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

[@mohammadjadidi233]

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

[@tejesdas3896]

Thank you Mr. Wimshurst, very good explanation.

[@milansekularac6196]

At 5:30, beware that the density can be brought outside of the total derivative (D/Dt) at , 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. :)

[@fluidmechanics101]

Great point. This is only something I spotted a few years later!

[@avinalexander]

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

[@hardiksharda9673]

I love the example ! Thank you Dr. Aidan

[@Thesportynerd16]

thank you, Aidan. Another great video.

[@prayashpanda7884]

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

[@BatistaR0X]

solid explanation man keep up the good work

[@fluidmechanics101]

Thanks Batista!

[@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!

[@parasghumare8067]

I have the same question. But I think it depends on the thermal expansion coefficient used in specific scenarios. Aiden please answer.

[@yogeshghadge5748]

Keep up the good work. Very concise explanation.

[@gaetanp.8728]

I believe there are 2 typo on slide 5/21 : \Delta p instead of \Delta ho. Otherwise great content!

[@danielgraebin242]

Thank you Aidan!

[@arefghayedi7000]

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

[@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

[@behzadamonfared8614]

Your videos are great. By the way there is a spelling mistake in the video title and the slides: “Buoyancy” is correct. It’s the only English word that I can think of in which “u” precedes “o” in “o-u” combination!

[@fluidmechanics101]

Well spotted. I always spell buoyancy wrong 🤦‍♂️ hahaha

[@mckackik]

Great, thanks

[@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?

[@fluidmechanics101]

Not yet. Hopefully coming soon 🙂

[@Johan-gl8fg]

I'm seconding this, @fluidmechanics101 ! It would be nice with a video on the algorithms used in buoyantPimpleFoam, i.e. for cases where the approximation in this video is not valid. Anyways, thanks a lot for making these videos!

[@parasghumare8067]

The diffusive term in equation 2 has an extra close bracket.

[@SHOPAH0LIC]

Very helpful explanation!

[@stellaakhigbe5496]

Just stumbled at this video because I am working in this area. A really nice video. Please can you show the derivation of the buoyancy force part when we are looking at a nanofluid. I'm confused and would appreciate an explanation

[@Thisalwerasekara]

Thank you so much. this is quite useful infromation.

[@benoitdequick2562]

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

[@fluidmechanics101]

Yes, there might be a typo here. It shouldn't affect the rest of the talk so I wouldn't worry about it 😉

[@mechanical4642]

Sir, Thanks for your explanation. Can you please make a video on how fluid structure interaction is implemented on such benchmark problem like flow past a cylinder with flexible splitter plate. Thanks once again for enlightening lectures

[@AmmarLaichi-r7m]

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

[@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?

[@rafaortwein6646]

Good knowledge

[@tipusultan148]

Thank you.

[@vivekananddhumal7853]

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

[@fluidmechanics101]

If you are unsure, i would not use the boussinesq approximation and just use the full density based calculation. For your operating density, choose the lowest density in your system. This will probably be air at room temperature or water at room temperature (but i dont know your system ... so just a guess)

[@gianhauenstein9003]

Very good! Keep going!

[@swrona90]

Hi. Great material. One quick question to slide 20, how to understand M

[@blindshellvideos]

I would be really careful to equate M

[@christianbarreto6195]

nice video

[@igazmondo2542]

Hi I like you videos they are just excellent! I would have a q for the applicability of Boussinesq approx. What does this Delta T > 15°C mean? Is it measured between solid and air? or the min/max temp within the fluid region? e.g. Heat sink surface temp can be 105°C while the cooling air kept below 60°C in this case the B approx can not be used? Thanks your thoughts in advance

[@fluidmechanics101]

The delta T is just for guidance really. You can look at the overall temperatures in your model. For your case the overall temperature difference is ~ 45 degrees, so i would just go with full buoyancy treatment. The increase in computational cost is not that great, so you may as well 😊

[@igazmondo2542]

@@fluidmechanics101 I have just learned Icepack from Ansys because I need to do some PCBA cooling calcs what does not make sense to do in fluent. The default is Boussinesq approx. The another option is ideas gas low. So most of the cases in Icepack the average user uses the simplified BA model instead of the more accurate ideal gas one... I was really surprised .... btw the Ansys learning HUB tutorial does not even take care of this... they just let the tutorial calculated with BA where the heat sink temp goes to 268°C while the cooling air is at RT. Anyhow thanks your response. I will do accordingly:)

[@mathsk1081]

I am a bit confused about the decision tree. I think it is not unique. I’m first it means M

