 Everybody understands what laminar flow is and we are able to explain nicely to most people. Turbulence also, I think all of us will be able to give nice explanation, well mixed flow so on and so forth. But from a point of view of fluid mechanics and heat transfer, it is important to understand the contribution of turbulence to increasing the heat transfer coefficient. Why it happens, how it happens is what we are trying to look for from a mathematical point of view. So, with this idea, let us just go and take a few things. First of all, in our everyday life, if we have various situations where turbulence is there. Normally, if you open the tap very slowly, very small opening for flow, if you give the flow will come out in a very nice manner and that is a good example of laminar flow. If the same tap, same water, you just open the tap fully, you are going to see lot of chaos in the flow from inlet to the bucket. So, turbulent flow basically is there in most daily situations. So, you are washing machine where there is mixing. So, all these things we observe in everyday life, now we just want to mathematically quantify turbulence and try to understand how to use these things to understand heat transfer. So, just a couple of introductory slides, to transfer required heat between solid and a fluid such as in coils of air condition etcetera, we would require enormously large heat exchanger if the flow were laminar. We will understand this the moment we understand how to calculate the heat transfer coefficient or Nusselt number. So, take this as a statement for now. Turbulence is important in mixing of fluid, smoke from a stack would continue for miles as a ribbon of pollutant without rapid dispersion within the surrounding air if the flow were laminar. And if you see exhaust of an automobile or why go that far in a simple example, if you take an incense stick, agarbatti, you light the incense stick and you just leave it in the room, if the air is still there is no motion absolutely, then you would expect the smoke to rise almost like the incense stick, straight line. But because of mixing turbulence etcetera, you see this diffusion, you see the smoke getting completely mixed over after certain distance into the atmosphere. So, that is an example of turbulence and of course, there are situations where you would need laminar flow, there are situations where you would definitely want turbulent flow. Pressure drop in pipe is greatly enhanced or becomes more in case of turbulent flow situation. So, pumping power becomes very high, it is low when the flow is laminar, blood flow through an artery is normally laminar except in large arteries, where high blood flow rates is there probably the aorta and aerodynamic drag on an airplane wing can be considerably small when laminar flow is flowing is there rather than turbulent. So, when we give examples, these are typical things that we keep telling you know when you have to talk to somebody about turbulence, these are things that we will normally say. Now, what is turbulence, is there a definition, this is from Taylor and von Karman. Turbulence is an irregular motion, which in general makes its appearance in fluids, gases or liquid when they flow past a solid surface or even when neighboring streams of the same fluid flow past one another. I am just reading, we will understand it from English point of view first and then physical point of view. Turbulent fluid motion is an irregular condition of flow in which various quantities show random variation with time and space coordinates. So, statistically a distinct average value has to be discerned a lot of blah blah. Now, forget fluid mechanics, let us just go to normal your road, most of us we see you know in on television or when there is a scene in a movie where they show that traffic in a foreign country. Traffic in a foreign country you see whichever time of the day it is though it might be crowded, but it will have a nice ordered flow. That means, there would be lanes drawn, white lines would be there and vehicles would be going exactly in that lane without randomly criss-crossing. Yeah, one or two bad apples will be there who will just want to cut through the traffic, but by and large if you see you will have one row for buses where only buses would go then a slow moving traffic, then slightly faster moving and the fastest moving traffic. So, when you have a very nice orderly flow at any given instant of time I can quantify various quantities very easily. So, if I want to locate if you are if in your room if you have a bookshelf and books are arranged in the alphabetical order of the authors very easily you can spot a book and take it out. So, it is a very nice arrangement whereas, if you know all types of books you know engineering novels all these things are mixed together and stacked in your library in your college library if there is no order then to find a single book is going to be very difficult. So, turbulence essentially says if now in our cities you see traffic any time of the day or night in any city any road even the smallest of the road you would have all kinds of vehicular motion in all possible directions. Suddenly somebody will come from some side somebody would want to turn right from the left most lane all these things what is going to cause it is going to cause an obstruction or if everybody is going at the same speed then it is ok, but if this fellow from the left wants to turn to the right the person coming here has to stop. So, that he lets the other fellow go what we are saying is this kind of chaotic irregular unpredictable let us put it that way unpredictable motion which is there in all fluid flow situations whether it is a gas or a liquid when a fluid flow passes over a solid surface that is flow over a solid surface where foil or aeroplane wing or when the fluid streams mix amongst themselves like water example like water when they are mixing amongst themselves that is called as turbulence and it is an irregular random it cannot be quantified mathematically at all it can be quantified