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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Course Curriculum

Introduction Details 58:4
Dimensional Analysis Details 58:33
Dimensional Analysis contd. Details 58:19
Physical Interpretation of Dimensional Groups Details 58:12
Continuum description Details 57:15
Mechanisms of diffusion – I Details 57:55
Mechanisms of diffusion – II Details 57:5
Unidirectional Transport Cartesian Coordinates – I Details 57:52
Unidirectional Transport Cartesian Coordinates – II Similarity Solutions Details 57:9
Unidirectional Transport Cartesian Coordinates – III Similarity Solutions Details 56:21
Unidirectional Transport Cartesian Coordinates – IV Seperation of Variables Details 55:36
Unidirectional Transport Cartesian Coordinates – V Seperation of Variables Details 57:13
Unidirectional Transport Cartesian Coordinates – VI Oscillatory Flows Details 56:7
Unidirectional Transport Cartesian Coordinates – VII Momentum Source in the Flow Details 57:10
Unidirectional Transport Cartesian Coordinates – VIII Heat & Mass Sources Details 56:51
Unidirectional Transport Cylindrical Coordinates – I Conservation Equations Details 57:12
Unidirectional Transport Cylindrical Coordinates – II Similarity Solutions Details 56:47
Unidirectional Transport Cylindrical Coordinates – III Seperation of Variables Details 57:15
Unidirectional Transport Cylindrical Coordinates – IV Steady flow in a pipe Details 57:4
Unidirectional Transport Cylindrical Coordinates – V Oscillatory flow in a pipe Details 53:52
Unidirectional Transport Cylindrical Coordinates – VI Details 55:1
Unidirectional Transport Cylindrical Coordinates – VII Details 56:6
Unidirectional Transport Spherical Coordinates – I Balance Equation Details 57:35
Unidirectional Transport Spherical Coordinates – II Seperation of Variables Details 57:30
Mass & Energy Conservation Cartesian Coordinates Details 57:17
Mass & Energy Conservation Cartesian Coordinates Heat Conduction in a Cube I Details 56:11
Mass & Energy Conservation Spherical Coordinates Balance Laws II Details 58:4
Mass & Energy Conservation Cylindrical Coordinates III Details 56:25
Diffusion Equation Spherical Co-ordinates Seperation of Variables Details 56:23
Diffusion Equation Spherical Co-ordinates Seperation of Variables contd. I Details 57:13
Diffusion Equation Spherical Co-ordinates Effective Conductivity of a Composite II Details 57:58
Diffusion Equation Spherical Harmonics III Details 58:22
Diffusion Equation Delta Functions IV Details 57:50
Diffusion Equation Multipole Expansions V Details 58:25
Diffusion Equation Oreens Function Formulations VI Details 58:27
High Peclet Number Transport Flow Past a Flat Plate Details 58:37
High Peclet Number Transport Heat Transfer from a Spherical Particle – I Details 56:42
High Peclet Number Transport Heat Transfer from a Spherical Particle – II Details 58:37
High Peclet Number Transport Heat Transfer from a Gas Bubble Details 58:2
Summary Details 58:17

This Course is provided by IISc Bangalore as part of NPTEL online courses.

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