Thermal radiation effect on Darcy-forchheimer flow of synovial fluid over heated disk: Applications of thermal engineering via two viscosity models

Abstract

The current study investigates the Darcy-Forchheimer flow of Synovial fluid over a heated disk with Marangoni convection, thermal radiation and heat source incorporating two viscosity models with magnetohydrodynamic effect. The areas around synovial joints contain synovial fluid, a viscoelastic fluid. Reduced friction during motion between the articular cartilages of synovial joints is the main purpose of synovial fluid. This study holds significant uses in the field of biomedical engineering and industrial processes. In the medical realm, this model could aid in understanding the heat and mass transfer dynamics within joints, potentially offering insights into conditions like arthritis. In industrial processes, the model could be used to optimize heat exchangers involving complex fluid mixtures with chemical reactions, enhancing energy efficiency. The resultant partial differential equation is highly nonlinear, coupled, and complex, and are converted into ordinary differential equations with the use of a suitable transformation. The shooting technique is used to solve the transformed ordinary differential equations numerically (Bvp4c). Higher surface tension gradients develop by rises in the Marangoni convection parameter, and this improves the mass and heat transmission inside the fluid by making the induced flow more effective. These characteristics spread more evenly across the fluid as the temperature and concentration profiles drop. A greater Weissenberg number also results in a slower fluid velocity. Examining the impact of different parameters on joint friction allows one to investigate the nature of the lubricant in fluids.