 but anyway yesterday we have been discussing about the effectiveness factor right and of course we have derived the derivation has come nicely and also we have plotted all the graphs to discuss what is the effect of various parameters and all that okay if you could have observed those derivations there is one very important thing there right how do you define that observable do you remember what is the definition of observable that is Carberry's number yeah okay you are seeing and telling no yeah but I think you do not remember at all okay yeah okay R O V by K G yeah so everything depends on the measurement of R O V and also measurement of K G whether you measure experimentally or whether you use the correlations so that is why I would like to say something about these mass transfer correlations so under various conditions how do you what kind of mass transfer correlations you get okay most of the time what correlation you know in mass transfer tell me one correlation some of these things we can that is why you know the school education fortunately is always rememberable right if you do not remember alpha beta I think you cannot do anything later no but somehow when you come to the college I think nothing to be remembered I do not know I mean I have been telling you all these you know except Reynolds number you do not remember any other number okay you tell me any correlation in chemical engineering forget about mass transfer correlation one correlation and you may say why so much interest you are telling are about correlations but only correlations are now used only for the design you do not have complete analytical solutions or closed form equations to design something right always you have only correlations you know no under no yeah in which course you have used so many correlations mass transfer mass transfer heat transfer you do not use it yeah so and also your equipment design I think you know if you are really designed you could have never escaped correlations so many correlations are there for final design so that is why understanding theory is different and finally when you are designing you have to only go for correlations so we will write some few correlations just to make you aware of what kind of correlations we may get first let us start with our industrial work horse particularly chemical industry work horse what is the equipment pump heat exchanger no any other at least I am happy you remember the equipment okay yeah it is called you know chemical industry work horse packet bed if there is any choice of using a packet bed first go for packet bed what is the reason yeah why because correlations are available so it cannot become work horse yes work horse means what is the meaning of that very hard work all the time it works without any problem so in packet bed there are no moving parts okay so friction packing you know so this is one of the main reasons and also what is the equipment you have a cylindrical tube right most of the time but we do not go for square or rectangular cross section and have 10 meters or 20 meters column we will not have why square cross section or rectangular cross section see all these fundamental questions you know like asking why are you here why I was born to only these parents not someone else so these are all basic questions where you know all of us can think you will never get answers okay but here at least you will get answers if you probe deep a little bit deep tell me yeah packing I can always put no but when it is big it fits very well when it big it fits very well because the particle sizes are small so happily they will go and sit if you have small diameter and then of course as we said rectangular flow flow is not uniform if you take rectangular or you know square cross section because in the corners in those corners the flow is not uniform as in the centre whereas if you have a circular cross section like cylinder you can expect almost uniform flow except may be near the walls where I think always I mean without walls you cannot do anything so we should have walls but you should minimize that effects that is why you go for bigger and bigger diameters so that is why for packed bed what kind of mass transfer correlations are used that is what first I want to tell you one is packed beds the problem is I think you are happily listening and then you may be understanding what I am saying now but I think next minute you are going to forget that is my problem that is why many times also I repeat okay it is not like that matrix movie know where oracle tells okay whatever we discussed the moment you cross the door everything will forget okay you do not even remember that we have discussed all that but that is reverse here it is matrix inverse matrix you should remember everything you should remember everything whatever we discussed here you can never forget kalpana did you see matrix movie why I will not give you grade unless you see that movie you have to see that movie I say it is a wonderful movie not once or two to three times you have to do yeah Kavya did you see no that means you are really seeing the movie because of seeing the movie if you don't remember also that is valid okay yeah but you know beautiful concepts are there after all you know that is what is innovation of the mind how beautifully it was the concept simple concept where we do all the time I mean philosophically I relate that in this way you are just looking at me but your mind may may not be with me your mind may be somewhere else that is what matrix also says but there I think technically you put a rod here connection and then go somewhere wherever you want right yeah but now you may be just looking at me but still your mind may be in Delhi India gate or may be gateway of India or Kutib Minar or in Hyderabad Charminar so you may be thinking all about that right so but anyway this concentration is not there that is why I think we repeat so many times I repeat so many times so that at least one point of time you will come to the real class to catch what I am trying to tell okay packed beds one of the correlation there are many correlations for for I mean what I am going to discuss in packed bed itself there are at least you know 10 to 15 correlations but what is the very I mean widely used okay correlation that is what only I am trying to give here we have JD JD definition yesterday we have seen JD equal to 0.4548 by epsilon b into Reynolds to the power of minus 0.4069 this is the correlation where Reynolds number is given as