[@fluidmechanics101]

If you are unsure, just go for full buoyancy treatment (no boussinesq). You will be fine and not need to worry about the results

[@husainiroslan8984]

Hello,can you make a video for full compressible formulation in which boussinesq approximation cant be used?high temperature variation

[@fluidmechanics101]

Hi Husaini, yes i an making a video for the full compressible formulation. It will be out on the channel soon! The key point with the full compressible form is to use a ‘density based’ solver (ANSYS Fluent terminology), where the continuity equation is solved for density. The bouyancy force in the momentum equations can then be evaluated explicitly and pressure is computed from an equation of state (the ideal gas law for example). Dont worry if this is confusing though! The video will be out soon :)

[@danieltarraf7881]

Very Helpful Thanks!!

[@mariyamali628]

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

[@fluidmechanics101]

Good question 😅 I think the derivation is still fine

[@mariyamali628]

Thanks for replying... But my doubt is still not clear... What I want to ask is can we come up with the same conclusion if you would have used the incompressible navier stokes equation?

[@fluidmechanics101]

If you check out the book 'Fundametals of Heat and Mass Transfer' by F. Incropera, there is a full derivation in there for incompressible flow. The key point is that in addition to the maths shown in the video, the Boussinesq approximation makes the additional approximation that the only effect of buoyancy on the flow is an additional body force acting on the flow. Other non linear effects like the change in the density which changes the convection of mass into the cell (think of the other terms in the NS equations which contain density) are neglected. The only effect is assumed to be the buoyancy source term! I may make an updated video to show this at some point in the future

[@mariyamali628]

@@fluidmechanics101 I got your point. Thanks Alot for the explanation and making time to reply. Your videos really helped me get a better understanding of CFD. 😊

[@CesarLopez-qt9mo]

Thanks a lot, A very good explanation. Regards.

[@fluidmechanics101]

Thanks Cesar! Im glad you found it useful

[@timothymills5149]

Is the understanding here that

[@DigitalSite-z9o]

Dr. Aiden would you please help me regarding solving my research paper?

[@ranulph314]

thanks

[@abhishekthakur-xt7fl]

Very great man!!!!

[@fluidmechanics101]

Thanks Abhishek 😊

[@bhanusharma8358]

Sir ; How Ma > 0.3 will be considered as criterion of compressible flows ?

[@fluidmechanics101]

The degree of error in assuming incompressible flow scales with Ma^2. So 0.3^2 = 0.09. This is a 10% error. So Ma > 0.3 are usually considered compressible 👍

[@bhanusharma8358]

@@fluidmechanics101 Thanks Sir!

[@bhanusharma8358]

​@@fluidmechanics101 Sir , I am third Year Mechanical Engineering Student . could you suggest me which software should i opt for deeper learning of C F D ? i.e. OpenFOAM / ANSYS.

[@fluidmechanics101]

If you have an ANSYS license, fluent or CFX tends to give more stable results than OpenFOAM. OpenFOAM is harder as you have to choose all of the settings yourself, there are no defaults!!

[@bhanusharma8358]

@@fluidmechanics101 Thanks Sir!

[@kennydoritos]

I am alittle lost about how he derived the acceptable temperature difference for air and water at rtp. I tried calculating it by myself but I dont seem to get anything similar. beta ~ (1/rho_ref)X(rho-rhoRef)/(T-Tref), beta(T-Tref) ~ (rho-rhoRef)/rhoRef If changes in density is negligible, (rho-rhoRef)/rhoRef < 0.01 (For 1 percent error/ changes in density?) beta(T-Tref)

[@gaetanp.8728]

beta is a function of temperature. For water, it goes from -50e-6 at 1deg C to 695e-6 at 90deg C so you need to choose carefully beta. For exemple, beta(T=Tmean) where Tmean is an estimation of (T+Tref)/2.

[@अण्वायुवरीवर्त]

I feel like piece of shit after watching it, even though I was understanding what u were saying n that's a good thing But really I don't use Ansys, that's a shame! We don't get much time to do the analysis Bcz of these short semesters.

[@अण्वायुवरीवर्त]

BTW is this from PG or UG

[@fluidmechanics101]

This is more for PG, so dont worry if you are UG 😄

[@अण्वायुवरीवर्त]

@@fluidmechanics101 Woah what a relief, I thought I did nothing in this semester n also in previous sem, as I had fluid mechanics in last sem n now I have heat transfer Thanx man I subbed, loved your other stuff too

[@shirunding6694]

thanks