mathematically for every given instant of time hopefully, but in general I cannot say that you know if I am going to have in your hospital in you will see various devices where you have this kind of things going up and down some meters which show some fluctuations. So, turbulence essentially will have all quantities of interest velocity pressure temperature all these things would vary randomly with space and time. So, mathematically any quantity that we take mathematically if we take any quantity let us take pressure or y pressure velocity u is x y z and t all these four variables dependent variable independent variables would be there. So, for me to quantify a velocity at a given instant it is not very easy whereas, if I am if I am on a road like this and two lanes are there if this is car a which is going in this direction no matter whatever I am I can spot the car a because it is behind another car b and another car c is following it it is a well ordered flow. Whereas, if this one is going all around the place at any given instant of time there is a high probability that it could be here or here or anywhere else same thing here our velocity is going to be three dimensional it is going to be a function of space and time and each quantity for example, velocity u v w pressure any quantity will have a different value at different instances of time. So, now we are measuring something next instant one second later half a second later it would have a different value values of all the components would also be different. So, much for the introduction and this figure this axis could be anything any dependent variable here we have shown u it could be v w temperature pressure anything this is a typical representation of any quantity which is affected by turbulence. What we are saying let us take the example of velocity velocity fluctuation with respect to time. So, if I have a sensor which is going to measure pressure gauge or whatever any sensor which is going to measure that quantity with respect to time you will get any sort of such random fluctuation. Now, nowadays this concept is applied everywhere to go to any television channel one channel will have this business news where the sensex would be shown up and down up and down up and down for every instant of time this company stock went like this that went like this so on and so forth. So, you will see such kind of graphs even you know on television for stock exchanges also what essentially we are saying is at every instant as if it is very important if you want to track that component stock of a particular company in our case velocity pressure if I make a plot with respect to time it is going to generally unless there is a serious problem you know in a particular company there is a serious problem or you know unforeseen circumstances not being there good or bad it is going to generally fluctuate about a mean quantity that is what we are trying to say all being well all being normal your body temperature all being normal is going to be roughly around 98.4 Fahrenheit all being normal. So, on a normal day it might go up or down a little bit which you probably do not even discern like this, but when you have fever of course you will have to track it very carefully same thing what we are saying everything being normal in a turbulent flow you would have a very random nature of fluctuation about some kind of a mean quantity. So, this mean quantity is shown by a black line in this diagram we will just represent it mean quantity mean value and if this axis is time and let us take u only which they have taken. So, this is u bar any mean quantity any quantity of interest whether it is u v w pressure temperature any of these things can be written as a sum of a mean quantity and a fluctuating component at that instant of time. So, for example, gold price on a given day it is whatever I do not know the rate 20,000 rupees per 10 grams whatever it may be if you are going to track the price of gold every instant of time after every 5 minutes let us say and make a plot it would be 20,005, 19,950 so on and so forth. So, the fluctuation that we have over and above this mean quantity that if I say is a local very very local thing. So, this is the fluctuation how much it deviates from the mean that is the fluctuation so this fluctuation is given by the primes this is we call this u prime this is called mean quantity is called mean value summation of mean and fluctuating quantity. Is the general definition for any dependent variable u v w p or t so if I plot this I will get some graph which goes something like this something like this I do not know this if I say at any instant I am always going to have this mean component and a fluctuating component. So, what is the usefulness of this I have all this information what is it going to help me do it helps me do something from statistics point of view we can say by and large if I take average of this what is going to happen the average is going to be something it is again going to be some value which is around the mean value it is not going to be somewhere here. So, that is clear as long as the fluctuations are around the mean value we do not expect any surprises in the average quantity. So, what we are saying is this we have to introduce this concept of time t naught let us say is our first reading and t naught plus capital T is our next reading. So, what I am going to do now is called as the time average by time average I mean I take data over a sufficiently long period of time how long is this long period of time this long period of time is chosen. So, that it encompasses all the lot of fluctuations I should not be taking capital T to be of the order of magnitude of this roughly this much that is not acceptable over a sufficiently that is when you go to hospital they say we will observe the patient for two days what are they going to do connect several things and keep and see that there is no abnormal behavior over the next two days then they say oh he is fit to go home. So, this time period over which the observations