Parametric influences on flow, heat transfer, and nutrient transport in the knee joint cavity, a numerical approach

A novel aspect of this study is the investigation of the impact of temperature-dependent Arrhenius reactions and metabolic heat generation on the overall heat transfer within a knee joint cavity. This is a unique contribution where the interaction between thermal effects and metabolic activity is shown to influence the transport of nutrients and the removal of waste products. For the first time, the study also aims to examine the influence of key non-dimensional numbers on the characteristics of mixed convection flow, providing new insights into the dominant physical mechanisms at play. An innovative feature of the model is the incorporation of a non-linear reaction term to address the balance between protein synthesis and degradation. By integrating both thermal and biochemical dynamics, this approach offers a comprehensive analysis of protein aggregation in the knee joint, with potential implications for understanding and treating joint diseases, particularly those related to the health of synovial fluid and cartilage, such as osteoarthritis. The findings have the potential to inform the development of improved therapeutic strategies for managing these conditions. In the context of knee joint cavity dynamics, a low Cauchy number Ca plays a crucial role in ensuring steady and laminar flow, which reduces inertia and ensures that the continuity equation is satisfied. This laminar nature of the flow is essential for maintaining stable synovial fluid movement within the cavity, which aids in the smooth transport of nutrients and waste products. Additionally, higher Peclet number Pe values indicate an increased dominance of convective transport over diffusion, thereby enhancing the supply of essential nutrients to cartilage and bone, while also facilitating the removal of waste products and inflammatory mediators. This efficient convective transport mechanism is vital for the overall health of the joint and for mitigating inflammation. Furthermore, the Zeldovich number /3 significantly influences the temperature sensitivity of the Arrhenius reaction term within the cavity, where higher values reflect increased reactivity to temperature changes. This temperature dependence impacts metabolic heat generation and protein dynamics, further influencing the biochemical processes that occur within the joint. Collectively, these non-dimensional parameters highlight key aspects of synovial fluid dynamics, nutrient transport, and biochemical reactions that are essential to the functioning and health of the knee joint.