dp u rho by mu this I do not have to explain so this is equation number one okay and this is valid this correlation is valid between Reynolds numbers 1 to 10 to the power of 4 Reynolds number 10 to the power of 4 that is where very large Reynolds number for packed bed okay it is not it is not like tubular flow where 10 to the power of 4 also you may not get complete turbulence whereas here in packed beds what do you when do you get turbulence around 400 okay and when do you get Reynolds I mean laminar I think I mean any idea about packed bed when do you get till what Reynolds number you get laminar flow in packed bed absolutely no idea around 1 yeah not a bad guess but why 10 because log 1 100 like that that is why you are just guessing next one yeah around 100 you are taking transport phenomena now you do not have course in our transport phenomena so you completed already so then it is there in that packed bed then what did you do transport phenomena vectors and tensors vectors and tensors you have done that means temporarily you have been shifted to mathematics department or what who taught you transport phenomena you only uncovered many things you only uncovered many things you know unfortunately this what is happening you know most of us we are not able to identify what is required for a student in the B Tech and M Tech classes but anyway yeah so this is the one that means it covers and the correlation was proposed by reference okay these are the others and there is a journal called industrial engineering chemistry process design process design okay design and development that is the journal process design and development and this was volume 16 page number 157 1977 these are we normally write one method of writing references the first one is volume number okay every year they will have volume in journals and then 157 is the page number sometimes we will also write 157 to may be 165 page numbers from starting to ending and then this is the year in this journal and these two people are from BHU when I was in the university upajaya I think still there are just about to retire or something and due they we may be I think may be student but they have done a wonderful work you know this is Indian research where we collect all the data and then try to analyze okay so whatever data on packed beds has been available so that data they have put they have taken and then analyzed and fixed in this format okay and mass transfer coefficient is there in the JD definition so what is epsilon B you could have guessed any respect then I better write epsilon B is porosity of the packed bed okay good so this is one correlation now I think you know the other one is like fluidized bed which is again very widely used so for that the correlation is I think I will write here to fluidized bed the correlation is little bit simple here JD and JH so heat transfer correlation also we can use the same thing so 1.77 D P G by mu 1 minus epsilon to the 4 of minus 0.44 this is valid okay this is valid between 0 less than D P G D P G mu 1 minus epsilon less than 5000 okay so that is 1 and for JD equal to JH 5.77 D P G mu 1 minus epsilon minus 7 8 so this is valid between okay 0 sorry this is 30 the above one is 30 this is 0 less than less than 30 there are two references for this reference 2 et al et al means you know some more are there I do not have other names 2 et al the journal is chemical dot chem engineering dot progress there is a journal called chemical engineering progress I do not know whether you have seen or not chemical engineering progress so this is 49 volume also underline that 49 volume 141 page number 1953 most of you why most of you all of you are not there at that time 1953 yeah and also another person may be this one correspondingly is Gupta and Thodos this is also chemical engineering progress 58 page number 1962 so these are the references okay by the by what is that in that group does that have a name D P G by mu 1 minus epsilon yeah this is also a Reynolds number sometimes based on voidage of the bed okay voidage of the bed so that is why it is there I think G is what are the units of G yeah mass flux in fact okay yeah good right so that is the one and then now some of I told you these are the conventional ones and also you have moving bed you have rotary kilns for all those things okay so that is why you have to just look I mean too very widely used it equipment we have taken and then just given just to have an idea what kind of correlations we are talking about when you are talking about K G A okay yeah and there are some novel type of reactors for example monoliths yesterday only suddenly I got the idea you know I can now give a MS project based on you know the catalytic converters I can take them even though they are used or unused new ones I can give an MS project you know on finding out hydrodynamics through that I do not think any publishing literature is there on hydrodynamics through monolith auto you know what is that automotive catalyst monolith it is very nice you know they will have a diameter of 4 inches or so yeah and length will be 6 inches or may be 8 inches and that is simply inserted in the exhaust pipe of the core okay so when the gases after the combustion coming out through the exhaust pipe they have to travel through this particular monolith so then it is a catalytic reaction so when the gases are passing through the monolith then you will have the catalytic conversion that means CO going to CO 2 and you have many hydrocarbons normally converted into hydrogen and you know CO 2 okay yeah different non harmful products where you can simply put into the atmosphere but you see the entire thing is one reactor that means diameter 4 inches length is 6 inches okay it is a wonderful idea but I think you know hydrodynamics vary the dead space for example whether there is really plug flow or not I do not think many one many people would have done it okay so because I have done yesterday the picture okay as a cylindrical and then you have lots of slots yeah each slot is a plug flow pipe that is what is the assumption but really we do not know whether there is plug flow or not so that is why we have to check in the laboratory whether really there is a plug flow you have to conduct a RTD test which is not that easy because the residence time of the gases through this 6 inch tube or 6 inch length monolith is very very small I mean may be less than seconds so if everything automated you can beautifully find out whether there is this plug flow or