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.
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