Undergraduate Program

We are working in the Department of Mathematics. Amongst the several courses of Fluid mechanics in the department, there are two courses at the undergraduate level. The contents of these courses are in the following.

1. MA 471: Fluid Mechanics

Real fluids and ideal fluids, Velocity of a fluid at a point, Streamlines and path lines, Steady and unsteady flows, Velocity potential, Vorticity vector, Local and particle rates of change, Equation of continuity. Acceleration of a fluid, Conditions at rigid boundary, general analysis of fluid motion, Euler’s equation of motion, Bernoulli’s equation steady motion under conservation body forces, Some potential theorems, Impulsive motion, Sources, skins and doublets, Images in rigid infinite plane and solid spheres, Axi-symmetric flows, Stokes’s stream function, Stream function, Complex potential for two-dimensional, irrotational and incompressible flow, Complex velocity potential for uniform stream. Lines sources and line sinks, Line doublets and line vortices, Image systems, Miline-Thomson circle theorem, Blasius’ theorem, The use of conformal transformation and Schwarz-Christoffel transformation in solving problems, Vortex rows. Kelvin’s minimum energy theorem, Uniqueness theorem, fluid streaming past a circular cylinder, Irrotational motion produced by a vortex filament. The Helmholtz vorticity equation, Karmans’ vortex street.

1. MA 472: Fluid Mechanics-II

Constitutive equations, Navier-Stokes’ equations, Exact solutions of Navier-Stokes equations, Steady unidirectional flow, Poiseuille flow, Couette flow, Unsteady unidirectional flow, Sudden motion of a plane boundary in a fluid at rest, Flow due to an oscillatory boundary, Equations of motion relative to a rotating system, Ekman flow, Dynamical similarity and Reynolds’ number, Flow over a flat plate (Blasius’ solution), Reynolds’ equations of turbulent motion.

Graduate Program

At this level, we have some courses describing the flows of viscous and non-Newtonian fluids. To be more specific, we offer such courses to those research scholars who are pursuing for M. Phil and PHD degrees. At present, there are 33 research students who are working in Fluid mechanics group. Out of these 33, 16 are working for M. Phil and 17 for PhD degrees. The contents of the courses at the graduate level are as follows.

1. MA-657: Basics of the theory of fluids

Eulers’ equation of motion, Viscosity, Navier-Stokes’ equations and exact solutions, Dynamical similarity and Reynolds’s number, Turbulent flow, Boundary layer concept and governing equations, Reynolds’ equations of turbulent motion, Magnetohydrodynamics, MHD equations, Fluid drifts, Stability and equilibrium problems.

1. MA 674: Non_newtonian fluid Mechanics

Classification of non-Newtonian fluids, Rheological formulae (Time independent fluids, Thixotropic fluids and viscoelastic fluids), Variable viscosity fluids, Cross viscosity fluids, The deformation rate, Viscoelastic equations, Material with short memories, Time dependent viscosity, The Rivilin-Ericksen fluid, Basic equations of motion in rheological models, The linear viscoelastic liquid, Couette flow, Poiseuille flows, The current semi-infinite field, Axial oscillatory tube flow, Angular oscillatory motion, Periodic transients, Basic equations in boundary layer theory, Orders of magnitude, Truncated solutions for viscoelastic flow, Similarity solutions, Turbulent boundary layers, Stability analysis.