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. :)
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!
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
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!
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?
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
@@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. 😊
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?
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
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?
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!
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 :)
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
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)
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
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
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 😊
@@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:)
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)
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.
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 👍
@@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.
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!!
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.
@@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
![[CFD] The Boussinesq Approximation for Bouyancy Driven (Natural Convection) Flow](/img/logo.svg){kind=logo}
