Hello guys, welcome back to the YouTube channel of the concept guy. And in this video, we will talk about dimensional fewer numbers in mass and heat transfer. So these are actually present in our books. Okay, we can really easily go through them. But the main problem is that we tend to forget these numbers why? So because there are so many numbers, literally there are many like Reynolds smith, Sherwood, Russell Randall and blah, blah, blah.
So the list goes on, and it's really difficult to actually memorize. These numbers, uh till death, maybe or some examination that we are going to face recently. So I will make this video on the different numbers. Okay, various numbers. And we will find some really tricks and tips to actually remember these till eternity. Okay. So first let's move on with our first very basic number that's.
Reynolds number, I know most of you know it already, but still let me just put it on the first number one number because here we start with the momentum itself. So what we do here. Is so guys let's just take the pipe. Okay, a pipe. We take here, the fluid flows and puts an inertial force opposing to which is a viscous force.
Okay, this is my viscous spheres' mu. And this is my inertial force that is MV. Okay. So, so then this will be my inertial force. Okay, this will be my inertial force, inertial force upon my viscous force. This girl's force that's.
My Reynolds number. Okay. And so what we see here we are considering two forces in Reynolds.
Number let's, write the final formula that we get. Um so the formula is really simple as it is just row b, l upon or d. Instead of this l, sometimes there is d, also the diameter so rho, v, l by mu. Okay, this is Reynolds number the simple formula. And this rho v is actually from signifying MV. That is momentum.
Okay? And hence, the upper part is inertial force this one and the lower part signifies viscous force, let's move on to the next number that smith number. And here we can see that there is an m. And there is a there.
M is mass. Okay, m. A double. S, mass and t is transfer okay. So it's a number of mass transfer and ah, let me rub this. Okay, m and t and a similar number to this is my Brandt number brand dirt number. Okay.
And here we see there is also a there. So for smith, number we take m, that's mass transfer. And here it is for heat transfer.
Okay. I hope it's clear, and you all know this already, but let's just see how to remember the formulas. So smith number, we took first the momentum in Reynolds number. Now we take mass and. Momentum, so momentum came first in this, Renault so momentum will be upper this. Upper part will be momentum. And this lower part will be mass.
So right. Momentum. Okay, I'm writing a short, it's momentum. And the movement smith and Brandt numbers. Here also we considered movement in a pipe. Okay because of momentum. Here also we will take a movement that's.
Why there is a diffusivity because this is our second number. Okay. So here is momentum. Diffusivity, divided by mass diffusivity, that's as simple as that. That's how we remember m and t, mass transfer. This is the second number because of which we compare it with the first.
And therefore this momentum is there. And we compare momentum with mass momentum being on the upper or that's, the numerator because it has more weightage. Similarly, for Brandt number again, momentum, uh, momentum, diffusivity. And let me kind of make this length short. And there is heat there's, a heat transfer diffusivity, uh, that's thermal diffusivity. Okay, that's thermal diffusivity. Okay.
So what are their formulas? Let me write it? So let me rub this and momentum diffusivity is quite simple. It is mu, which is actually equal to my mu viscosity upon density.
And my mass diffusivity, the molecular diffusivity is actually denoted by my d. So it is the number smith number is actually new by d. Okay. And here for the number, it is mu again, mu because momentum, diffusivity upon alpha thermal diffusivity moving on to the next number. We have Sherwood number and for sure wood number, uh, again, we need to. See what we find here? Okay, we find wood, share wood.
Number. Okay, we find it has wood. Now we know that wood, actually this wood, doesn't con conduct heat.
Okay. So, but it is actually a mass. What is mass?
Okay, so that's, how we can remember that it is related to mass transfer only because this is the third number. And here we will take mass transfer only for the first number momentum on the upper numerator and momentum down. Then, uh, actually, not momentum down.
We are taking overall momentum, no mass and heat. Then we take momentum and mass momentum and heat. And now only mass okay, that's, why we take it as flux? Okay, so flux is like convective, flux, convective, flux. Okay, by conductive flux, that's, just Sherwood number. Okay.
And if you see this convective, flux is actually the total flux. Okay, it is the total flux. Actually that means convective flux here is actually, including both convective plus conductive, which is also not given in most of the books. Okay and let's write their.
Formulas, okay, so for convective flux, we have convection. Okay. And here we need the mass transfer coefficient, k, l into concentration gradient and down here. We require d, the diffusive molecular diffusivity upon l. Okay.
And this is also delta. So this will cancel. And we finally have k l into l by d. This is mass. This is mass flux, mass flux. And we get these values. Similarly, we have a number called Russell number for heat transfer and for heat. Okay, this is this was for mass.
But for Russell number, we. Have heat let's, take different color. So for my Russell number is similar to my Sherwood number okay, but for heat only heat. Okay, it is also same convective heat flux to the heat flux due to bulk, uh, heat, flux due to conduction. Okay.
So again, here we take the h into delta, t and down here. We take k by l into delta, t, again, delta, t, will cancel. And this will give us HL by k. Okay? And the next number will be our Stanton number Stanton, number be precise. So standard number is means that stand on? Okay? So.
That's the remembering technique stand on here, it is instead of d, we have written b and stand on. So what should stand on what okay so stand on? Now we need a heavy number a heavy number like sure would which is quite big number like if you see the word limit here, the word length here is big. So Sherwood number okay, is big, so it's standing on and putting a lot of force over, uh, your small numbers, small numbers where the first Reynolds and Schmidt numbers.
So we will put smith number and Reynolds. Number that's, the Stanton number similarly, for instead of shareholder, we can write Russell instead of server, you can write Russell for heat. And instead of SC that's smith, number you can put Brandt for heat. Okay. And so the remembering method is stand on what should stand on the heavy sure would number that is so long word?
Okay, that should stand on these small numbers. Okay, which were defined. This was the first number.
This was the second number. This was the third number. Okay. And then we see here. That the bottom part of this okay, this bottom part is actually nothing, but packet number back. Let number now how to remember this is that Sherwood is standing on standing over this smith and Reynolds and smith and Reynolds are letting it stand it let if it is. They are saying smith and all that let Sherwood stand on them so peck let it is letting it stand these numbers.
And the stand on number, the Sherwood is standing on them. Okay, that's how we have done the backlit number that is SC. Into Reynolds for mass transfer for mass transfer and for heat transfer it is Brandt into Reynolds, because it is letting it stand okay, guys. I hope you like the video there are much more numbers.
But these are the really basic numbers, uh and let's. Just hope I can cover more numbers in the part 2. Thank you.