Thermal bio-convective transport in biological fluid using two viscosity models

This article models the diffusion process of heat and mass transfer in synovial fluid (SF) which is viscous non-Newtonian and is present in the articular cartilage of the synovial joint. The viscosity of SF is a function of the concentration of hyaluronan (HA) and shear rate. The physicochemical properties of HA and the use of antioxidants is the main motivation for considering Brownian motion and thermophoresis in the synovial liquid. The mathematical models for viscosity depending upon concentration and shear rate dependent are coupled with conservation governing equations. To explore the behavior of material parameters on the lubricant nature of the SF models governing laws are solved. The impacts of parameters on friction between joints are examined which helps to analyze the lubricant nature of SFs. Subsequently, it also noted that, in a quantitative sense, viscosity models (model-I and model-II) behave slightly differently under parametric variation. Brownian motion (BM) of particles for the case of the model-I is higher than that for the case of the model-II. The concentration field decreases by increasing the BM of particles. However, the concentration field increases when thermophoresis effects are increased. It is also found from the simulations that thermophoresis effects for the case of a model-II are stronger than those for the case of model-I. BM of particles is responsible for an increase in the temperature for the case of both models.