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Course Co-ordinated by IISc Bangalore
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Prof. V. Kumaran
IISc Bangalore

 

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Physical and chemical transformations of raw materials to products are accomplished in unit operations which involve mixing, heating/cooling, reactions and flow. The efficiency of these processes is critically dependent on the transport of heat and mass carried along with flowing fluid, and across solid/fluid interfaces. The transport across interfaces is entirely due to molecular diffusion, which is the transport in a stationary fluid due to gradients in concentration or temperature. The combination of convection (transport by flowing fluids) and diffusion determine the rate of transport, and the overall efficiency, in unit operations. In this course, we will obtain a physical understanding of how the balance between convection and diffusion determines the overall transport rates in chemical processes, and gives rise to many of the empirical correlations used in chemical engineering design.

Week

Topics

1

1. Introduction
2. Dimensional analysis & Correlations.
3. Dimensional analysis: Physical interpretation

2

4.Convection & Diffusion. Diffusion as a molecular process. Constitutive relations.
5. Diffusion due to random motion. Derivation of diffusion coefficients from molecular perspective.
6. Diffusion in gases and liquids. Turbulent diffusion

3

7. Steady and unsteady diffusion in one dimension from a flat plate. Equivalence of heat, mass and momentum transport for unsteady one dimensional transport.
8. Solution of unsteady balance equations in infinite domain; similarity solution.
9. Solution of unsteady balance equations in finite domain; method of separation of variables.

4

10. Shell balances and conservation equations in cylindrical co-ordinates. Heat transfer across pipe wall. Viscous heating in a pipe.
11. Steady conduction in a cylinder.
12. Shell balance in spherical co-ordinates. Heat transfer from a spherical particle. Unsteady mass diffusion from a point source.

5

13. Effect of pressure and body forces in fluid flow. Steady & unsteady flow down inclined plane.
14. Steady and unsteady flow in a pipe.
15. Oscillatory flow in a pipe. Complex analysis for oscillatory flow. Boundary layer analysis.

6

16. Conservation equations in Cartesian and cylindrical co-ordinates.
17. Spherical co-ordinate system.
18. Conservation equations in vector notation; simplifications of mass and energy conservation. Brief description of incompressible Navier-Stokes.

7

19. Heat transfer in Cartesian co-ordinates. Separation of variables
20. Heat transfer in spherical co-ordinates. Spherical particle in temperature gradient.
21. Thermal conductivity of a composite.

8

22. General solution for diffusion equation in spherical co-ordinates.
23. Delta function representation of point source. Multipole representation of higher harmonics.
24. Method of images. Greens function in bounded domains. Boundary integral technique.

9

25. Boundary layer theory. Heat transfer in flow past a flat plate.
26. Correlations for heat exchanger. Heat transfer from heated sphere.
27. Mass transfer from falling film.

10

28. Forced convection boundary layer for an object of arbitrary shape. 29. Natural convection --- Boussinesq equations. 30. Boundary layer equations at high Grashof number.

11

31. Heat transfer from a heated vertical plate.
32. Correlations at high and low Prandtl number.
33. Combined forced and natural convection.

12

34. Transition to turbulence, and characteristics of turbulent flows.
35. Correlations for turbulent flows.
 
Engineering mathematics including ordinary differential equations, complex variables. Undergraduate course in Unit Operations.
Course notes.

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