Advanced Transport Processes

By Prof. V. Kumaran | IISc Bangalore

Learners enrolled: 127 | Exam registration: 1

ABOUT THE COURSE:

The study of transport phenomena an essential part of chemical engineering, and other disciplines concerned with material transformations such as biomedical engineering, microfluidics, reactor design and metallurgy. Material transformations require the motion of constituents relative to each other, the transfer of heat across materials and fluid flow. This course introduces the student to the fundamentals and applications of transport phenomena in a single volume, and explains how the outcomes of transformation processes depend on fluid flow and heat/mass transfer. It demonstrates the progression from physical concepts to the mathematical formulation, followed by the solution techniques for predicting outcomes in industrial applications. This course also provides a foundation for advanced courses in fluid mechanics, multiphase flows and turbulence.

INTENDED AUDIENCE: BE/B. Tech Final year/M. Tech. First Year Chemical Engineering/Biochemical Engineering/Materials Engineering

PREREQUISITES: Undergraduate mathematics, linear algebra, ordinary differential equations.

INDUSTRY SUPPORT: Companies that design or operate processes for material transformations.

Summary

Course Status :	Upcoming
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Chemical Engineering Minor 3 in Chemical
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	26 Jan 2026
Exam Registration Ends :	13 Feb 2026
Exam Date :	25 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Conservation equations: Mass conservation.
1.Ch.7, Sec.1: Conservation equations, Cartesian co-ordinates.
2.Ch.7, Sec.2: Conservation equations, Spherical co-ordinates.
3.Ch.7, Sec.2: Conservation equations, Spherical co-ordinates.
4.Ch.7, Sec.2: Conservation equations, Vector operators, Gradient Divergence, Curl.
5.Ch.7, Sec.2: Conservation equations, Vector operators, Gradient Divergence, Curl.

Week 2: Conservation equations: Momentum conservation.
6.Ch.7,Sec.3.1: Conservation equations, Navier-Stokes mass conservation, stream function.
7.Ch.7, Sec.3.2: Conservation equations, Stress tensor.
8.Ch.7,Sec.3.2: Conservation equations, Stress tensor, pressure.
9.Ch.7,Sec.3.3: Conservation equations, Rate of deformation tensor.
10.Ch.7,Sec.3.3: Conservation equations, Decomposition of rate of deformation tensor.

Week 3: Conservation equations, Transport into infinite medium.
11. Ch. 7, Sec. 3.4: Conservation equations, Newton’s law of viscosity.
12. Ch. 7, Sec. 3.5: Conservation equations Navier-Stokes momentum equation.
13. Ch. 7 Sec. 3.6: Conservation equations, Potential flow.
14. Ch. 4, Sec. 4: Similarity solution. Transport into infinite medium.
15.Ch. 4, Sec. 4: Similarity solution. Transport into infinite medium.

Week 4: Unsteady transport: Similarity solutions.
16. Ch. 4, Sec. 4.1: Similarity solution. Diffusion into infinite film.
17. Ch. 4, Sec. 5: Similarity solution. Decay of a pulse.
18. Ch. 4, Sec. 5: Similarity solution. Decay of a pulse.
19. Ch. 4, Sec. 6: Similarity solution. Time-dependent length scale.
20.Ch. 5, Sec. 1.3: Similarity solution. Heat conduction from a wire.

Week 5: Unsteady transport: Separation of variables.
21. Ch. 4, Sec. 7: Separation of variables: Transport into finite medium. Cartesian co-ordinates.
22. Ch. 4, Sec. 7: Separation of variables: Transport into finite medium. Cartesian co-ordinates.
23. Ch. 5, Sec. 1.4: Separation of variables. Heat conduction into a cylinder.
24. Ch. 5, Sec. 1.4: Separation of variables. Heat conduction into a cylinder.
25.Ch. 5, Sec. 2.4: Separation of variables. Heat conduction into a sphere.

