Galerkin finite element technique for cross-viscous fluid modeling in nonlinearly tapering stenosed artery

The arteries possess muscular walls that may change their diameter to increase or reduce the amount of blood that travels to a specific region of the body. This is called vasodilation. In this post, we explain the flow of blood via an artery that has stenosis. The existence of stenosis in a valve creates a barrier that inhibits the circulation of blood through all the vessels. Aortic valve stenosis is associated with the progressive thickening and shrinking of the valve that resides between both the left ventricle of the heart, which is the primary pumping chamber and the aorta, the body’s largest artery (aorta). As a result of the narrowing, the passage by which blood may flow is becoming smaller in size. There is a limitation and obstruction of blood flow away from the heart and into the rest of the body. Since employing grafts with tapered lumen gives benefits in surgery, the bigger blood vessels upstream, such as blood flow in tapering stenosis arteries, are also very beneficial to prosthetic blood vessel design. This numerical attempt presents the performance of blood flowing over the geometry of a nonlinear tapering stenosis artery. As blood is a non-Newtonian fluid so, for this purpose, the mathematical model of Cross Fluid is being utilized. Cross fluid has the potential to check the characteristics of liquids flowing at highly elevated and significantly lower shearing rates due to its viscosity model. Mild stenosis is considered, and its governing equations are derived. The regulating modeled differential formulas are tackled with the support of the Galerkin finite element method (G-FEM). The physical quantities like speed, surface shearing stress, shearing stress field, and endurance at the stenosis throat are determined with a positive variation in various dimensionless parameters which emerge during the computational solving of the model. From the obtained results, it is noted that the resistance impedance escalates by the honesty of magnification in the nondimensional factors cap We and m. The growth in We results in an overall reduction in the wall shear stress. The impact of blood flow on the nonlinear tapered stenosis artery’s shape while taking non-Newtonian cross fluid into account has not yet been examined in the literature.