are made that becomes important. So, this time period is sufficiently larger than the time for individual fluctuations. So, we are what we are going to do is what we call as time averaging, but how do we get this mean quantity I wrote here on the wide board I wrote there is a mean component and a fluctuating component of velocity similarly there is a mean component v plus v prime w bar plus w prime p bar plus p prime t bar plus t prime very nice. So, what who gives me all these quantities these quantities the barred ones mean quantities I get measurements at every instant of time t and the value 1 2 3 4 several measurements I will get and I will get these quantities. So, time averaging basically does the following u bar mean quantity value is actual value integrated with time between the limits t naught when you start the measurement till the time you end the measurement t naught plus t and obviously for a time average you will divide this by the time period of interest. So, what we have done is essentially integration is summation. So, I take all the values price of gold if you say it is going to be whatever is the amount 20,000 5 20,000 10 19,000 950 all these things you keep adding divided by time gold of course time is not this one, but in velocity etcetera you are going to take the time aspect. So, at 3 15 this is the velocity 3 16 next is the velocity so on and so forth and you get the time average quantity. So, time average quantity u bar is what we get u is what we know therefore, I can get what I call as the fluctuating component u is equal to u bar plus u prime u bar plus u prime will tell me this is measured this is computed therefore, I will be able to get u prime is equal to u minus u bar u minus u bar I am going to get what is the use of this similarly if I put this why is this useful we will see in a minute. So, u if I take average time average of this fluctuations on a given day your body temperature we say I am doing fine it is 98.4 momentarily if you keep measuring it would have gone up or down by 0.1 or 0.2 degrees, but on an average when everything is normal your you say the summation or average of these fluctuations is going to be equal to 0. So, that is what we are saying here the next thing time average of the fluctuating quantity u prime when I do this when I did what I did here at time t 1 I had a u time t 2 I had another u time t 3 I had another u so on and so forth for all this I could get 1 u bar therefore, after computing this I will get 1 u prime u 1 prime u 2 prime which is obtained from this relationship u 3 prime so on and so forth. So, this is the fluctuating component at each instant of time now what I am saying is if I do a time average of this fluctuating component that mathematically I will put this as u minus u bar d t 1 over capital T going from t naught to t naught plus t if I do that this I am splitting this u d t minus u bar d t and separating these two whatever I get u bar prime u bar prime essentially this first this u bar is a constant. So, u bar can be pulled out of the integral sign so integral of d t is nothing but time t applying the limits I will get capital T I will get u bar t here second term first term is u d t integrated u d t integrated essentially gives me t times u bar how did I do that u d t integrated is this one from the first part this is the definition. So, this is t u bar and this is u bar t which is going to cancel to give me 0. So, time average of any fluctuating quantity is equal to 0 that means u bar prime prime is for fluctuating quantity bar is for the average it is bar represents average prime represents fluctuation or fluctuating quantity. So, time average of any fluctuating quantity is equal to 0 very good that is that was quite easy for us to understand also because we are saying that these two quantities are if I sum up the randomness is such that by enlarge it is going to add the positive side fluctuations summation would be equal to the negative side fluctuation summation and it is going to add up to 0 that is easy. Now, what we are saying is you will come across terms where you have square of the fluctuating quantity where you will see that once we go back and put this in the Navier-Stokes equation we will see u d u by d x those kind of terms product terms where they are you will see the product of the fluctuating quantity. Obviously, if you look at two points let us say this one fluctuation is say plus 0.1 fluctuation here is say minus 0.1 square of that is definitely a positive quantity. So, summation of these things are a time average of the square of a fluctuating quantity is therefore, definitely not equal to 0 this is something which we have to keep in mind fluctuating quantity has been squared time average of that is definitely not equal to 0 time average of the fluctuating quantity is 0, but time average of the square of the fluctuating quantity is not equal to 0 this is very important because this quantity contributes to the fluctuating part of the kinetic energy term etcetera you see u bar square that that will be definitely having a u prime squared etcetera. So, this time average is defined as 1 over capital T u u prime squared integrated over d t from t naught to t naught plus capital T then turbulence intensity or intensity of turbulence is given by this how much how far from the mean is this going you know if somebody is going if you are when you take measurement you know doctor says every one hour take the fever and let me know. So, if there are sudden jumps it is a cause of alarm same thing here the fluctuations intensity of fluctuation is going to be a measure of the turbulence. So, higher the intensity I know that it is more turbulent this is intuition nobody has taught me this higher the intensity means greater is the number associated with the fluctuation you know it is going to be more turbulent. So, this intensity turbulence intensity is given by this fluctuating quantity time average value square of the fluctuating quantity time average that will give you a positive number square root of that