 క్ర్ల్ల్ క్వ్ల్ల్ ఆవ్రిందాడింపికెకిక్డికెందిత్డంూటిఇనోక్టాదెకొర్డాత్రి హినోక్ప్నింట్వైనిక్నిటిక్కడికెటికోల్సోాను� Maybe you put it in presentation mode. Yes, yes, yes, it's okay. Can you see? Yes, now it's, yeah. Dear professor, you have 20 minutes. Okay, thank you very much. Thank you very much. This talk, let me start by thanking the organizers of this conference for permitting me to share part of what I'm doing over the years. Some of the areas of my research over the years. This talk deals with the modeling magnetotama, banjileya flow of nanoflufts and its engineering cooling applications. The presentation of a view is as described as follows. We have introduction and review from the interquestions, model, formulations, numerical approach, numerical result, conclusion inference. Now, what is MHD? Because we look at the title deals with magnetonato fluid. So MHD deals with a magneto hydrodynamics. And the study of the direction of magnetic field with conducting fluids. And this is as similar important to study because of its engineering applications. MHD deals with the conducting fluid, especially nanoflufts, which are made up of nanoparticles, that are metallic particles that are susceptible to magnetic fields. And you can see that the concept of MHD is a very great concept in science and engineering. And it has won the kind of prize for our friend who got the prize on the work on MHD. Now, what is in bandelier? Bandelier just simply means when a fluid flow on the surface, when you have a fluid to flow on the surface, for instance, when the surface is very, very hot, you want to cool the surface. What we normally do is to put fluid on the surface, to extract the heat out of the surface. So when the fluid flow on the surface, the dynamics of the flow need to be studied. And when we study it, we will be able to know how to enhance the cooling rate of the surface. And some of the applications are very wide. For instance, although in this talk I am talking about the industrial cooling, the generic cooling of surfaces because so many engineering devices they do generate heat from time to time and they need to be cooled. And the modelling we enable us to be able to know the right type of fluid to use and under what condition can we get the best result. So this and the bottom line, that for the bottom lines of the work I am presenting. So bless us in 1908 this with the concept of bandelier flow and there was a student of Prandtl the issue but his own motive is to look at the flow over airfoil the dynamics of airfoil you see aircraft moving in the air that is his own motive to study this kind of bandelier flow for the airfoil and was able to have some what we call similarity solutions that give some reasonable solution that predict the drag on the airfoil and also how to reduce the drag. But in this we are going to look at the concept of nanofluid what is nanofluid? Nanofluid as you are aware of from what I have been talking previously you can see is a mixture of nanoparticles nanoparticles you know nanoparticles obtained from nanosize particles so you fabricate metallic or non-metallic material in form of nanoparticles and these metallic and non-metallic materials they are highly conductive they have high thermal conductivity but you have a liquid like water, oil and polymer solutions so the thermal conductivity is very small very low but the nanoparticles have high thermal conductivity where you mix nanoparticles just small percentage you mix it like 1% of nanoparticles you mix this volume of water under laboratory condition you see that the thermophysical properties of this outcome which is called nanofluid will be very different from this ordinary water because it will have better thermal conductivity and better magnetic susceptibility based depending on the nanoparticles you use so this is what is called nanofluid you can see what I have mentioned here if you look at here you can see that ordinary fluid liquids like NG oil and nuclear cold water the thermal conductivity is very low but when you get to aluminum silicon aluminum copper sliver they have high thermal conductivity so and for you to extract it from the earth surface you need a liquid of high thermal conductivity that can conduct the heat so if you marry the metallic nanoparticle with the liquid a small percentage of this it improve the heat transfer enhancement of the base fluid which can be oil and nuclear cold water it can be any of this fluid you will get a very excellent coolant which will be able to enhance the cooling rate of the surface and that is very important in terms of engineering applications of all surfaces so these are the concepts what are the applications the applications you can see various applications the applications electronics cooling electronics gadgets they generate heat with the use with the help of nanofluid to get a better cooling rate for efficient performance also you know in the transport industry most of our vehicles we use coolant in the vehicles aircraft to make sure that it reduces the heat produced by the engine for efficient operation even in industry where you want to in meta casting or you want to cast metal you have to cool them using nanofluid you can get a better shape a smooth material a smooth shape in a better efficient material using nanofluid for cooling also you can see nuclear power plant in nuclear power plant nanofluid can be used for cooling of nuclear power plant medical application is there even in military you can see some of the military equipment when they are in operation they generate a lot of heat and when they generate a lot of heat nanofluid is used in cooling them for efficient operation under operation so these are many many applications of nanofluid now let's go to the model itself the fundamental concept in the modeling of nanofluid is based on the continuum mechanics the continuum mechanics involve the fundamental law of conservation of mass which is continuity equations conservation of momentum and conservation of energy here we are dealing with a single phase nanofluid model so you have this we assume that the fluid the liquid we are talking about is incompressible then you have continuity equation given the advantages of the of the velocity factor to be zero and the navier-store equation if you assume that you are talking of Newtonian liquid Newtonian liquid then you can use navier-store equation you can assume water or in this case I am using Newtonian liquid you can have non-Newtonian then we have when you mix this Newtonian liquid with nanoparticle then you have the equation the density of nanofluid and this nanometric density of nanofluid and then you have this one which is Lorentz force Lorentz force is given as the force where you apply magnetic field to the flowing of nano of conducting fluid there is a Lorentz force which is a force that try to slow down the movement of the fluid and this is very important in cooling surfaces because you don't want the fluid to flow very fast you want to slow it down so you apply this Lorentz force which is a current density across the magnetic field factor so you have this one then this energy equation which comes from the first law of thermodynamics and you have this one at jou-eating which is the effect of magnetic field then you have the mass equation which also come into play