3:50 okay okay okay so now all right okay so once again good evening to all of you good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening
4:36 good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening good evening how's the juice now okay 1. Reduce your hours of sleep 2. Reduce your meals 3. Reduce your time with friends 4. Start bunking college classes as max. In case you will hear from the principal
5:24 or director of the college then this is wrong. Go to college as much as possible because you have that time left where every day is very important for you. Every hour is very important. If you are taking college exams, then go at that time. In two months, they will not let you go out of college. Once the rank comes, the college students will also be happy. You can show it to them. See, sir, this is why they were not doing classes. This is the under 100 rank. So if you get under 100 rank, even if your classes get bunked, it will still be beneficial. And lastly, you don't count yourself as a bad student if you get rank from the educators of your college. Right? Very good. Great. High. Super high. Sir, now I have given you the test paper,
6:14 you can continue to give the test paper. I have provided the details of the test paper, you can continue to give it side by side. Let's start, this is all about myself, you can see and read it. Let's complete it in short. After this, I will tell you the important things. For GATE2026, our batches have started. So, those children who want to join our support batch, they can join. For that, classes have started. Secondly, we are starting a new course, crash course mechanical operation. Whose date is 5th of December. In the morning, classes will be at 11 o'clock. Those who have to complete the entire mechanical operation in 10 to 15 lectures, they can do it. I have completed the course of plant design in 10 lectures. Those who have to do it, say crash course of these two subjects. Small subjects, low scoring subjects,
7:00 you can do it with plus. The next subject you will If you are planning to do a mechanical operation then you can continue with that. If you are planning to do a batch for 2026-2027 then join the telegram group. You have to take mentorship once. You can connect with me in the afternoon between 1-2. I will guide you on which batch and which subject you have to start. After this, we will talk about the Gate Expected series. Today is our day 3. In day 3, we are taking two subjects Mass Transfer IPC. Both are the most scoring subjects for Chemical Engineering. We are taking both simultaneously because So, if you have selected both the subjects, then your revision touch will be very good. From here, your mass transfer IPC is
7:46 complete. After this, the target of today, which is going to be our target here, that will be the subject, our mass transfer will run. Today's target will be two important topics. We will start from the second chapter. The second chapter you must have read. Mass Transfer Coefficient. Although we will leave nothing in it. But the more important things in it. We will discuss them here today. One is your share board number. And. mass transfer theories right i have included this also second one interface mass transfer ok so interface mass transfer also we will complete here in this controlling resistance how to count its flux etc we will talk about this mass transfer theories we will see in compact form and second one Share board number is a very important term and very important number. We are going to read it in detail. So today we
8:33 will complete three important topics and the whole mass transfer coefficient chapter will be completed within two hours. Within two hours we will complete with the top quality questions. We will also do two to three questions here. We will do very good questions. You will also get practice from those questions. So lets start our day 3. So we will put heading as "share board number" Before reading share board number, we will try to read about flux. Now stop this for a while. Don't put heading here. You put heading here and we will read it. No problem. We will put heading as "share board number" No issue. We will cover all the things in this in the share board number itself. Done done done done done. Brother 45
9:22 students should be 50+ regularly. Right? Children ask for 50+ right? So 50+ students should be continued mentors anyhow. Okay? And along with this I am providing you with many more things. I am providing you 5 questions daily basis. Till this series goes on for 15 days, 10 days, 15 days or 20 days, you will get 5 questions daily basis. You will do 5 questions daily basis in case of mass transfer operation. Suppose you get 50 lectures. So, if you have transferred 15 lectures, then 15 multiplied by 5, 75 new questions will be provided to you. Out of 75, 4-5 questions will be asked from your GATE exam. Right? So, you will do that somewhere easily. Similarly, this will happen in IPC also. In IBC also, I will provide you about
10:11 75 questions. In case, 15 days of class is going on in IPC, then there also you will have practice of 75 questions. There also, 4-5 questions will come. That you will... you will do it easily. Okay maximum chances will be that you will get stuck with those things and we are covering theory here. From here you will get things in compact form. Right? So, all the kids who are doing live, they are getting all these advantages. On special group, I am telling you on a daily basis I will send you the questions and today I have sent you the solution of the pdf. So I will try to give you the pdf of the questions one day before and on the next day on a daily basis I will give you the solution of the 5 questions. So in case there is a child who is stuck in one question, someone is doing something, So at least he will have
10:58 a solution so all the questions will be clear. You are solving and sending it to the group. Today a child solved and sent it. It was very good. Whenever you solve, try to convert all the solutions in that PDF form and send it to the group. So that all the children who are in trouble will do it easily. So everyone is getting problems right? Everyone is getting problems right? Anyone who is not getting any? Everyone is getting problems right? So let's start. Everyone is ready? Don't click too much time. Come to the direct point and start. Everyone is ready? I will add all the students who have messaged me. Join the telegram group. You will get the details here. You can