divided by the mean value of the velocity that is what is we call as a turbulence intensity. Now, things that we we are going to come across very frequently in turbulence that we will take up quickly we will define almost always come up with this need to use this term u square we will see this in the navier stokes equation first term itself this is u bar plus u prime the whole square and can write with me it is there in your slides anyway this is u bar square plus 2 u bar u prime plus u prime square I have just expanded the bracket. Now, if I take time average of this that means what I am going to integrate this from t naught to t naught plus capital T over a finite time period integrate both left hand side and right hand side. So, if I do that the left hand side becomes u squared bar this is equal to let us take this term u bar squared time average of a constant which has been squared is the same thing. So, you are not going to get anything new from that. So, this u bar squared bar I will write second quantity is this one 2 u bar u prime whole bar plus u prime squared bar which is the third quantity. So, what does this tell me which of these terms on the right hand side are going to go to 0. So, we have let me put this properly given here already this quantity u bar u prime because of the fact that this is given here I do not want to write this because of the fact that u bar u prime is nothing but 1 over t this definition of time averaging I am using I am going to expand this u bar u prime when you are integrating u bar is a constant it comes out. So, you are integrating u prime d t essentially and integral of the fluctuating quantity we saw in the previous slide was equal to 0. So, therefore, this second this term 2 u bar u prime time average of that quantity will be equal to 0. Therefore, I am left with u squared bar is equal to u prime squared bar plus u bar squared with a bar I can take that out because time average of a constant quantity does not matter. So, it is just u bar time u bar. So, this definitions we will use very frequently I will just complete one more thing and then we will stop we will also need to have product of 2 different quantities that is u times v that time average of that that is u bar plus u prime times v bar plus v prime you will expand that you will get 4 terms u bar v bar u prime v bar v prime u bar plus u prime v prime when I take time average of that that is left hand side and right hand side I do this summation integration business this one is the time averaging thing if I do this on the left hand side and right hand side I would get by similar logic as I had in this slide this term went off to 0 same thing will happen this one and this one bar and a prime product will go to 0 I will get u v bar time average of the product of 2 different quantities is u bar v bar product of the mean quantity plus product of the fluctuation time average remember u prime squared bar was not equal to 0 product of 2 fluctuations is also definitely not equal to 0 time averaging of that is also not equal to 0 there is no reason why it should be equal to 0 by chance if it comes out to be 0 in a given situation ok. So, be it, but in general we cannot say that product of fluctuations of 2 different quantities equal to 0 that is not possible. So, these are the general rules time average of a mean quantity is nothing but the mean quantity if I have 2 quantities which are added under the time average it is going to be the average of each of them product essentially the same thing and integral and differential also the same thing. So, next class that is on Monday what we will do is quickly we will substitute we will write the turbulent form of the linear stokes equation which means we will substitute where let us say we will this is the continuity equation we will substitute u is equal to u bar plus u prime v equal to v bar plus v prime w equal to w bar plus w prime expand the brackets and we will say that when I do the time averaging of these equations I will lose out certain terms and then I would get the turbulent form of representation on the continuity equation I will write the turbulent representation of the Navier stokes equation and this is the turbulent representation of the Navier stokes equation and similarly we will do for all the three equations of the momentum equation. Then we will go to the energy equation. Mufakkam Jha college Hyderabad any questions please. Rotating cylinder. No. For two dimensional, two dimensional product solution equation if not how to calculate or how to see the temperature distribution in a rotating cylinder for two dimensional. The question asked by one of the participants is that in a rotating cylinder can I use multi dimensional approach for transient conduction problems. In a rotating cylinder let us take the rotating cylinder problem. What is there in a rotating cylinder problem? See in conduction problem one of the major assumptions is that my body is stationary that is the major assumptions that is the condition not just the assumption that is the condition for which my conduction problems can be solved. Now if it starts rotating what is that which comes into picture? The heat transfer coefficient in a rotating cylinder from one location to another location is going to change that is now I am going to have an additional body force because of rotation. So I can answer number one is that directly the solutions which we have derived for transient conduction are just not applicable number one. Number two I have to set up the equations for rotating cylinder that I can set up only after my convection that is I have to take both with the rotation I have to take with all velocity profiles I have to solve for velocity profile get the heat transfer coefficient and then solve. No if you say that no I do not want to use velocity profiles I somehow want to make a shortcut and solve this problem ok. In that case for a rotating cylinder from location to location what is the local heat transfer coefficient if it is available in the literature that heat transfer