what will be the pressure drop you know the pressure drop I do not know whether you have seen nowadays movies I think they do not show old movies when you see black and white movies if you do not want your opponent to start the car you take some kind of lemon or yeah and then just stuff the exhaust so outlet gases cannot come so engine will not start because the pressure is not developed there so okay so that is the kind of thing that means why I am telling is what you are doing by putting this lemon or some other obstruction you are creating pressure drop okay very high pressure drop so similarly if the monolith is there inside beyond certain pressure pressure drop then definitely you may have less combustion efficiency oil may be injecting but still it is not burnt so that is why is there optimal pressure drop across that I mean all these things they would have done in their research time like you know all these food companies or all other bench companies all these companies would have done but it is secret for them they would not tell but only academicians would not have any secret all things we talk okay so that is why that kind of information is really wonderful information okay anyway good so now we are going to have one monolith reactor where this monolith is given something like this we have plates like this yeah so then it is extending in this direction so I think I would also draw so till here yeah it looks like monolith okay good the flow is in this direction and then coming out good that is monolith and each slot is like a plug flow each slot and there is a plate here where both sides the catalyst is coated coated this side and that side both sides so then gases going in this will react here here here here that is what what we call as hydraulic diameter correct no wherever it is weighted good so all that things will come there and the correlations for this is for this Sherwood number equal to 6 plus okay let me also give the dimensions here so this one this is the height H this is W and this is the length of course yeah that is the lengths so yeah and I can also say that this is the width that is B width of the slot yeah so the correlation is 6 plus 0.00 how many zeros 306 Reynolds by L by 2B whole thing to the power of 1.36 where of course all the meanings are there we have B and all that but anyway let me check this one also Sherwood is defined as 8 kg B DAB that is the definition of Sherwood and Reynolds definition is 8 BU is the velocity by nu yeah I think I lost equation that is equation 1 2 3 this is 4 yeah so this is given by some Arashi reference Arashi et al I hope you know what is et al now I also wrote here et al somewhere yeah et al means yeah plus some more and when you write et al normally how many more than 2 and you have more than 2 this question I am asking still many PhD scholars when they come to me for synopsis meeting okay I think after 5 years also some of them at least may be 20 I do not say 20 15 percent at least they do not know when to write et al okay even for one writer they one other also they write et al okay because safe know no problem I think there was one of the oldest movies I remember all these things because I also passion for movies so when the you know new bride groom and bride when they are entering house they want to you know you have to enter only with right leg you know you put your right leg first before entering I do not know what is this entity right leg if you do not have or left leg you do not have you cannot walk anyway so I think you know people say that right leg is better than left leg okay we do not know all these things are unnecessary things are unnecessarily defined parameters which really troubles us this kind of left leg putting right leg putting and all that so you have to put the right leg so the bride groom does not know which is right leg which is left leg so then his father tells you put two legs one will be right one will be left so I think that is a very good session so like that we also have here et al okay yeah so this arashi et al where you have international chemical engineering is the journal this abbreviation also you should know as chemical engineers so volume 23 and sometimes you write in the bracket means that is issue issue means I mean every month they will have one issue so then totally you will have 12 in a year okay good so 22 this is 3 means may be March okay and then you have what yeah 489 phase number this is 1982 so that is the correlation they use yeah you see here I have given a different correlation for RE see here it is different straight forward which you can see correct no DB and here we used mass flow rate or mass flux and here we have used kinematic viscosity okay that means mu by rho or rho by mu directly combined here so that is why this is one of my favorite questions in asking students when they come for interview tell me Reynolds number in three different ways okay yeah this is one of the simple nice things I say and also of course this B is the distance we say in the definition of Sherwood number or Reynolds number it is not always D it is the characteristic length okay so the characteristic length for the packet bed is particle diameter but not the tube diameter even in fluidizer bed it is the particle diameter rather than tube diameter even in moving bed it is particle diameter why and only simple tube will take diameter completely diameter of the tube Prabhu matrix are here here only physically here mental I am asking here only yeah why you understood the question what I am asking Reynolds number if you have the tube empty tube flow then we will say that you know you take the tube diameter but in packet bed you take particle fluidizer bed you take particle moving but you take particle why not you because there is also a tube correct no flow happening then you should take why it is yeah all the phenomena is taking place around the particle so that is why the characteristic length will be the particle rather than the tube okay so that is why I mean these things many people will not repeat I mean will not say but I think if you know all that that is happy think you know that simple simple things are very very important in fact it is most of the time simple things which give you happiness complicated things always give you problems okay good so that is why we say that before marriage I was very happy so after marriage no happiness that means that is a complicated thing simple thing is no marriage so this is the kind of thing okay so this