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Course Description

This course is an introduction to the underlying foundations of continuum mechanics, with specific emphasis on transport processes of fluid flow, heat and mass transfer.

Course Content

  • Introduction to continuum mechanics
  • Derivation of equations governing transport processes of fluid flow, heat and mass transfer
  • Shell balance approach to derivation of conservation laws
  • Eulerian and Lagrangian frames of reference and their interconversion using the celebrated Reynolds transport theorem will be introduced.
  • Derivation of Cauchy momentum equation, Navier-Stokes, energy, and species balance will be carried out.
  • The importance of scaling will be elucidated with several working examples.
  • The course will be aimed at mathematical formulation of transport processes; there will be a strong emphasis on arriving at analytical solutions by means of similarity transformation, separation of variables, perturbation methods as well as the method of asymptotic matching.
  • Isothermal as well as non-isothermal equations of change will be dealt with, along with specific examples.
  • Singular perturbation theory will be introduced motivated by its application in Boundary layer theory.
  • Lorentz reciprocal theorem to arrive at integrated surface transport characteristics on non-convenient geometries will be introduced.