 న౿ న౿కాడరం నాస్సిసి నారారిప్స్ మౙమ్థై ఇదిందాడాందాం మ౒ందిరోదికైమాస్ నైరాసిసంసి తమరందింది మానుందికినే మాసాందాం౦ి. uhh I think answer you got almost same, you know. Yeah I think answer you got almost same, you know. yeah So, again this is the problem. Most of the m tech students are not doing that. Only MS PE3 students are doing. I think MS also is equivalent to m tech. Because in the mind and all that age wise, emotions wise, so that is why I think MS equal to m tech, they are also not solving the problems. But do not blame me if you do not get the mark. Again I am telling you. Ok one way of learning subject is, when yesterday or Friday when we solved that problem, I gave the hint how to solve, if you would have solved you would have been happy. Ok now you told something I did something it came alright I am happy. Confidence always comes. But the moment you postponed one till the third quiz you are going to pay for it. I know third quiz I think, ok I will see just one day before third quiz that is what the mentality of many people if you do that you will never get marks, okay good so batch reactor i think you have not solved only Ramakrishna you solved you also solved it, okay i know most of these non isothermal problems you will not have analytical solutions you have to draw the graphs and idea of giving assignment is for you to experience the graphs formulae the way you write the balances all that that will give you experience if you solve the problems in your room i know most of you are not listening to me also, okay yeah if you start liking graphs i think that is the most beautiful way of doing problems really i think analytically you may make the mistake but graphically you cannot generally make the mistake, right so that is why i am trying to maximize your learning as much as possible and your optimization is you are trying to minimize learning as much as possible and maximize marks as much as possible, okay so now i think particularly non isothermal reactors unless you do many problems i am going to send today tomorrow another assignment on non isothermal but not many problems again may be five six problems, right but unless you do that i think you will not get happiness in learning forget about marks but your learning your happiness is only getting marks without solving a problem how do you get 100 out of 100 correct no most of you feel that you should not work but you should get 100 out of 100, right how is that possible i say it is impossible right i think you know on this planet even if you want to have child you have to wait nine months you cannot have i want child in two days how can you have planet i think the nature of the planet is totally different that is why even learning also it is different for learning it takes time talking in chemical engineering words learning is by diffusion you see he is happily like that he is telling, okay that is an indication that i have to stop, right because whatever you are saying i am not listening so i think why are you saying so if you have that kind of attitude early morning eight o clock what do you learn you tell me you can level learn anything that is what is happening in India, okay absolutely that learning happiness is totally gone, right so i think that is now it is left to you but that is your will now, okay so now plug flow reactor we will start i think batch reactor we have done i think also problem we have done, yeah actually batch reactor i gave the simplest one adiabatic reactor in fact the same problem you can solve by taking for example i will write here this side which side maybe i do not know where you can see, okay so this corner i will write for UA equal to that is only data missing for solving non isothermal reactor i will give you some two three values and then you can try that, yeah so maybe you can try UA equal to point zero point five and also four i have in between but i am just giving you this the units of this is kilo calories per second Kelvin, UA delta T, right the other term where you are removing some of the heat, right it is exothermic reaction you have to remove the heat so UA value is given as point five and also four those two values you can now take now it is no more even of course area under the curve also you will get later but now you have to do by trial and error, no no no you do not have to draw the graph there but you have to draw the graph in all these problems as conversion versus time and also temperature versus time in all non isothermal reactors volume directly you can get area under the curve if you have adiabatic reactor but in general what we do is we try to plot X A and T versus length if it is plug flow reactor, okay yeah and if it is batch reactor this will be tight if it is mixture flow reactor very happy I think because I think distance dissolves itself because Z equal to zero because there is no variation inside the reactor so that is why you will have easy solution there, right so these things X you will it may increase this is X and T depending on whether you have adiabatic reactor or non isothermal non adiabatic non isothermal non adiabatic heat removal if there is sufficient heat you may go like this and then come like this is T if you are removing heat if it is adiabatic simply again increase it so these are the things and then normally you will be given that okay 90 percent conversion then you have to draw the line here okay this is 0.9 sorry, okay this one this one is 0.9 X A 0.9 so automatically now when you are solving X A 0.9 also given by length, right so you have the length of the reactor anyway in the beginning itself you should assume some diameter, right so the diameter length and diameter will give you total volume of the reactor, okay otherwise if it is time same thing again X 90 percent I draw this line, okay sorry, okay so this line it is crossing here X graph then this is the time R Z so once you know time you know now how to calculate volume of the batch reactor you know we have done that right time means that is the reaction time plus you have discharge time and all other times okay filling up cleaning all the timings you have to add and then total capacity must be given so much you have to produce so based on that you calculate what is the total volume of the batch, okay good so that is the procedure now let us go for plug flow reactor where once you understand batch plug flow also is not difficult we will show that we have the reactor something like this, okay good so now anyway we have the jacket outside