11:48 message to me. start and add your gadesh name and message me at the end. no problem. one more thing after the session is completed, everyone will give the review of the session. You can put the link of this session on your status All students can put the link of this session on their status The advantage of this is that the students who don't have knowledge will at least get to know about this series So I want to get maximum knowledge to the students And the 50 numbers that are visible here should be converted to 100 and it will be fun If it is converted to 100, then I will
12:34 provide you with another series from my end So you can try to click on share option and put it on your status because there is no harm in it. You are not putting anything on your status that is ruining your status. You are only putting a link on your status. It will not have any impact on your status. So at least you will be in a learning environment. You will be involved in the activities that are happening in your day. So everyone will try to put this link on their status. Before going to the shareboard number, I will talk about flux. We will start from here. We will talk about flux. We will start from flux. What is flux? You know that
13:20 any substance or anything passes from per unit area per unit time is known as the flux in case your moles are passing per unit area per unit time then that is molar flux in case mass is passing per unit area per unit time then that is mass flux in case momentum is passing per unit area per unit time from a particular section then that is momentum flux in case heat or energy per unit area per unit section so we call it heat flux and heat transfer so here we are talking about flux mass flux or molar flux because we are studying flux inside mass transfer so basically you will study flux of two types molecular
14:07 diffusion right so molecular diffusion per second its unit will be Kmol/m2/s. any of these units can be there. this can be your mol, mol/m2/s, kg/m2/s. we will represent this as Na. this is called flux. the flux we have read in the molecular mass transfer till now is Na= concentration into diffusion velocity into diffusion velocity so we have read diffusive flux means the flux we have read till now is also flux unit is same but this flux we
14:54 used to represent concentration into diffusion velocity the flux used to come from its multiplication so this concentration used to be of a particular molecule and velocity used to be of a molecule so velocity is also of a molecule So this concentration is also of molecule So this flux is called as molecular flux Now in this particular chapter, mass transfer coefficient chapter or when we talk about convective mass transfer So here convection will be involved what will be involved? convection will be involved so here we are going to write flux here we are going to write flux here flux is equal to we will define
15:40 here mass transfer coefficient mass transfer coefficient multiplied by driving force multiplied by driving force so now we can write the flux like that n is equal to kc into delta ca this way we are going to write flux here so delta ca means specific driving force so I have taken mass transfer coefficient kc in case your driving force is delta ca so mass transfer coefficient In case of flux unit, it will be delta per meter square per second and concentration per meter square per second. meter cube so someone can tell me in case
16:26 your flux is in kmol/m2/s and your concentration is in kmol/m3 so what is the unit of mass transfer coefficient? the unit of mass transfer coefficient will be meter/s you can calculate from here the unit of mass transfer coefficient will be meter/s so everyone be careful that whenever Any correlation will be applied to the share board number. Right. Now any correlation will be applied to the share board number. So the mass transfer coefficient there will be the mass transfer coefficient of your case. any mass transfer theory you will study in that the analysis of mass transfer coefficient will be Kc whose driving force will be delta C because as you
17:15 change the driving force your mass transfer coefficient changes you must have studied Kc, Kg KY and KL all these mass transfer coefficient changes as you change driving force but now I will talk about king of mass transfer coefficient that is KC because for mass transfer dominant driving force is concentration difference so that is why I have written concentration difference King of mass transfer coefficient I gave his name KC so from mass transfer coefficient and driving force multiplication wherever you are putting mass transfer coefficient and driving force multiplication then from there also you will get flux we will talk about this in second chapter in first chapter we have taken flux NA is
18:04 equal to concentration into velocity gradient at the same time at the same time in case you have to take flux and if you multiply diffusivity into concentration gradient then also you get flux from first law so remember there is a third way to get flux in molecular mass transfer that is diffusivity into concentration gradient so your question is made in MSQ so one MSQ is made in MSQ that how is flux defined concentration into velocity. This is also one way to write flux. Second way is diffusivity into concentration gradient from fixed first law. Second option will also be corrected. And third option will also be corrected. Mass transfer coefficient into driving force. This is also one type of the way to represent the flux. So these
18:50 are the three ways to represent the flux. So if MSQ ever comes, then these can be in all three options. So all three will be corrected. All three you should know. Write down all of you will do. So this is all about the flux. Now after this we will start the share board number. Now we will start the share board number. We will read everything very well. I will provide you the actual concept. As soon as you write in the copy, you have to write the whole theory point wise. As soon as you write your things, everyone will put a done in the comment box or you will put a thumb sign or you will give a
19:37 green signal. Provide me any signal so that I get an idea that everyone has completed the things. And all the students present here, everyone will make a thin copy, write from the Get Expected series to the top. And everyone write all these formulas again and again. You might have read this but you will write again because you have to store things. When I explain here, you can understand things better and you will have a good graphing. Because whatever I will discuss here, I will do it in criffs and shorts. Things will improve somewhere, so everyone has to write again and again. Now I will erase
20:23 this. Now I will erase this and go to the next page with the shareboard number. Now everyone will put the heading again, share board number. Now everyone will put the heading again, share board number. Everyone will put the heading again, share board number.
