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, Ficks 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.