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# Fundamentals of Transport Processes

IISc Bangalore, , Prof. V. Kumaran

Updated On 02 Feb, 19

##### Overview

Contents:
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.

## Lecture 29: Diffusion Equation Spherical Co-ordinates Seperation of Variables

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###### Lecture Details

Fundamentals of Transport Processes by Prof. V. Kumaran, Department of Chemical Engineering, IISc Bangalore. For more details on NPTELvisit httpnptel.iitm.ac.in

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###### Comments

Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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