21:12 All about the share board number. You will read it hard, share board number will start to jump in an hour. Now let's talk about the share board number. Sir, we will discuss about the share board number for about 45 minutes. We will discuss about this number for 45 minutes because it is very important. How we will represent this shareboot number? First of all we represent this shareboot number with SH and sometimes we represent it with NSH This is our shareboot number How is this defined? In case I talk about it, shareboot number is defined and what is the significance of shareboot number? Suppose, I will show you
22:00 a little bit of practical knowledge which is very popular on YouTube Why shareboard number in picture? This is water and I have put ink in it. How many types of mass transfer can be done here? Because mass transfer is of two types. One is molecular mass transfer and other is convective mass transfer. In case I put one drop of ink in this water, how many ways of mass transfer are there? How many ways in which mass transfer can be occurs? How many ways can mass transfer occur? There are
22:47 two ways. One way is that you took water and put it in rest position and you put ink and water is not moving at all. It is stagnant medium. Now how will mass transfer occur in this? In case you have stagnant medium and you put ink in it and you did not shake it after putting ink, then what type of mass transfer is this? This is molecular mass transfer or conductive mass transfer. Because your bulk is not in motion. So this is known as conductive mass transfer. What did I do in the second case? I put ink in it and I took a spoon and stirred it with a spoon. I generated
23:33 the current in it. So now what will be the mass transfer? Now which mass transfer will be there? In case I put ink in it and took a spoon and moved it with a spoon Now which mass transfer will you get to see here? Now which type of the mass transfer will occur here? After springing, you are saying that it is a convective mass transfer. No, this is wrong. No, not convective mass transfer. Now here both the mass transfers will be there. Here convective mass transfer will also occur and conductive mass transfer will also occur. but the dominant will be convective. In
24:20 comparison to convective, conductive will be negligible. You know, I had done an experiment for 28 years, that in case you do molecular mass transfer, you will remember the water-salt experiment. So, it took 28 years for mass transfer to happen. That same experiment, in case I take it to convective mass transfer, then you will remember the same experiment, salt-water experiment. So how much time did it take? One minute. The thing that was happening in your 28 years through conductive mass transfer, the same thing, the same mass transfer happened in one minute with convective mass transfer. It took only 1 minute. So both things will be
25:06 yours. The ink will not be diffused due to the drop in concentration. It is not like that you put ink in it and you generate EDs. So the ink will not have molecular mass transfer. It will have. You will see at the molecular level. It will also have mass transfer. But in comparison to convective, we neglect conductive. In comparison to convective, conductive is neglected. That is why you are saying convective. Whenever you have to give an answer, you have to give both. Whenever you are asked this type of question in an interview, you have to give both. It will be both convective and conductive. Then they will say, how? Yes sir, both will be here
25:51 but convective mass transfer will be more due to current generation. and the conductive mass transfer will be very slow. I have taught you an experiment behind that salt water experiment. You can explain that too. So both things will be here. So this is why your Sherwood number comes in the picture. Now you have to see the relative importance that convective mass transfer is how much faster than the conductive mass transfer. that how much faster is the convective mass transfer than the conductive mass transfer. So, between these two, a relative importance is generated, that is the sharewood number. So, it is the ratio of convective mass transfer to the conductive
26:37 mass transfer. Or, convective rate of mass transfer to the conductive rate of mass transfer. So, this is the actually significance of the sharewood number. So, we will write down the sharewood number. Convective mass transfer is the ratio of convective convective mass transfer convective mass transfer to the conductive mass transfer conductive mass transfer right now convective mass transfer now there would
27:23 number is defined a convective mass transfer co-licking a to convective a pass a taking a mass transfer coefficient Casey into driving force Delta see it right driving force data see a conductive a mass transfer co-licking a the better licking a diffusivity fix first law fix first law is defined for molecular mass transfer dA b into delta C A by dZ right so this will be your delta C A for some time I am writing delta C A and So, I am writing the dz as lc for a while. This is dab dcy dz. So, I am representing it like this. So, delta c will cancel out. So, sharewood number will be ac into lc is the characteristic length lc upon dab. So,
28:12 this is known as the sharewood number. this is known as the Sherwood number write down this is known as the Sherwood number so Sherwood number is the ratio of convective mass transfer to the conductive mass transfer convective mass transfer we will write like this both will cancel out this will be Sherwood number while smiling this will be Sherwood number while smiling we will see some more things it will be fine with time Sherwood number because it is important It is very important, not a small amount. If you get the question, you will be stuck here. Now you will understand from the Gate Expected series that which things are important. Although when I teach a conventional course there, I never teach in this way
29:00 that what is important and what is not important. You have to cover everything. But now in this series, I will tell you what can come in the gate. What can be asked in the gate. You will know in this series. I will teach you a lot there. I will also teach you how to calculate diffusivity. I will also teach you this T1-T2 experiment. You will never be asked. But I will teach you there. Because there are different things. Very big. Great. Now see. Now let's talk here. You know. Kc is the mass transfer coefficient. Dav is the diffusivity. This is the molecular diffusivity. This is the convective mass transfer coefficient. Now. Lc is the characteristic length. Lc is the LC
29:49 is the characteristic length. Everyone knows that what is LC? Characteristic length. We will understand about LC very well. We will understand about LC very well. LC is diameter. LC will be diameter. When will LC characteristic length be diameter? When will it be cylinder. Let's say this will be in cylinder. Let it be. This will be your cylinder. and your sphere will be, I am writing it in short, this will be your cylinder and the second one will be the sphere, this will
30:39 be in two things, diameter when we have a cylinder, either we have a cylinder of this type or what we have is a spherical geometry, this is our spherical geometry of this type, any spherical geometry, any of your spherical geometry any spherical geometry is this spherical geometry for any sphere or cylinder, its characteristic length will be diameter second one, characteristic length will be the x when will be your x? when x is the distance from the leading edge leading edge means that you have a plate the starting point of the plate
31:24 is called leading edge So distance from the leading edge, if you want to calculate the sharewood number here, then this distance is x. In case you want to calculate the average sharewood number, then x will be LV. length of the plate so average number so x is the distance from the leading edge x capital distance from the distance from the leading edge x will be distance from the X is the distance from the leading edge of the plate. The distance from the leading
32:14 edge of the plate is the distance from which you have to calculate the sharewood number. So whenever you have to calculate the shear board number, we will take X and the cylinder we will take and if it is a sphere, then we will always take the diameter in it. Characteristic length, you read in heat transfer, the lumped heat capacity model, so the characteristic length is different there. Right there is volume upon surface area, for the sphere, RY3 comes and for the cylinder RY2 comes. So don't put this one there, it is different here and there. Yes, now you are telling about cylinder and sphere. Here I am telling you a very miraculous thing. Tell me, tell me.