so for easy assumption it is T C entering and T C leaving otherwise I have to also find out the logarithmic temperature difference between you know this is T C 1, T C 2 then I have temperature 1, temperature 2 or temperature in is T 0, T final then you have to find out what will be the logarithmic temperature difference but that is one thing normally we do not take in the simple problems unless you really go to industrial problems there you have to do all that right, okay so this is the one but as usual here we need the mass balance and heat balance so let me write V 0, T 0, okay X 0 equal to 0 of course CA0 is there something here also I have FAF, V F, T F, X AF and CAF all this and earlier we have taken a small strip here and then wrote what is entering what is leaving but now for this energy balance we will take that strip somewhere very near so that I will know T 0 and what is the increase in temperature T then I will go to T 2 or T 1, T 2, T 3, T 4, T 5 like that because here also because of the distance Z, okay or correspondingly time, presence of time in the batch reactor I have only two I am going to have only two equations and three variables here also same thing same thing here it is Z earlier it is T right delta Z will come and capital T temperature and conversion X so again by trial and error so by trial and error it is easy to start with this small strip and then go one by one right so that is why we will show that our strip just slightly exaggerated strip something like this oh okay something like this we will have this is the strip then my outside heat transfer also till here only and this is T C everywhere T C so this is also T C this is also T C right okay so this is the one and this area because heat transfer is taking place in this area because the tube is okay like this correct tube is like this and of course entry for reactants outside we have this jacket and heat transfer is only through this area how do I get that that area phi into D right yeah okay so that is the one which we will have but total area of heat transfer let me say this is D A dash okay in that small strip D A dash is nothing but phi D into delta Z if I take this one as delta Z or D Z okay delta Z delta Z here also I wrote that but anyway small one so let me write then now the M B for this M B is always for key reactant and in our case it is A going to R R is only one reactant that is the key reactant or if I have two also normally we are taking A and this I do not have to tell you F A naught D X A equal to minus R A into D V this is equation 1 and now this D V I can write in terms of D Z so that will be minus R A into if I take A as the cross sectional area that is why A dash I put there this is D Z okay so that means volume of this element okay this A is nothing but again phi D square by 4 okay good if D is the diameter yeah so now energy balance for the entire mixture that is entering yeah will be heat inflow equal to I think we are writing for exothermic so this will be generation heat generated okay heat yeah equal to heat outflow plus heat removed heat removed by external means that is the one okay Sushmita you are looking at that I think I am not able to follow this my delta Z is only this yeah phi D into phi D is only length area is multiplied by D Z D Z this one this is the area not able to follow okay this is the strip and what is the diameter D if I open it what is the length of that if you say phi D it is only this length you are taking then thus so now this is the area through which it is transferred so that is how okay yeah so now writing the equations for this for individual things here for all total streams you have to take f of i sigma of f of i C P i T not that is what is entering because we are taking here okay plus I have heat generated heat generated is minus R A yeah tell me delta H R into d V right yeah so minus R A into d V as one word as one thing multiplied by minus delta H R minus delta H R exothermic heat you are taking so minus delta H R is a positive quantity okay yeah so now this is equal to again same thing out at this point outside if I take outside if I take that will be sigma of C P i T plus heat removed by external means is U A delta T right what is A here U R so this will be U D A dash T minus T C okay T minus T C correct okay so naturally even in this problem or even in the batch reactor problem unless you take that strip very very small you will not get very accurate results correct this strip this should be as small as possible if you take okay let me take 50 percent as one D Z the remaining 50 percent as another D Z then you do not get much I mean you will get something but I think it will not be very accurate volume if you are asked to find out volume for given conversion so that is why that should be as small as possible because that will be see the T we are telling here correct no this is inlet this is outlet T is coming out here right but if I have sufficient distance inside also I have many other T's so that is why the average that means if I take smaller and smaller then you will get this T as close as possible then you are slowly going step by step with a small increment then your results will be more accurate this I do not have to tell you any difference equation method always tells you that and you are doing mathematical methods in chemical engineering correct no you have that course now or next semester yeah so idea of those courses are is only you know to help you to solve all these difference methods and all that good so now this is the one so now I think numbers gone this is three this is four equation four yeah so as usual this equation I will try to rearrange that is sigma F i C P i T minus T naught now we are more comfortable instead of writing T naught here and T there yeah so that is equal to not that is equal to plus U A U D A dashed yeah T minus T C minus minus delta H R equal to zero okay so now of course I can write what is this number phi phi now let me write specifically even though I have not written now D A dashed is phi D D is the diameter of the tube okay so now substituting equation six and two you have to write somewhere substituting equation two and six in five two and six in five what you get is sigma C P i T minus T naught plus U okay phi U capital D D Z T minus T C minus R A D V minus delta H R multiplied equal to zero so this is equation seven yeah good so now of course we simply substituted equation two and equation six in five and then we got this but equation two oh I did