The objective of this course it to provide a fundamental understanding of the convection and diffusion process in fluids, and how these determine the rates of transport of mass, heat and momentum.
Course details:
- Introduction.
- Dimensional analysis.
- Limitations of unit operations approach.
- Diffusion due to random motion. Estimates of diffusion coefficient from kinetic theory and for turbulent flow.
- Steady and unsteady diffusion in one dimension from a flat plate.
- Equivalence of heat, mass and momentum transport for unsteady one dimensional diffusion.
- Steady and unsteady transfer to a cylinder - balances in cylindrical co-ordinates.
- Effect of pressure in fluid flow.Steady and unsteady flow in a pipe. Method of separation of variables.
- Oscillatory flow in a pipe. Use of complex analysis for oscillatory flow. Boundary layer analysis.
- Free surface flows down an inclined plane. Combination of convection, diffusion.
- Derivation of balance laws for stationary control volumes as partial differential equations for heat, mass and momentum transfer.
- Balances in cylindrical and spherical coordinates.
- Diffusion dominated transport in three dimensions. Fourier's law, Fick’s law as partial differential equations.
- Solution of temperature field in a cube using spherical harmonic expansions.
- Temperature field around a spherical inclusion. The use of separation of variables.
- Spherical harmonics. Equivalent point charge representations.
- Thermal conductivity of a composite.
- Effect of convection at low Peclet number. Regular perturbation expansion for streaming flow past a sphere.
- Convection at high Peclet number. Boundary layer solutions for streaming past a sphere.
- Computational solutions of diffusion dominated flows.