33:01 This will not always be for cylinder. This will not always be for cylinder. I am telling you a very miraculous thing. You will not get this thing in books. But if you think, then you will get it. I am telling you a miraculous thing. Pay attention. But this will not come in your gate. But I am telling you very carefully. In case, listen to me. This is your cylinder. In case your flow is like this, the characteristic length will be your diameter. In case you
33:51 have a pen suppose this is a pen, now this pen is getting diffused so tell me the characteristic length, in that case characteristic will be the length of the pen this case will never come in gate, but remember that if you get any question in test series Leave the series, if someone asks you a question, then keep in mind that the characteristic length is the length in that case. Right? Always use diameter when you are using gate. But for
34:36 your knowledge, I have told you when is the length. When the pen starts to diffuse. In that case, we will take the characteristic length of the pen. Be careful about that. So this is all about the characteristic length mass transfer coefficient. Now we will discuss about this. You know diffusivity. Write down it. Yes, YG. Done, done, done, done, done. Great. Sharewood number will work. I said we will talk about sharewood number for 45 minutes.
35:26 Right? Then after this we will do its second topic. We will talk about the number of sharewood in detail because it is a very important point. You can revise all the numbers later. I will talk about it in detail because it is important. If someone asks you to talk for half an hour on one number, then you will agree that there is knowledge. Then you have read it. If someone asks you to talk for half an hour on a standard number, then you will understand that no one can save you from bringing you under 100. 100% will come along with it, you will go anywhere, it will happen everywhere. Because of this, I will talk about the sharewood number. Whose function
36:13 is this? This sharewood number, whose function does this vary with? This varies with the reynold number re It depends on many parameters but to reduce those parameters we have taken two unknowns. Inorder and parental number. Ultimately the number depends on your velocity, viscosity, density, characteristic length. heat capacity of the fluid depends on these variables. So we will write all these variables in short. To reduce those variables, we have taken only two variables here. We took a renal number and parental number. So the function of the sharewood number is of renal number and parental number. Not parental number. The sharewood number is of the
37:03 symmetry number. If we write Nusselt number here, we will write parental number. So, it will depend on the cement number and the renown number. Now, let's talk about how it will vary. There are some things here. There are some correlations with which it will vary. So, how is the Sherwood number defined? Listen very carefully. There are some correlations. Although these correlations will be given to you in the GATE exam. These correlations will be given to you in the GATE exam but still I will give you some confidence to write it down. In case you have taken a pipe, any circular pipe. In case
37:48 you have a circular pipe, then the correlation of your sharewood number is, listen very carefully and write down. The sharewood number for circular pipe for circular pipe or pipe or tube instead of pipe it can be tube also right tube also can be for turbulent flow i am writing so shear boot number will be 0.023 reynald number to power 0.8 or limit number to power 1 by 3 always 1 by 3 correlation will be 1 by 3 so this will be for circular tube this is for circular tube
38:41 This will be given in the GATE exam. So, shareboard number will be 0.023, renal number 0.8, and cement number 2.1y3. I have written this for turbulent flow. Now, in case you get a plate, this will be given in the GATE exam. I am writing this because you will get a little bit of confidence. So in case I talk about plate geometry, then how much will be your sharewood number? I will write here that sharewood number will be 0.664 Re
39:27 to power 0.5 for laminar and cement to power of 1/3. This will be for laminar in case there is turbulent flow on the blade then 0.8 will be there. I have written this for laminar, you can write in bracket. After this, if there is a spherical geometry, then write down the shear wood number. In this case, the shear wood number will be 2+ 0.664 renal number to power 0.8 or cement
40:15 number to power 1.3 so if it is a spherical geometry then the shareboard number varies like this and if it is a plate then the shareboard number varies like this and it also depends on different flow and for circular pipe it varies like this this is not 100% correct this is not 100% correct this is your value instead of 0.8 it can be that you have a gate exam so give 0.82 what should we give? 0.82 this is written as 0.023 this constant can be given if this constant is not given then another constant can be given 0.024 or 0.26 here 0.664 is written so it can be given 0.67 here there can
41:03 be some value that you can change according to your look so these correlations will be given to you in the GATE exam just because you have been given this you have been given some confidence in this you have been given some confidence in this This will be given to you in the GATE exam. So, no need to remember this. You just need to have awareness of everything. This is written for turbulent flow, this is written for turbulent flow, this is written for laminar flow, this is written for your spherical
41:51 case, not for turbulent flow. This is for turbulent, laminar, mixed flow. you can call a turbulent flow above the spherical or you can call a mixed flow above the spherical. We do not predict which flow is there, that is why the mass transfer coefficient has come in your picture. We cannot predict whether it is a laminar flow or a turbulent flow. Yes, a flow is happening above the spherical, that is why the prediction cannot be made that what exactly is the flow. whether it is laminar or turbulent that is why we are studying correlations that is why we will study mass transfer theories to do exact prediction of those things that is why you
42:42 will never get 100% correct answer because many assumptions are based on that so for some range of the velocity this is your profile done? ok so far everyone has written their answers now see now what will happen here one more case is important write one more thing here I will slightly shift it up slightly I will slightly shift it up and listen very carefully I will write one more point here note one point and write it all in case whatever your fluid is in case whatever fluid is surrounding it is stagnant right in case there is no any bulk motion
43:28 surrounded by the sphere in case any fluid is surrounded by a spherical particle and bulk motion is not present in that case your shear wood number will be 2 if no bulk motion so here your shear wood number will be 2 in case of the stagnant air we can also say stagnant air for medium Shareable number will be 2. Remember this. You have to remember this.