not substitute it okay right right right okay so we will write that sorry that is all I think I have to write only that minus minus yeah F A naught D X yeah F A naught D X yeah okay good so now I have the relationship between temperature and conversion the way we expected for energy balance please remember do not forget that the extra information what you need for non isothermal reactor design is the relationship between temperature and conversion and that relationship you get from energy balance right okay so now I have to solve equation eight equation seven and yeah using equation two for me to get that kind of profiles concentration versus temperature sorry concentration versus length or temperature versus length right okay and you would have seen now again we have only two equations that is all these two two and seven okay and I have three variables of course I can also write this in terms of writing those two equations F A naught I am writing this one delta X A equal to minus R A A delta Z that is one this is may be in terms of difference delta then I am writing this one as eight and ninth equation is these sigma F I C P I delta T this one I am writing delta T plus pi U D delta Z this we will leave it as T minus T C minus because this is outside temperature F A naught okay minus delta H R F A naught delta X A equal to zero please check I think whether I have written something wrong or not so eight and nine are the equations what we have to use good yeah now what is the procedure to solve that because I have these two equations right this equation will give me the relationship between X versus T and this equation will give me I mean it will not give me actually I have here temperature conversion as well as length all three are there in this whereas here we have only two that is temperature and conversion because minus R A is not there right minus R A contains T and X both correct no and also Z because of this balance d V minus R A into d V so that is what you have to remember these are the basic things which you have to remember if you remember those you know the basics then automatically whatever problem is given to you you will automatically try to solve that because you know the procedure that is why I was telling you fifty percent you know problem is solved if you know the problem clearly what is the problem here my problem is I have two equations and three unknowns how do I solve that and I know that my energy balance gives me only relationship between conversion and temperature okay good yes so the procedure is exactly same as yeah what you have given in for batch reactor so first one what is that step to solve this choose yeah delta X A may be for example point one or point not five okay or if you are very very passive person I think more accurate and more sophisticated more what you call I think not sincere but I think there is one word yeah if you want to be very very accurate right then you have to go for delta X A equal to point not not one that will take you two years okay yeah I mean because every step when you want to calculate but that is why reasonably as engineers you have to take that step such that you will not get inaccurate results but still you will not get okay I mean you will get accurate results okay so those that is the balance and that balance no one can tell you that balance should be only with you okay I mean as teachers you only just tell but finally you have to walk through the door okay dialogue from matrix okay yeah you have to walk through that so choose delta X for example point one and then next tell me I think the procedure you should know by this time now guess value for delta T that means in this increase I think you know physics also if you want to remember okay now I have chosen delta X as 10% conversion so now your guess will be okay for 10% increase in conversion what should have been the temperature increase that is what that is what is the guess value right so now guess delta T right that is how I think you know initially we started with 100 degree centigrade and let me say that you know you may have okay 110 may be the temperature degree okay that T so now once you know that then we have to yeah three calculate now I know T X and then calculate okay I will only calculate T from here no no delta Z also is there sorry DZ also is yeah DZ also is now I will calculate DZ from here sorry I think I told you wrongly that means I was telling that this will give me only temperature and conversion that is only for adiabatic system not for non isothermal system I think why no one I think all of you are sleeping definitely so this delta Z is there you should have told me no sir delta Z is there how can you say that it gives you only temperature and conversion temperature conversion only comes for adiabatic system how do you know expression is known to you but RA contains temperature and conversion what conversion and what temperature that is what what we are trying to find out what conversion and what temperature okay understood or that is a good question all of you I told you know all Indians are brothers and sisters but only one brother or one sister may ask in the class okay so that is why I think you know most of you may be having the same doubt so RA is written in terms of K naught E power minus E by RT if it is first order reaction then CA naught into 1 minus XA right so it has T it has X but I do not know what is in this element in my small delta that strip you know delta Z what is that T and what is that means theoretically what I should have is at every cross section I should have the R and corresponding X so once I know that then I can plot 1 by minus RA versus XA area under the curve will give me the volume okay but here I do not know I have to find out that R right but I do not have to draw the graph here and then I can yeah so what if I know T and X I can calculate delta Z right you can also guess for example for this delta X right what will be the length right may be 5 centimeters right so then calculate delta T delta T means delta T is nothing but T naught T minus T naught so that T I am able to find out here so that is why I have been telling you unless you take this one smaller and smaller that R will not be accurate okay because Ramakrishna asked that question do I know at least R zero that means entry R zero entry R zero what is the equation is just imagine what is the equation R equal to yeah T 4 minus U by R T CA naught right temperature is known and conversion also that means R