is another one equation then we have another example why gauze why gauze reactor this I have been telling you many times you know why gauze why gauze and all that okay good so if you look at one why gauze you will have something like this okay this is the plan if you put that plate and then look at that that will be looking like this and these why gauze are normally put in a reactor and then that reactor just to show you how that can be yeah you have class now which class not Ravi know Ravi means you should have warned me in the beginning itself yeah okay this is one sleeve I mean one see this is another looking like sleeve so there is another one here the flow is looking like see you kept in the tube not looking no yeah okay so the flow is in this direction what problem you see yeah good yeah but cream biscuits cannot be used but here only see is one I have to use yeah it is like a cream biscuit very happy good yeah good yeah so now when I have this kind of flow then again you know you may have you may have to put sometimes 3 sometimes 5 sometimes 10 it is not always you know 5 10 like that but any number whatever is required for the design so these okay these these are the wires which are woven in the form of sieve and those are the sieves which we will just keep there and you can see now if I have for 1 2 3 screens in this correlation if I have 1 2 okay I think I will dash 1 1 2 3 screens you will have JD equal to 0.94 divided by Reynolds to the power of 717 so this is valid for 0.4 less than Reynolds number less than 9 of course where JD definition again you know I mean it is not actually the other definition what we have given JD definition JD definition in terms of dimensionless numbers do you remember too much to okay let me write that at least once JD equal to Sherwood number by there are two numbers here Schmidt number Reynolds number Reynolds number so that is this is one third and this will be half that is was the actual definition always remember you know when whatever correlation we have for mass transfer you should have something to take care of hydrodynamics something to take care of properties properties of the fluids you go and you get what is that ratchet 0.717 this is 0.717 okay yeah so this is what what you have to remember always you know to take care of properties which number we use Reynolds number you cannot take properties Schmidt number to take care of the hydrodynamics or flow around the particle or inside that is the Reynolds number so these two are must even for heat transfer that is but only thing is Schmidt number is replaced by Prandtl number so that is why you have something connected okay good so this is the one then of course where Reynolds number is defined here as you see every time you have to define Reynolds number depending on your convenience this is new into epsilon is the voidage of the sieve epsilon is the voidage of the sieve or porosity of the sieve epsilon is the porosity I mean the same voidage and porosity we are using okay so that is the one and okay if I have five screens if you have five screens this is B one two five screens same thing I am continuing for wire gases then you have something called okay alpha JD equal to 0.664 Reynolds by alpha to the power of 0.57 and for Reynolds number 3207 yeah where alpha equal to 1 minus n into d whole square where n equal to mesh size in number mesh size in number of wires number of wires per square inch very good in square that is n and d is diameter of the wire yeah this also has been done by you know few people like I will tell you one reference I will give one of the oldest professor who was in MIT reference Satterfield Satterfield was excellent in mass transfer mass transfer through heterogeneous systems and cottage yeah so this one is industrial engineering chemistry fundamentals f industry engineering fundamentals engineering chemistry fundamentals 9 is the volume number page number is 613 and here is 1970 okay one reference just I just would like to give you okay good so these are the kinds of references or correlations what we have and you see this one and this one is in 70s 80s 90s so that means the original thinking of you know packet beds conventional systems are slowly being replaced by non-conventional systems like this monolith reactors this wire gauzes and all that that is how chemical engineering evolves okay but originally packet bed and fluidized bed very happy 50s 40s and also 60s 70s 80s and all that new thinking so this is what and this is what I thought I will tell you but still it is only the tip of the iceberg right so we have so many other systems so many other systems the message I would like to give here is that whenever you are going for non-conventional chemical reactors or non-chemical non-conventional chemical engineering systems in terms of equipment then you have to find out from every time you have to do research and then find out the mass transfer coefficients heat transfer coefficients hydrodynamics hydrodynamics means what you find out the velocities that are possible flooding that is you know when can that that can occur if it is movement of the solids then you have to also find out when the particles fluidized or when the particles go away all this information you have to find out through research that is why still we are surviving okay so something new something new something new equipment something new I mean correlation or something new theory if it is possible so all multi-phase systems and you are now taking multi-phase systems that also you have taken already so you don't have at all it is only for dual degree yeah I mean entire chemical engineering is only multi-phase systems and when you go to multi-phase systems even two phases then mostly theory cannot be understood so easily so that is why we go to empiricism okay so with this I think the external mass transfer thing is over in terms of effectiveness factors and also we have the correlations because all that analysis is depending on these correlations why because k g is very important or k l or whatever mass transfer coefficient is very important in defining that observable okay so that is the reason why we have to spend sometime to let you know what kind of correlations you may be having at least you may not remember but at least later also in your life and sometime comes I think you have to say that yeah we know this kind of correlation somewhere I have seen so that is the main reason why we have done this so I think this is fine okay good thank you