44:18 You should know this anyhow. You have to learn this. You have to remember this anyhow. So, what we have discussed till now in the share board number, I will recall you once. Sir, what we have discussed till now, we have discussed the definition of the share board number, what is the share board number, how does it come out, what is the characteristic length, we have discussed for this. After this, we have discussed some important correlations, how does the share board number vary, this correlation will be given to you. This correlation will be given to you that how does your VARI work. Based on this, I will discuss a little bit that how questions are made. Everyone should understand this. Based on this, how
45:06 questions are made. Everyone should understand this. I will tell you a little discussion here. Later, I will ask you a nice question. Here, see how questions are made. Listen very carefully. That brother, you have a correlation of a shareable number. That your given is 0.023. Re to power 0.8 and Sim to power 1/3. This is given. Now how does the numerical form in the GATE exam? It asks from here mass transfer coefficient. It asks from the share board number that how is mass transfer coefficient varying. Because mass transfer coefficient is written in the share board number. Now ultimately what is the objective of all correlations to find out the mass transfer coefficient. from here all the correlations you have studied, what is the ultimate goal of all of them to find out the mass transfer coefficient so it says that the mass transfer coefficient will
45:54 also vary like your sharewood number will vary so like the sharewood number will vary, the mass transfer coefficient will also vary and how will the sharewood number vary? in case you change the geometry then your sharewood number will change in case you keep the physical properties same You kept the same physical properties and changed the geometry. Geometry means you changed the diameter and length. or you have increased the velocity then your share board number will change immediately so it says that in case of any operation in case I am changing your velocity then how fast is the share board number changing means ultimately what impact does it have on mass transfer coefficient we will calculate that from you so how do we calculate that? like it will say that we have increased our
46:42 velocity by 2 times Right? Blast G is done 2 times. Diameter is done half. Right? This diameter is done half. So, this type of questions are made. So, it says, KC2 how changes with KC1? How will KC1 function? Will it happen 2 times? Will it change 3 times? Will it change 4 times? How? How? So, we will calculate the factor of change of KC1 to KC2. So, for that you have to do some exercises. So that things will be easy for your questions. So, what you have to do is that you don't have to tease the summit number at all. Why don't you have to tease it? Because what is inside the summit number? You know that the summit number is µ/ρ*dA. this is your simit number
47:30 mu y rho dA and all these properties are of your fluid I am not changing the fluid, I am changing the geometry of the pipe. I am changing the flow of the fluid. so ultimately mass transfer coefficient vary we have to check reynold number rho v dy mu so density is not varying so velocity will change or diameter will change So
48:15 how to write Sherwood number? Always keep the renown number open and write velocity into diameter to power of 0.8. Serapode number is 0.8 and in renown number, velocity and diameter will vary. So, you have to extract velocity and diameter and put it here. Now, you have to do it twice. Do it twice for velocity and half for diameter. And then solve it. You will get the answer. We will do questions like this. So, we will ask you a question. Will you do
49:01 it? We will ask you a question. Are you ready to do it? yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes is what is what is what is what is going to do? What is going to go? What is going to go? Can you go to go to go to go to go to go to go to go to go to go to go to go to go to go to go to Geometry will be spherical only. So, you wrote shear wood number 2 plus some constant renown number 2 power of m and cement number 2 power of m. So, in case velocity is 0, then your renown number is 0. So, if this is 0, then shear wood number will be 2. Like this.
49:50 so this is the only case for spherical geometry yeah packed bed so packed bed may be spherical particles are present so it will also come inside so it will be either spherical or packed bed packed bed is also valid for that and also for spherical geometry is also valid for that clear? come on, you will be given a question what will you all say? come on, ask this question and then I will discuss it a little more so everyone try to make this question it is a very nice question All the problems I have brought here, you will get some courage in every problem, that's why I have considered here. Read it carefully, see what is
50:39 being asked, see how we have to do it. Read it carefully, some people will try to solve the problem here, keep a rough copy, do it in it and you can go home and read the problem down in it by doing the lecture backwards. Now you should be completely focused in the lecture. By the time you write the problem, half of the people will have
51:28 answered. So you have to see the problem only on the board and do the calculation in your rough copy. So you have to do the calculation of all the numericals here in your rough copy. See the answer came four times. Great. 3.55 times.
