Analytical solutions for hyaluronic acid flow and heat transfer between joints with periodic oscillations under the magnetic field

Abstract

Osteoarthritis (OA) is a globally prevalent disease that poses significant challenges to the daily work and life of patients. Viscosupplementation is one of the most commonly used drug treatments for OA, which involves injecting hyaluronic acid (HA) into the joint cavity to alleviate synovial inflammation. The current research aims to explore the rheological and thermal behavior of HA between joints by studying the axisymmetric squeezing flow and heat transfer of incompressible Maxwell fluid under the action of static magnetic field between two rigid spheres with partial wall slip. The analytical solutions for velocity and temperature are obtained by using the Laplace integral variational theory. Detailed explanations are provided on the effects of different fluid parameters on velocity and temperature, presented in the form of charts. It can be shown that as the magnetic field intensity increases, the viscosity of HA increases with the increasing of relaxation time, thereby fluid motion is weakened and a strong damping effect is produced. As the frequency of joints motion increases, the velocity distribution becomes more uniform in the central region, and the overall distribution deviates from a parabolic distribution. In addition, as Reynolds number, Prandtl number and squeezing depth increase, the heat transfer capacity of the fluid decreases, resulting in a lower temperature at the top wall and a higher temperature at the bottom wall. This study provides theoretical support for exploring the rheological and thermal behavior characteristics of HA in the treatment of OA.