coefficient has to be taken and solved then there is no closed form solution I have to take the recourse of numerical methods. So that is the answer for this question ma'am yeah. Again considering the combined effect check hydrodynamic boundary layer and thermal boundary layer for a flat plate for a flow over the flat plate what will be the effect of each phenomena over the another. What ok the question asked is by one of the participants if we take flow over a flat plate we have velocity boundary layer and thermal boundary layer what is the interaction between these two boundary layers. I think we will have to postpone this question for some time because it depends on the Prandtl number of course very cursory professor has touched and went in the morning but we will answer this question in great detail after we derive energy equation on Monday's lecture. So I am sorry I will have to postpone this question but crucially if I have to answer it is dependent again on Reynolds and Prandtl number ok professor. Thank you sir. SDS, ITS indoor you have any questions please. Is it possible that the viscosity can vary in the different directions is it possible for a fluid? Ok at least I have not the question asked by one of the participants is that viscosity can viscosity vary in various directions. This is a very good question why because I do not know the answer the viscosity to the best of my knowledge I have not come across viscosity variation in direction I have come across only thermal conductivity. So I cannot say that it cannot vary with direction we will look into it but to the best of my knowledge at least I have not come across viscosity variation in the direction because why I say this because for a fluid which is flowing how I cannot imagine how the viscosity can vary with the direction. So but anyway I will do the homework and come back to you thanks for your good question. Yeah another thing another way of looking at it is let us say I have flow over a flat plate and in the flat plate there is temperature varying in various locations then viscosity is varying in various locations because by the virtue of the flat plate temperature varying in a different locations. That way we can perhaps imagine the viscosity variation with direction actually it is not with direction it is with temperature but so happens that it manifests in terms of direction by virtue of temperature. Is that okay professor? Amal Jyothi college Kerala any questions? Sir you are given the rotational equation as wx is equal to half of dou v by dou x plus dou v by dou x minus dou u by dou y. Yeah. In that equation sir can we actually say it as a rotation or an angular deformation equation because it is basically deriving the equation on the basis of the angular deformation. Is that terms very different rotation or can we use specifically as rotation or can we use it as only angular deformation? Yeah. See the question asked by one of the participants is that can I use the rotation and angular deformation replacing very good question very good question. I would say why very good question because there is a subtle difference which I forgot to mention you have brought it out very nicely. See the rotation what am I saying if I tell if this is what is happening this is the fluid element which was there OABC. Now what has happened to OA it has got rotated to OA prime and OB has got rotated to OB prime. So this is the rotation this is the rotation because of the velocity gradient rotation if I have to tell that is omega OA and omega OB. But the same thing I express for shearing strain but for shearing strain whatever I done for shearing strain I have taken that delta alpha plus delta beta that is the total deformation what my fluid particle has undergone. But in terms of rotation in terms of rotation of course here just for the sake of being what to say explain both the things in one shot it is shown but usually rotation means we mean the rotation of a fluid particle means it will be in this form in this form. So it is just that is for presentation we have presented it that way but most of the time rotation is going to be in one direction both the fluid that is both OA and OB would have rotated in the same direction but not equally that is delta alpha need not be equal to delta beta however rotation means both are in the same direction this is just that we have represented it that way. So I think that would answer your question is that okay. See now you see now you see if I make any difference see positive or negative sign does it make a difference what would be the sign for this what would be the sign for this this would be del V by del sorry del U by del X plus sorry what is this del V by del Y del V by del X plus del U by del Y it would become in this case. So there would not be negative sign. So the negative and positive is depending on the clockwise or anti-clockwise. So there is no confusion on this course. Is that okay thank you yes professor any questions I would like to know about the book you have mentioned is it available or it is out of print which book I have given a number of foundations of fluid mechanics by you are available or out of print you are yeah just give me the idea where I will get that book yeah okay one of the participants question is one of the part of the fluid mechanics you have just mentioned yeah one of the participants question is fundamentals of fluid mechanics you want is it available yes it is not available it is very much out of print it is not available but if you go to infibream or amazon.com used books you will get number one option number one or option number two I know you are from IIT Bombay if you come to IIT Bombay you will get that book in IIT Bombay library that book is there Nagpur VNIT Nagpur that is mixed convection which is the combination of free convection and forced convection okay both participate and combine and they form the mixed convection so sir can you give me practical example how that mixed convection occurs yeah actually we are in fact this is one of the participants