52:15 Four times. Very nice. Applause for everyone. Eight times. Very nice. Four times. 0.44 times or going 0.435 times okay okay okay now you are coming to close with answer 0.885 times very nice very nice now you have come inside one till now your answers were coming outside one right now all your answers were coming outside one and now
53:05 you have come inside one now you have come inside four times eight times ten times This is what you do in the gate. These kids outside 1 are a bit safe. Some of them have entered inside 1. 4.35 10 to the power minus 3. This one has entered inside. This one has entered inside a little too much. Should we solve it? I said that read the questions carefully and then solve it. There is no hurry. There is no hurry. There is only need for focus. Now you will understand what mistakes actually happen. What
53:52 are the mistakes you make when you solve in pressure environment? What are the mistakes you make when you solve in pressure environment? This question is not of PYQ, that's why you are putting the answers of all different. Now try to solve this problem. Now everyone should see where you are making a mistake. Because I think 90% of students' answers are wrong. 90% of the people's answers are wrong. So now we need to see the solution very carefully. Where did you make a mistake? You have to understand this and not repeat such mistakes. what
54:40 is asked in the question first of all you read the question carefully one correlation has been given you will be given it easily if the diameter of the pipe is quadrupled what does it mean what does quadrupled mean anyone here in case diameter of the pipe quadrupled what does it mean what is the beta of this tell me what does it mean that means diameter is quadrupled so it will be four times three times it will be two times How many times will it be? It will be the 4 times or 2 times or 1
55:30 by 4 times. Tell me this too. Or 1 by 4 times. Quadrupled means 1 divided by 4 or 4. Tell me. What does quadrupled mean? There is still a chance, Google it. There is still a chance, Google it. There is still a chance,
56:18 Google it. There is still a chance, Google it. Tell me. Did everyone Google it? Ok, Ayush has googled Sir. He has googled Lata Sir, 1Y4 is coming. How many people agree with 1Y4? How many people agree with Quad Rapport? How many
57:05 people agree with 1Y4? He is telling 4 times. No student is confused in this. Let's go. So, whenever language of this type comes, you will have to understand it. Like if it comes quartered. So, I have taught you that how much value of m comes in 4 times. In that case, how much value of m comes? It becomes 4. You had read Plant Design Economics. So, whether it will be 4 times or 1 by 4, clear this first. All of you. All of you clear this first.
57:52 Sir is telling this in Google 4 times. Sir, this is some such term. Sir is telling this in Google 4 times. Okay, go. Yes, he is telling 4 times, all the boys have done google, he is saving 4 times, no one has any doubt in this. In this, if any of the children have no doubt, all the people have done google, confirmed, whenever things do not come, in case you are practicing with them, then you can do google. Okay, Sivam, Sharma, right, so how many times will it be? 4 times. Okay, so this came, son, 4 times. 4 times, write it in the bracket. So your diameter is being multiplied by
58:38 4, right? Google, multiplied by 4, yes so diameter will be 4 times velocity of the fluid will be half this is half, there is no problem velocity will be half 1/2 length of the pipe will be half again means length will be half the rate of mass transfer will change by factor so rate of mass transfer will change by factor so now we are being asked that from which rate will the rate of mass transfer change So here we don't have to calculate the rate of mass transfer coefficient and share board number So we will talk about the rate of mass transfer later but first we will
59:24 calculate the ratio of mass transfer coefficient So here we have share board number, now see carefully Now see here, velocity, diameter and length are being changed Whenever we talk about Reynolds number, how will I write Reynolds number? Rho V characteristic length/diameter. Now the characteristic length here will be our diameter or length. Because here the length is also being multiplied. Now think and tell me the characteristic length here. Rho V Lc is there in Reynolds number. in renown number LC is upon diameter E this is your Rho V LC upon mu write this
1:00:11 as mu Rho V LC upon mu so tell me the characteristic length will be diameter or length why? because whatever flow is happening is happening in circular pipe in this way means whatever flow is happening is actually flowing so whenever there is actually flow in circular pipe then characteristic length will be the diameter characteristic length will be that diameter so be careful about that so here we will talk about diameter so that means ultimately the sharewood number which will be your beta function it will be changing with your reynold number 0.83 because your physical property is there in your cement number viscosity diffusivity and density that is not changing with this
1:00:58 your variation will not happen I have put it in proportional. Only your reynold number will be changing. And what will I write? rho v dy mu to power 0.83 0.83 yes. And this proportional density is not changing. Viscosity is not changing. Velocity and diameter are changing. So can I put velocity and diameter to power 0.83? We can write like that. so now tell me this, and how will I write the sharewood number? mass transfer coefficient Kc into diameter because flow is happening axially so this diameter will come upon diffusivity DAB
1:01:44 now this will be your proportionally velocity and diameter to power of 0.83 so do you think this is the result? first we will tell you this, do you think this is the result? yes or no So, Kc diameter upon DAV velocity diameter to power 0.83. Now, look very carefully. Here, I am going to solve it immediately. Now, see how to solve this. Your diameter is being multiplied by 4 and velocity... Yes, velocity is being halved and diameter is being multiplied 4 times. Listen very carefully. So, diameter is being
1:02:30 multiplied 4 times. So, learn here. Make this diameter 4 times and velocity is being halved. So half of this is cancelled out to 4 and 2 is left. So here 2 is left and diameter is multiplied 4 times so cancel it out and write 4 here. This is the way to solve in sort. Velocity is being done half instead of 4. Diameter is being multiplied 4 times so write 4 instead of 4. If you multiply both then it will be 2 times. because 4 divided by 2 will be 2 and diameter is 4 times so do it immediately leave the rest later now the variation of Kc will
1:03:15 be Kc2 Kc2 will be Kc1 will be 22 power 0.83 22 power 0.83 divided by this one 4 times Someone tell me the value of this. Tell me the value of this. 22 power 0.83 divided by 4. Is this clear to everyone? First we will tell you. Is this clear? As soon as the diameter is multiplied by 4, then add 4. If the velocity is half, then add half. This is the way to solve in sort. The value of this is 0.44. How many students were giving this answer? How many students were getting this answer?
