[CFD] The Boussinesq Approximation for Bouyancy Driven (Natural Convection) Flow

An introduction to the Boussinesq approximation for bouyancy driven (convection dominated) flows in CFD, what the approximation is and how it is implemented. The following topics are covered:

1) 1:43 Why is the Boussinesq approximation needed?

2) 4:28 How is the Boussinesq approximation implemented in the momentum equations?

3) 14:10 When is it valid and when should I use it?

===============================================
The following references may be useful:
===============================================

1) J. Ferziger & M. Peric, 'Computational Methods for Fluid Dynamics', Springer, 3rd Edition (pp 14-15)

2) ANSYS Inc. 'ANSYS Fluent User Manual'

3) COMSOL Multiphysics Cyclopedia

#cfd #boussinesq-approximation #bouyancy

============================================
Want to learn more?
============================================
Grab a copy of my CFD Fundamentals Course (for beginners):

Learn how to write your own CFD code in MATLAB and python (for intermediates):

Learn how I draw my figures and diagrams in Inkscape (for everyone):

============================================
Did you like the video?
============================================

Download the lecture slides from my website:

Buy me a coffee to say thanks:

Support the channel on Patreon (and get useful extras for your CFD studies):

============================================
Donations:
============================================

1) PayPal

==================================
Disclaimer
==================================
The methods, algorithms, equations, formulae, diagrams and explanations in this talk are for educational and demonstrative purposes only. They should never be used to analyse, design, accredit or validate real scientific / engineering / mathematical structures and flow systems. For such applications, appropriate trained, qualified and accredited (SQEP) engineers / scientists should be consulted along with the appropriate documentation, procedures and engineering standards. Furthermore, the information contained within this talk has not been verified, peer reviewed or checked in any way and is likely to contain several errors. It is therefore not appropriate to use this talk itself (or any of the algorithms, equations, formulae, diagrams and explanations contained within this talk) as an academic or technical reference. The reader should consult the original references and follow the verification and validation processes adopted by your company / institution when carrying out engineering calculations and analyses. Fluid Mechanics 101 and Dr. Aidan Wimshurst are not accountable or liable in any form for the use or misuse of the information contained in this talk beyond the specific educational and demonstrative purposes for which it was intended.

[mohammadjadidi]

I really like the way you talk about fluid mechanics and CFD. Thank you very much.

[milansekularac]

At 5:30, beware that the density can be brought outside of the total derivative (D/Dt) at <<all times>>, i.e., be it constant (incompressible flow) or not. It is a convinient property of the material derivative D/Dt which comes by virtue of the continuity equation. Excellent videos, as usual. :)

[tejesdas]

Thank you Mr. Wimshurst, very good explanation.

[prayashpanda]

Fantastic effort man!
I have watched multiple videos of yours!

[BatistaRX]

solid explanation man keep up the good work

[avinalexander]

Excellent explanation, I had doubt on Boussinesq density aprox. which is absolutely cleared.

[Thesportynerd]

thank you, Aidan. Another great video.

[hardiksharda]

I love the example !
Thank you Dr. Aidan

[yogeshghadge]

Keep up the good work. Very concise explanation.

[AmmarLaichi]

Hello Dr, I have questions about bousinesq hypothesis,
in mixed convection in circular duct we use bousinesq to define density, the results of temperature give a higher difference temperature in each cross section because a higer Grashof number or heat flux when using water or nanofluids as working fluid so, what do we do in this case?

[achyuth_rj]

I wonder why the acceptable variation in temperature for water is so much lesser than air. Seems a bit counter-intuitive considering how compressible air is comparing to water.
Would be nice if anyone has views on this.
Great content again Aiden!

[AmmarLaichi-rm]

Thanks Dr, the difference between temperature for water in heated circular tube varies in which range?

[lupocci]

A few points:
1) Diffusive term is approximated too. You divide by rho_0 and mu becames ni
2) You should discuss also the primitive form. If you start from that one, you cannot get eq 9, because primitive looks like eq 9 except that you have rho everywhere instead of rho_0, and rho/rho in the gravity term disappear. How come the two forms are not giving the same result once using the boussinesq approx on them? Worth discussing, maybe just in this comment

[EclecticVibe]

Hello Mr.Aidan thank you for a great explanation once again!. Did you ever get around to making the video on COMPRESSIBLE FLOW ? I am currently not able to find the video in your playlist. If you did make a video can you please mention the video?

[benoitdequick]

Hello, thanks for your well explained videos. Small question... Could it be that the brackets are wrong in Eq. 2? Thanks.

[mariyamali]

when boussinesq approximation is used for incompressible flows, why did you use the compressible Navier stokes eq for the derivation?

[timothymills]

Is the understanding here that <<1 is equal to <0.01? I.e. density fluctuations much less than 100% are taken to be density fluctuations of less than 1%?

[arefghayedi]

hello dear Aidan. your video solve my problems for natural convection in cavity flow. thank you very much

[Thisalwerasekara]

Thank you so much. this is quite useful infromation.

[vivekananddhumal]

Thank you for explanation.. I’m working on thermal stratification... does this has limitations at higher temperature gradient.. also what should be the operating density if I am working on closed system