CH5541 Advanced Topics in Momentum Transfer


Applications of principles on momentum transfer/fluid mechanics are important in various areas such as non-Newtonian flows, thin film flows and atmospheric pollution dynamics. The objective of the course is to address fundamentals of vectors and tensors, frame of reference (static or rotating), complex curvilinear coordinate systems, momentum balance equations in various curvilinear coordinate systems, principles of stress tensors and applications on various complex flow systems.

Course Contents:

Fundamentals of Vectors and Tensors; Dot and Cross Products; Gradients; Divergence; Curl;  Dyadic products; Vectors and Tensor identities using Einstein summation convention;  Higher order isotropic, permutation tensors and their relationships;  Concept of generalized curvilinear coordinate systems: cylindrical, spherical, ellipsoidal, paraboloidal, spheroidal, bipolar;  Gradient, divergence and curl operators in various curvilinear coordinate systems. Continuum approach; Lagrange and Eulerian coordinate systems; Reynolds transport theorem, Conservation equations for mass, momentum and energy; Cauchy’s theorem; Concept of stress tensor: normal stresses;  Conservation of angular momentum and symmetry of stress tensor; Principal stress and stress invariants; Shear stresses; Kinematics; Strain rate tensors.Relationships between stress and strain rate tensors; Derivation of Navier Stokes equations for various curvilinear coordinate systems; Navier Stokes equations due to earth’s motion and analysis of Coriolis force;  Closed form solutions to Navier-Stokes equations for few cases, Creeping flow, Drag, Boundary layer theory, Flow separation, Laminar flow, Transition to turbulence, Turbulent flow, Special Topics: Non-Newtonian fluids; Flow through porous media; Thin film flows; Atmospheric transport and planetary boundary layers; Second law analysis and entropy generation during convective transport.

Text Books:

  1. A Course in Fluid Mechanics with Vector Field Theory: Dennis C Prieve (Online Print, 2001)
  2. An Introduction to Fluid Dynamics:  G K Batchelor (Cambridge University Press)
  3. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes: L. Gary Leal (Cambridge University Press).

Reference Books:

  1. Introduction to Continuum Mechanics: W M Lai, D Rubin and E Krempl (Elsevier)
  2. Numerical Simulation of Non-Newtonian Flow: M J Crochet, A R Davies and K. Walters (Elsevier)
  3. An Introduction to Boundary Layer Meteorology: Ronald B Stull (Kluwer Academic Publishers)
  4. Entropy Generation Minimization: The Method of Thermodynamic Optimization of   Finite-Size Systems and Finite-Time Processes: A. Bejan (CRC Press).