Numerical and analytical study of two-layered unsteady blood flow through catheterized artery

The pulsatile flow of blood in a catheterized blood vessel is analyzed. The flow of blood in vessel is modeled as the flow of two immiscible fluids. The fluid in the core region is characterized as a non-Newtonian viscoelastic fluid satisfying the constitutive equation of an Oldroyd-B fluid. The fluid in the peripheral region is treated as a Newtonian fluid. The catheter inside the vessel is modeled as a rigid tube of very small radius. The resulting differential system for velocity in each region is computed numerically by finite-difference scheme and analytically by Laplace transform. A comparison of numerical solution with Laplace transform solution is carried out. Various physical quantities of interest through the computed velocity are also analyzed.