naught I know but only thing is this point R corresponding to that one point you know may be if I call that one RA1 that I do not know right so that is why you can imagine this as a smaller strip and then find out if you what you have to do is if you are imagining slightly bigger strip like point one also may be bigger strip if the reaction is very fast particularly right point one so that is why then you may have yeah so here I have R naught here I have RA1 some people more accurate people will say that average of that two I will take understood no not understood started sleeping no okay this is R naught this is RA1 RA naught RA1 but actually there is a distance what I need is for each and every cross section so if I make this one as smaller as possible then that will be very close to RA1 and then because there is a reaction there will be depending on we do not know whether increasing or decreasing because temperature increases and the concentration decreases that effect will be there and initially anyway R increases so that one I have to take that is why when you take slightly bigger strip for example delta XA equal to point one strip then I can take this is RA1 this is RA naught now in between the average of those two arithmetic average simply if this is let us say 10 and this is now 20 as an example so in the strip the average rate is 50 okay so that is the kind of thing you have to slowly start doing that okay now calculate now tell me calculate what you can tell Z X line yeah delta Z anyway Z equal to 0 in the beginning I am guessing no see 100 I have guessed 100 is the T naught 110 I guessed right so that means delta T is 10 degrees delta T only 10 degrees raise so T naught plus that delta T will give me T at this point right so that means at this point at this point at this point I have T XA and also I know Z because Z I am calculating T I am guessing and I have chosen my delta X as point one so all three I know that means I can now calculate what will be the rate at this point right okay good now how do I know that this is correct or not now check this in this equation that is the fourth step you know yeah what do you write there for the fourth step calculate not calculate I think check probably check equation 2 here I have written 2 here check equation 2 okay if LHS is not equal to RHS yeah check equation for LHS and RHS I mean checking means only checking RHS LHS but still I am writing there okay so now if you are not able to get LHS equal to RHS then yeah now 5 if LHS is not equal to RHS now go to step 2 and repeat yeah go to this is difficult step 2 and repeat now okay go to step 2 okay what is the sixth one so that is all 5 what we have written there last time problem that is all repeat 2 to 5 so that is the one so really it will be very very good when you do this kind of you know trial and error because you need patience that will also make you learn patience okay because problem with present generation is with us we have patience with you there is no patience and you also need all the results instantaneously have you instantaneously that is what I think you know you time concept you do not have the moment you think you should be happening that only happens in old mythology and all that where god god wants to appear means chick you will come there disappear means again chick you goes out okay good we will stop here this is over then I have to talk about something about adiabatic reactors and of course next is CSTR okay yeah yeah how or what delta Z yeah but how do you know that is correct no but delta Z also should vary no same thing only what we are doing that is what same thing only whether you choose delta T or delta Z does not matter or here also delta X this is what in the last class also that is a good question again this is also I was telling you choosing delta X is not the ultimate okay I chose because that is convenient for me to have 10 percent conversion what he says is let me take delta Z here that is what you are telling you know you can take delta Z and correspondingly in that length what is the conversion that is also logical what is the temperature right you can also do that right so that is why I mean X I have chosen because most of the time we talk about X delta Z also can be chosen in fact anything even delta T also you can choose this is what I also mentioned in the batch reactor 0 to X only 0 to Z that is why I have written here from the beginning here here here here you have to go yeah because T not I know if I take somewhere here I do not know what is T entering what is T leaving that is the reason why T not here and Z not also I know 0 so like that it is easy for me X is 0 so 0s we know very well so that is why we thought from that point what is that what you get you have to just guess if you guess is not wrong guess is not right then you have to again change okay delta Z you can guess I mean like for example 10 centimetres what should be the conversion minus r a initial minus r a I know I know X equal to 0 there T not and then what is the other one that is all only T and X in the in R right so at this point I am calculating all that here from the from these three steps so I know now T I know X I can calculate R here that is what is your question now how do you know R a R a contains what T and X a so now by I am guessing one X a and I am calculating okay delta Z anyway I am also sorry choosing X a guessing this and then calculating this and then checking there once the check is right then I know what is X that is what I have written here somewhere yeah what is T what is X what is that all three I know at this point so unless you do one problem you do not enjoy that I say one problem you have to do it delta X or delta Z is big then this problem is inaccurate this method gives inaccurate result yes as small means that the smaller the accurate more accurate that means every cross section you are touching almost if you are able to go to that level equation we have taken split into delta Z and delta T that is what difference method that is why you should take as small as possible yes okay and if you want some problems which have been solved the problems have been solved by Smith in 13th chapter I do not know in the 13th chapter is heterogeneous systems but procedure is same there packet bed is the plug flow reactor okay so along the length you will go so 13th chapter if someone is interested you can just go and see next semester anyway they have to be interested but it is the same procedure okay they take