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.
- 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.