Week 6: Unidirectional flow: Oscillatory flow in a pipe.
26. Ch. 5: Sec. 4: Oscillatory flow in a pipe.
27. Ch. 5: Sec. 4: Oscillatory flow in a pipe.
28. Ch. 5: Sec. 4.1: Oscillatory flow in a pipe. Low Reynolds number.
29. Ch. 5: Sec. 4.2: Oscillatory flow in a pipe. High Reynolds number.
30.Ch. 8: Sec. 1: Diffusion equation: Separation of variables. Cartesian co-ordinates

Week 7: Diffusion equation: Separation of variables.
31. Ch. 8: Sec. 1: Diffusion equation: Separation of variables. Cartesian co-ordinates.
32. Ch. 8: Sec. 2: Diffusion equation: Temperature around a spherical inclusion.
33. Ch. 8: Sec. 2: Diffusion equation: Legendre polynomials.
34. Ch. 8: Sec. 2: Diffusion equation: Temperature around spherical inclusion.
35.Ch. 8: Sec. 2: Diffusion equation: Effective conductivity of a composite

Week 8: Diffusion equation: Separation of variables.
36. Ch. 8: Sec. 2: Diffusion equation: Separation of variables: Nonaxiysmmetric.
37. Ch. 8: Sec. 2: Diffusion equation: Separation of variables: Nonaxiysmmetric.
38. Ch. 8: Sec. 3: Diffusion equation: Multipole expansion: Point source, dipole.
39. Ch. 8: Sec. 3: Diffusion equation: Multipole expansion: Quadrupole.
40.Ch. 8: Sec. 3: Diffusion equation: Separation of variables & Multipole expansion

Week 9: Diffusion equation: Method of images; Forced convection.
41. Ch. 8: Sec. 4: Diffusion equation: Method of images.
42. Ch. 8: Sec. 4: Diffusion equation: Green’s function method.
43. Ch. 8: Sec. 4: Diffusion equation: Green’s function method.
44. Ch. 9: Sec. 1.1: Forced convection: Flow past rigid surface.
45.Ch. 9: Sec. 1.1: Forced convection: Flow past rigid surface

Week 10: Forced convection: Flow in a pipe, flow past a particle.
46. Ch. 9: Sec. 1.2: Forced convection: Heat transfer in a pipe.
47. Ch. 9: Sec. 1.3: Forced convection: Flow past spherical particle.
48. Ch. 9: Sec. 1.3: Forced convection: Flow past spherical particle.
49. Ch. 9: Sec. 1.4: Forced convection: General flow-fields, no-slip condition at surface.
50.Ch. 9: Sec. 2.1: Forced convection: Diffusion from a gas bubble.

Week 11: Forced convection: Diffusion from a bubble, Taylor dispersion.
51. Ch. 9: Sec. 2.1: Forced convection: Diffusion from a gas bubble.
52. Ch. 9: Sec. 2.2: Forced convection: General flow-fields, slip at the surface.
53. Ch. 9: Sec. 2.3: Forced convection: Flow in packed column.
54. Ch. 9: Sec. 2.3: Forced convection: Taylor dispersion.
55.Ch. 9: Sec. 2.3: Forced convection: Taylor dispersion.

Week 12: Natural convection.
56. Ch. 10: Sec. 1: Natural convection: Bousinessq approximation.
57. Ch. 10: Sec. 1: Natural convection: Bousinessq approximation.
58. Ch. 10: Sec. 2: Natural convection: High Grashof number limit.
59. Ch. 10: Sec. 2: Natural convection: High Grashof number, low Peclet number
60.Ch. 10: Sec. 2: Natural convection: High Grashof number, high Peclet number

Books and references

V. Kumaran, Fundamentals of Transport Processes, Cambridge-IISc Series, Cambridge University Press, 2022.

Instructor bio

Prof. V. Kumaran

IISc Bangalore

Prof. V. Kumaran is Professor, Department of Chemical Engineering at the Indian Institute of Science, Bangalore. His research interests include statistical mechanics, fluid mechanics and the dynamics of complex fluids. He was the recipient of the Shanti Swarup Bhatnagar Prize for Engineering Science for the year 2000, and the Infosys Prize for Engineering and Computer Science for the year 2016.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: April 25, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc Bangalore. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team