1:04:02 Please tell me in the comment box. How many students were getting this answer? Please put it in the comment box. Raise your hand. How many students were getting this answer? So I will understand that you have the strength in those students. Tell me honestly. Tell me honestly, all of you. How many students are honest with themselves? Tell me honestly, no problem. How many students were getting this answer? All of you were giving 0.44 in the comment box. So how many students were getting this answer? All the children who have got the answer,
1:04:49 they are all wrong because the story is not over yet. All the children who have got the answer are wrong because the question is, "Rate of mass transfer will change Y factor." So, what factor will change the rate of mass transfer? This is what I have asked. What rate will change the mass transfer coefficient? This is what I have asked. So, what factor will change the rate of mass transfer? And this is the mass transfer coefficient. Some students must be thinking
1:05:36 that as the rate of mass transfer coefficient changes, will the rate of mass transfer change in the same proportion? No. No, brother. No. rate of mass transfer rate of mass transfer, what is it? everyone knows it is WA and what is WA? you know that flux into area how many of you are understanding this? flux into area is the rate of
1:06:22 mass transfer we had studied it yesterday in diffusion rate of mass transfer flux into area now everything will be clear you will not have to ask again I will solve all the doubts by taking it flux into area, keep adding yes in the comment box, you will not need anything else keep adding yes, that this happens, you should know that this happens, you have read this now see, now this is the rate of mass transfer wa, what will I write this flux, how will I write this flux mass transfer coefficient into driving force into area, I will write like this, tell me, is any driving force changing here?
1:07:09 here we are talking about driving force means your diameter is half and length is half your diameter is 4 times and your velocity is half and length is half so they are changing the geometry and velocity not driving force so driving force remains constant so ultimately your rate of mass transfer is directly proportional to mass transfer coefficient into area now how will I write area this is the pipe Now how will I write this area? Because I am talking about rate of mass transfer here. So now you will not take this flow area. Now when I talk about mass transfer rate here, always write area down in the mass transfer chapter and mass transfer subject in the mass transfer coefficient chapter. So here the area
1:07:59 will always be surface area. So tell me what is the surface area of a cylinder? Pi*dL? So here it will come, smiling, pi*dL and I will write the area as pi*d*L and in proportional, your pi will go. So here I can write d*L. How many children have understood this? pi into dl means rate of mass transfer of second case and rate of mass transfer of first case means which factor will change this is our value so kc2 upon kc1 we have found out its value here d2 upon d1 is there and here l2 upon l1 is there so we have found out
1:08:46 its value listen very carefully we have found out its value 0.44 0.44 multiplied by diameter is 4 times cancel out it is 4 times length is half cancel out it is half solve it and tell me how much answer is there solve it and tell me how much answer is there 1 minute tell me how much answer is there 0.88 how much answer is there 0.88
1:09:33 here it is 0.88 this is the right answer They are asking this. They are asking you this. And what is the answer you are getting? 0.44 So actually this is the question. This is the question. So what are they asking you? From which factor is the rate of mass transfer changing? So now here, the length will also be used. Which was not used in the previous question to change the rate of mass transfer coefficient. It will be used here. Tell me. This is called quality question. Right? This is called a quality question. Are you feeling
1:10:20 it or not? Ask such questions, it will be fun and children often get wrong questions. Then 50% of the people will stand up and say that they are wrong. Because we do not read the question properly, we are in a hurry. We are in such a hurry that the 3-hour paper of the gate, our thought is that we have only been given 1 hour. What do you think? We are only provided with one hour, not three hours. Three hours is a good time, but we are so in a hurry that the paper will be finished in an hour. And in that case, we are not able to capitalize those three hours properly. And we make a lot of silly mistakes. There was nothing that you didn't know. In
1:11:09 solving this question, you knew everything. Just not rearranged properly. Here, maximum children's answer was more than one. More than one answer was coming. Now where were the mistakes of those kids? See it. Where were the mistakes? See it. And I will tell you a good thing. This question has been picked from your test series. The kids who have given test series. Good topic wise test will be given. One question is this one. So the kids who have given test series in the right way. This is the question of that test series. If someone has given, then he must have done it. and if you have not given test series then you can't do it
1:11:54 this question is for test series you can see it you can see it and this question will be written in test series you can write it so did you enjoy or not I said I will make you do selected question in which all the things will be covered now you do any questions of gate after doing this question there are 4-5 questions in gate all will be solved by you that's why you did right now right so brother now you do any question No matter how much you do, all your gates will be made. There is no need to make the gate because you have done this question. Now let's move on to a different topic. Whoever gave it must have done it. Now the thing is that there is a little problem. Do you know what happened? The nook in front of the
1:12:42 pen that we write has broken due to falling. Now either let me find it, where is it, so that I can get stuck in it. Now the pen has fallen, so the nib in front of it has fallen, it has broken, it has come out. Now wait a minute, I think I have found it, I found it, I found it, I found it, I found it, I was looking for it, where did it go? It's not that big, it's small. I thought that your lecture can be a little long, it's great, great, super. So drink water, we will teach you a little concentration profile here. I have done this in plus but here I am going to tell you in a tough way. The
