www.b-u.ac.in Bharathiar University : M.Phil, Ph.D Applied Mathematics Syllabus

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BHARATHIAR UNIVERSITY : COIMBATORE 641046
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 the 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.

http://www.b-u.ac.in/links/syllabus_textbook.html
http://www.b-u.ac.in/syl_mphil/2011oct/1.pdf

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.

Text book 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.

Text book 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.