temperature, and nanoparticle concentration. Additionally, the pressure gradients, streamlines, and axially generated magnetic fields have also been included. These results are presented for numerous physical parameters. The mechanics of trapping are thoroughly examined through the use of streamlines.