Newtonian and non-Newtonian fluids, Constitutive equations, Some important class of non-Newtonian fluids, Fundamental equations of motion and continuity.
Unit II:
II
Blood rheology, Cardiovascular system, Hagen-Poiseuille flow, Steady laminar flow of blood in a circular tube (Newtonian fluid and Casson fluid), Oscillatory flow of a viscous fluid through elastic tube.
Unit III:
III
Oscillatory flow through a circular tube (Newtonian fluid and two phase fluid), Oscillatory blood flow, Blood flow through artery with mild stenosis (Newtonian fluid case), Peristaltic flows in a channel and a circular tube.
Unit IV:
IV
Regular and Singular perturbation: Examples of regular and singular perturbation problems. Method of Multiple Scales: Flow of fluid in a channel of slowly varying cross section, Solution of Mathieu’s equation, Solution of the Vander Pal equation by the two-variable method, Lindstedt-Poincare method.
Unit V:
V
Matched Asymptotic Expansions: Prandtl’s matching principle deduction of the boundary Layer equations for the flow of fluid past a flat plate, Improving Stokes’ solution of flow past a sphere at low Reynolds number, Whilehead’s paradox, Van Dyke’s matching principle.
Essential Readings:
Matti Heiliö and Timo Lähivaara, Mathematical Modeling, Springer, 2016.
Lindsay A. Skinner, Singular Perturbation Theory, Springer, 2011.
James G. Simmonds, James E. Mann Jr., A First Look at Perturbation Theory, Dover Publications, 2nd Revised ed. Edition (July 10, 1997).
