Influence of Two Viscosity Models and Activation Energy on Synovial Fluid Through Thermophoretic Particle Deposition

Synovial fluid is found in synovial joints, which act as a lubricant and shock absorber, that is crucial for the detection and treatment of diseases and injuries associated with the joints. It is significant for enhancing joint health diagnostics and treatment, improving drug delivery systems and advancing the understanding of complex fluid behavior and particle transport mechanisms in biomedical and engineering applications. The biological field utilizes complex analyses of condyloid, hinge, pivot and shoulder joints for current development. This work uses two viscosity models to examine the impact of activation energy and nonlinear heat source on the synovial fluid (SF) with thermophoretic particle deposition. The current model shows how the viscosity of an SF is affected by concentration and deformation. The impact of MHD and variable thermal conductivity on a heated disc is also investigated. The flow has been examined using the Arrhenius equation, which offers a mathematical explanation of how activation energy works in our system. PDEs are transformed into ODEs by employing the similarity transformation. The problem is solved by using the modified shooting method (bvp4c). This study focuses on the velocity, temperature and concentration profiles while presenting the physical significance of all the fluid parameters involved. These profiles are thoroughly described and shown graphically. The results show that when the magnetic parameter rises, the temperature profile rises and the velocity profile declines. The concentration profile decreases with higher values of the reaction rate parameter and the thermophoretic parameter and also increases with a higher value of the activation energy parameter. The flow of SF for model-I is significantly larger than that for model-II.