1:13:28 pen is also stuck. The pen is also stuck in the same way as you have maintained the strength of 50. I liked it because the students were continuously maintained. Otherwise, in the first class, there were 50 students and then 35 students. Today, at least 50 students are dedicated students. They are not running away students. This is good. The number is constant. It is not fluctuating. It is not fluctuating. It is very good. So, energy is maintained and things are going on at a different level. When you make a good atmosphere in the session, the educator who stands here gets a lot of motivation. Trust me. Always keep your educator
1:14:18 motivated because only through you educators are motivated. Because the camera is here, there is no student here. The educator gets motivated by seeing the atmosphere of your chat box. So it totally depends on you how much the educator is motivated and how much the educator can give you. Now you will see the concentration profile, it will be fun. The share board number has not ended yet. The class is over an hour. The share board number is not over yet. The share board number is still continuing. Right now see the sharewood number is not over yet. Now the sharewood number is running and it has been over 1 hour. I will talk about 1 number in 1.5 hours. Because you will have a lot of chances of getting a question on this number. Very very important that the question is stuck from here. Right. So because
1:15:05 of this, the sharewood number is not closed yet. Because the strength is continuously maintained, otherwise the sharewood number would have been over in 45 minutes. Now this time has increased a little. Now let's talk about sharewood number with concentration profile. We will add heading. Everyone is good. Shareable number with concentration profile. Learn this. This will be a good discussion. We will talk about qualitative discussion. We will talk about qualitative discussion. Okay. Tell me. The concentration profile I am going to tell you is for shareable number. Do you want me to correlate the NUSSAT number based on the concentration profile? What do you say? The question based on the profile, should I correlate the
1:15:54 NUSSAT number based on the NUSSAT number? then you will enjoy it. So what you do is, I will give you some of the tricks of Nusrat number. You will understand that you are at a very good level. You will understand that you are at a very good level. First you make a plate. First I will define the sharewood number well. Then I will talk about it. Then I will talk about your Nusrat number. Suppose this is your plate
1:16:39 and the concentration of solid on this plate is Ca surface concentration. What is around this plate? This is your solute. This solute is diffusing in its bulk. If the solid is diffused in bulk, then the concentration will be more and the gradient will be more. As it goes into bulk, the concentration will decrease. The concentration will decrease and gradually the bulk will be equal to the concentration. Gradually the bulk will be equal to the concentration. The concentration in bulk will be equal to the concentration
1:17:24 in bulk. And the gradient will be zero. So the concentration gradient will be zero at some distance. So the concentration of the surrounding fluid is CaInfinite. Listen very carefully. The concentration of the surrounding fluid is CaInfinite. The concentration of the surrounding fluid is CaInfinite. So, this is continuously diffusing and decreasing the concentration. After decreasing, it will become constant after a certain time. The CA will
1:18:11 remain at infinity in the entire bulk. So, you can see that the concentration is not changing. so here you are getting a little bit of driving force on the surface and after this a length will come which we call concentration boundary layer thickness so as long as your concentration is changing, it is called concentration boundary layer thickness after that no change will come in your velocity gradient no change will come in concentration so what we call it where this thing is achieved, we call it concentration boundary layer thickness CA is infinity and CAS is Now, if I talk about mass transfer in a steady state, how will I talk? The surrounding megalopolis, you will hear my voice, I will not show my face here,
1:18:58 you will hear my voice. So listen to the sound. So the mass transfer here on its just surface. What kind of mass transfer will it be? Someone will tell me. What kind of mass transfer will be happening on its just surface? Will it be a conductive mass transfer or a convective mass transfer? On its just surface, this molecular mass transfer will be done in one way. There will be no convection here. On its just surface. That means y is equal to zero. If I take y here. So at y is equal to zero. I will write here. Here I will write diffusivity. I will write flux here. Here I will write flux. Here I will write flux. Here I will write flux. Here I will write flux. Here I will
1:19:47 write flux. Here I will write and into dCy dz dCy dy and at y=0. This concentration is decreasing in this direction continuously. So, I will put minus in front of this. So, this is our flux on molecular mass transfer. As I move up on the surface, the fluid is coming in motion. Due to motion, for convective mass transfer when I write flux then mass transfer coefficient into driving force so how will I write? mass transfer coefficient and if you write
1:20:38 along the length then write kx or you write k let it be mass transfer coefficient into driving force how much will be driving force? CAs minus C A infinity So this will be the driving force. So this equation should be known to everyone very well. Should be known very well. Did everyone understand this line? this line is clear to everyone that the flux is the molecular mass transfer and it is solid on its surface and the fluid of solid is just conductive mass transfer and it is just y=0 position and as we move ahead of bulk on
1:21:24 steady state then it is equal to the convective mass transfer clear? let me tell you once again, everyone is understanding this statement? Why did we put minus sign? Because as you move along the y direction, concentration will drop. Concentration will decrease with y. That is why we are putting the minus sign before the equation.
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