M.PHIL. / Ph.D. – (FT/PT) - APPLIED MATHEMATICS
PART – 1 SYLLABUS
(Effective from October 2011 onwards)
Note:
There is no change in the existing papers except Paper III- Special Paper: Convection
Heat Transfer and Magnetohydrodynamics.
The revised syllabi for Paper III- Special Paper: Convection Heat Transfer and
Magnetohydrodynamics & Newly framed syllabi for the Paper III – Special Paper :
Hamiltonian Dynamics and Chaos is furnished below.
Paper III SPECIAL PAPER
CONVECTION HEAT TRANSFER AND MAGNETOHYDRODYNAMICS
Unit I : Laminar Boundary Layer Flow - Fundamental Problem in Convective Heat Transfer -
Concept of Boundary Layer- Velocity and Thermal Boundary Layers - Integral Solutions -
Similarity Solutions-Methods- Flow Solution - Heat Transfer Solution.
Unit II: Laminar Boundary Layer Flow - Other wall heating conditions - Unheated starting
length - Arbitrary wall Temperature - Uniform Heat flux - Film Temperature - Effect of
longitudinal Pressure Gradient: Flow past a wedge and stagnation flow - Effect of flow through
the wall: Blowing and suction - Effect of conduction across a solid coating deposited on a wall.
Laminar Duct Flow – Hydrodynamic Entrance length - Fully Developed Flow -
Hydraulic Diameter and Pressure Drop.
Unit III: Laminar Duct Flow - Heat Transfer to Fully Developed Duct Flow - Mean
Temperature - Fully Developed Temperature Profile- Uniform Wall Heat Flux - Uniform Wall
Temperature - Tube Surrounded by Isothermal Fluid - Heat Transfer to Developing Flow - Scale
Analysis - Thermally Developed Uniform (Slug) Flow - Thermally Developing Hagen -
Poiseuille Flow.
Unit IV: Introduction and Fundamental equations of MHD and Steady Laminar Flow -
The electrodynamics of moving media - The electromagnetic effects and the magnetic Reynolds
number - Alfven’s theorem - The magnetic energy - The mechanical equations - The mechanical
effects - The electromagnetic stresses - Steady laminar motion.
Unit V: Magnetohydrodynamic waves and stability - Waves in an infinite fluid of infinite
electrical conductivity - Alfven waves -Magnetohydrodynamic waves in a compressible fluid –
Stability – Introduction - Simple illustrative examples - Instability of linear pinch - Flute
instability - A general stability criterion- The method of small oscillations - Boundary conditions
- Solution of the equations - Illustrative example.
Textbook for Units I, II, III
A.Bejan, “Convection Heat Transfer”, Third Edition, John Wiley & Sons, Hoboken,
(2004).
Unit I – Sections 2.1 to 2.5 from Chapter 2.
Unit II – Sections 2.6 to 2.9 from Chapter 2 and Sections 3.1 to 3.3 from Chapter 3.
Unit III – Sections 3.4 to 3.5.3 from Chapter 3.
Textbook for Units IV & V
V.C.A Ferraro & C. Plumpton, “An introduction to Magneto-Fluid Mechanics”
Clanendon Press, Oxford, (1966).
Unit IV – Sections 1.1 to 1.7 from Chapter I and Section 2.5 from Chapter II.
Unit V – Sections 3.1 to 3.3 from Chapter III and Sections 5.1 to 5.3 from Chapter V.
M.Phil. /Ph.D. Applied Mathematics. From October 2011 onwards Page 3 of 3
Paper III - Special Paper : Hamiltonian Dynamics and Chaos
Unit I: The Dynamics of Differential Equations
Integration of linear second order equations - Integration of nonlinear second order
equations - Dynamics in the phase plane - Linear Stability analysis.
Unit II: Hamiltonian Dynamics
Lagrangian formulation of Mechanics - Hamiltonian formulation of Mechanics Canonical
transformations - Hamilton-Jacobi equation and action - angle variables -integrable
Hamiltonians.
Unit III: Classical Perturbation Theory
Elementary perturbation theory - Canonical perturbation theory - Many degrees of
freedom and the problem of small divisors - The Kolmogrov- Arnold-Moser theorem.
Unit IV: Chaos in Hamiltonian systems and area-preserving mapping
Area preservingmapping-Fixed points and the poincare-Birkhoff fixed point theorem
Homoclinic and heteroclinic points-Criteria for local Chaos.
Unit V: Nonlinear Evolution Equations and Solitons
Basic properties of the Kdv equation - The inverse Scattering transforms: Basic principles,
KdV equation - Other soliton systems - Hamiltonian structure of integrable systems.
Treatment as in:
Chaos and Integrability in Nonlinear Dynamics by M.Tabor, John Wiley and Sons, New York,
1989.
Unit I Chapter 1 Sections 1.1 - 1.4,
Unit II Chapter 2 Sections 2.1 - 2.5
Unit III Chapter 3 Sections 3.1 - 3.4
Unit IV Chapter 4 Sections 4.2 -4.5
Unit V Chapter 7 Sections 7.2 – 7.6
