MATHEMATICAL MODELING AND PERTURBATION METHODS

Paper Code: 
MAT144B
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00

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 viscous fluid through elastic tube.

 

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.
 

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.

References: 
  1. Matti Heiliö and Timo Lähivaara, Mathematical Modeling, Springer, 2016.
  2. Lindsay A. Skinner, Singular Perturbation Theory, Springer, 2011.
  3. James G. Simmonds, James E. Mann Jr., A First Look at Perturbation Theory, Dover Publications, 2nd Revised ed. Edition (July 10, 1997)
     
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