Knee synovial fluid flow and heat transfer, a power law model.

For the purpose of understanding, the governing system of partial differential equations for synovial fluid flow velocity and temperature distribution in the knee joint has been successfully solved for the first time. Therefore, such an article is shedding light on the convective diffusion of the viscous flow along the articular surfaces of the joints through the introduction of power-law fluids with different features of permeability, and stagnation point flow along a magnetic field. Henceforth, the frictional energy causes the knee joint's temperature to increase. By way of filtration, heated synovial fluid reaches the articular cartilage and provides heat to the bone and cartilage. The lubricant in the joint cavity is properly mixed with this cooled fluid. A rectangular region flow and diffusion model is used to define the issue, thermal diffusion and flow inside the intra-articular gap, as well as flow and thermal diffusion within the porous matrix covering the approaching bones at the joint. Using the similarity solution approach, the linked mixed boundary value problem is addressed. The fluid has been shown to resist moving into or out of the cartilage in certain sick and/or aging synovial joints, causing the temperature to increase. By changing the values of the parameters from their usual levels, it is observed that the temperature did increase in aged and sick joints which impact cartilage and/or synovial fluid degradation.

Nonaxisymmetric disturbances in compound liquid jets falling under gravity.

The disintegration of a compound thread of fluid can be utilized in a wide variety of applications including the production of compound droplets or capsules. In this paper we investigate the linear instability of a compound inviscid liquid jet falling under gravity in a surrounding gas with respect to nonaxisymmetric waves. We derive an analytical expression for the dispersion relation, which takes into account the non-uniform nature of the jet, and which we then solve numerically. Particular attention is paid to investigating the effects of the liquid-to-gas density ratio on the growth and development of different wave modes as well as the influence of gravity. Our results show that there exists some nonaxisymmetric long wavelength disturbances that are more unstable than their asymmetric equivalents and that the influence of gravity can alter the behavior of these modes.