Design the modeling of synovial fluid with two viscosity models on a surface: Biomedical engineering applications

• The heat, mass transfer in Synovial fluid is considered. • A heated two-dimensional stretched sheet is utilized. • Two viscosity models in the transport phenomenon have been used. • Soret and Dufour effects are used. This manuscript exhibits the role of synovial fluid in mass diffusion and heat energy on a stretching surface involving the stagnation point flow and Darcy's law. The mechanism of synovial fluid is used in condyloid joints, hinge joints, pivot joints and saddle joints. The correlation of the ternary hybrid nanofluid, named the Yamada Ota and Hamilton crosser model, is used to determine the cooling and thermal energy process. Joule heating and a heat sink are considered. The mathematical modeling is based on rates of shear rate dependent and concentration, which are coupled momentum equations. Two kinds of viscosity models, named model I and model II are considered in the current modeling. The governing equations are obtained in the form of ODEs using transformations. The numerical approach called the finite element method is used for numerical results. It is included that the maximum heat energy can be produced using the heat sink parameter, while the cooling process can be generated with a change of the heat sink parameter. The velocity field associated with synovial fluid for model I is greater than that of model II, while the concentration and heat energy for model II are higher than those of model I. Ternary hybrid nanofluid adds more heat energy than the nanofluid and the hybrid nanofluid.