MATHEMATICAL MODELING AND PERTURBATION METHODS
Newtonian and non-Newtonian fluids, Constitutive equations, Some important class of non-Newtonian fluids, Fundamental equations of motion and continuity.
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 various fluid through elastic tube.
Oscillatory flow through a circular tube (Newtonian fluids 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.
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.
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.
- 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 Edition(July 10,1997)