question is there are no two more two types of convection actually there are three types of convection that is forced convection natural convection and mixed convection mixed convection is essentially a situation where in which both natural convection and forced convection are important or both are important or are equal order okay so in fact we are going to cover this at the end of natural convection okay if you have to imagine there is a flat plate and there is a fan also and there are gradients also we are going to cover this mixed convection at the end of natural convection so we will have to wait till the end of natural convection professor okay thank you sir any other any other question from this center yes sir yes sir first question is can we physically control this process of boundary layer formation that is velocity boundary layer and thermal boundary layer yeah the question is yeah the question asked by one of the participants is that can anyone control physically the boundary layer velocity boundary layer for example so I think it is possible it is little early but nevertheless you have asked the question so I need to answer so let us say I have a flat plate I have a flat plate and the boundary layer is being formed so now one way of controlling the boundary layer is let us say I make holes in this plate I make holes in this plate and either blow air or suck air then what is happening I am playing with this boundary layer I am just removing this boundary layer so boundary layer can be controlled either through suction or blowing either through suction or blowing boundary layer can be controlled is that okay professor same thing same thing if I am in thermal boundary layer yeah see the question now asked is velocity boundary layer is controlled how about thermal boundary layer if velocity boundary layer is controlled thermal boundary layer also gets affected automatically and what professor is saying is that not only suction and blowing I can put some enhancers that is what we have been talking since so many days what is that enhancers ribs or vertex generators or springs various things whatever we are putting what is that we are trying to control we are trying to control the boundary layer break the boundary layer we are trying to break the laminar sub layer so that the complete boundary layer becomes turbulent essentially what are we doing we are controlling the boundary layer is that okay okay city boundary layer and thermal boundary layer is loss or benefit from the point of view of losses associated with the fluid flow or heat transfer rate of heat transfer okay we will ultimately while we are studying this concept whether it will last or benefit from the point of view of heat transfer or losses okay the question is that formation of hydrodynamic or thermal boundary layer is it useful or is it causing some loss in terms of the heat transfer and the fluid mechanics aspect so I would ask the question back to you what is the bound cause for this boundary layer formation it is viscosity right what is happening because of viscosity what is viscosity causes shear stress okay because of stress shear stress what is going to happen yeah so what is happening because of shear stress you are going to have friction shear stress is manifesting itself in terms of delta p okay and that is not something which we like we have to overcome that right so it is not it is not wanted definitely it is not wanted but we would like to everywhere the flow to slip but that is not possible viscous forces are there because of viscosity so it is unwanted but it is not avoided it cannot be avoided so it is unwanted no doubt about that but we have to overcome and put and fix a pump how to decide that size of the pump by overcoming this frictional losses which are caused by viscosity is the question what we are trying to address this is for friction but similarly we can think of heat transfer coefficient also yeah we are back as promised hello yes sir we have some doubt regarding the role of conduction between the first layer and the boundary layer we know that the heat transfer from surface to the first layer is purely by conduction but sir can we always neglect control of conduction between second layer and the boundary layer question by one of the participants is that yes we can understand it is the conduction in the first first layer of the boundary layer but the whether the conduction is there in subsequent layers as well conduction will always be there see I think there is a misconception here why cannot conduction occur even if the fluid is flowing why it cannot occur it can still occur right but yes how effective it would be it is a different question but even in a moving fluid conduction can still be there why it cannot be there in fact that is what is the energy equation you have convection part on the left hand side right hand side is conduction or and all other parts so conduction is always there what we are saying is in the on the first layer when the fluid is at zero velocity that layer of fluid there is no convection heat transfer is purely by conduction that is what we are trying to say it does not mean that in the next layer convection conduction is not there that conduction gets manifested in terms of this heat transfer coefficient because advection plus diffusion is what is convection so inherently when I say convection is there it involves conduction though we cannot bring out its effects separately like that is that okay that is a good question you are really good question but from design point of view we always neglect that portion but from design point of view we neglect the value amount of heat transfer by conduction in that layer no the participants question is we neglect the conduction in the second and the subsequent layers where do we where do we differentiate first layer second layer and third layer whatever we are telling as the heat transfer coefficient is the net effect of this advection and diffusion over the complete thermal boundary layer thank you thank you good question good question