because of the presence of Lorentz force and jou-eating in the energy equations these are body force and these are internet generation due to magnetic field so when you have all these the concept of mass equation into magnetic field comes in which you have to apply to get this Lorentz force and so on now without wasting time remember this one is Ohm's law which you have there and the further there is this and Ohm's law and this one they all forms what you call mass equation then the thermo-physical properties of the base fluid and nanofluid is needed for us to predict when we do the experiment in the lab we want to predict how each of these nanofluids we work which will give us a better result in this case I'm using pure water as my base fluid which is a heavy density as follows and copper nanoparticles is heavy density as follows and alumina data these are the specific heat properties and this is the thermal conductivity and this was electrical conductivity of each of these and this one can be obtained from the literature they are there and under laboratory condition we can obtain all these properties which can be obtained now this is a relationship between nanofluids density and this F is for nanofluids and it is for base fluid and S subscript denotes that of nanoparticle and F is the amount the quantity of the nanoparticle mixed with the base fluid if F is one that means you fill up the whole base fluid with nanoparticle and that cannot work we have to use up to maybe 10% maximum you can use 0.1% of nanoparticle it creates a lot of difference than using only base fluid so this F can be 0.01% 0.02% and so on very small amount of nanoparticle so these are the thermal thermal physical properties which we have to use and this one is electrical conductivity all these are in pre-care result which are in the literature based on experiments on the relationship between nanoparticle and base fluid so we have this one the thermal conductivity of base fluid and so on and this one is the dynamical viscosity of nanofluid and this one is the natural base fluid anyway let's go to the model this is the model the model is assuming that it is a chemical reaction taking place here that is generating heat or you are having nuclear reactor generating heat now you want to put a nanofluid to make sure it cool the surface because if the heat is generated here if you have the heat generated and the direction of heat is continued then this surface can be damaged if the heat is not taken out so then also the surface it can zoom this surface due to the heating of the surface there can be stressing of the surface the surface can stress or the surface itself can shrink there can be shrinking of the surface you can have shrinking surface stress in surface so all these are working on this so yeah I don't know what is going on with the program it is not responding there is freezing here in the program I guess I don't know why it is freezing I think you were removed from the full screen mode maybe I don't know maybe what I do here let me share again let me share again sorry for that in all this technology one can have all this the earth is just frozen now I am sorry I am putting it again to share yes okay now I will move very fast you want to use for 20 minutes yeah okay can you see me yes we see on the screen let me share now share okay let me just go very fast now okay you have 3 minutes left 3 minutes yeah okay you have this so let me go to the result so when you do that we have the model this model is what we got the model equation is this we solve this model equation these are the parameter we have there these are the solution the method we use these are the solution for the solution here we see that can you see now for shrinking surface yes for shrinking surface we realize that we have dual solution for shrinking surface the third one and you have this one so for shrinking surface we have dual solution the upper solution and the lower solution that's what we have this upper solution is what we discover in the experimental observation this is due to the non-linearity of the problem and this is what we have here and also for we have this one for shrinking surface we also do the endodynamic stability analysis of the problem to know which one is the correct solution so when we do the endodynamic stability of the problem this is what we get we see that the upper solution branch is one that is stable the lower solution branch is unstable because it giving us the negative again value and full negative where it will diverge the one that converges is the that manages the stopper to go to zero and give us the basic solution which is observed in engineering experiment is what we have as the dual part solution which means when you look at the solution the solution you get on the experiment is this what are we saying the solution which you have here is saying if you have nanoparticle you have nanoparticle in the fluid you are going to get a better cooling rate and at the same time you are going to have the skin friction which you have the effect of the fluid on the surface will be more however you get a better cooling rate that is what we have under the velocity profile sorry yes you can see here now from here you can see the what you have here for alumina and copper copper will be a better coolant will flow closer to the surface than alumina water so this one the boundary layer thickness of copper water which you have here of copper water is smaller than that of alumina water so copper water will keep you a better coolant and that is what we have there and you see where you have is five zero that means no nanofluid then the fluid flow away from the surface very fast but as you increase the nanofluid 10% open to hand move closer to the surface and that is what you see here also in the result display here you can see now from here copper water is this the temperature is very high it takes it more than where you use ordinary water the temperature at the surface is very very low so it takes low heat than using copper water because it has heat transfer from the surface and the cooling rate so those are the things we have anyway let me give you the conclusion in question time prior we were able to to be able to speak more in the question time nanofluid velocity increase from the wall I mean from the wall towards the free stream the free stream is away from the surface velocity increase and because of the shrinkage and stretching velocity boundary layer thickness for aluminum water nanofluid is greater than that of copper water which means copper water will be a better coolant for the surface and also you can see here now that have increased the magnetic field cooling rates increases as well because it make the fluid it decreases the thickness of boundary layer increases the the magnetic which is M and increases nanofluid decreases the boundary layer thickness and which means you can take on more heat from the surface that is the fact of the magnetic field and you can also see here the surface is slippery slippery of the surface so these are what we have here do you have a solution where you have a shrinking surface due to heat you have to expect the upper solution branch will be the least solution which will be observed from the experiment so when we are using this to predict in the engineering fabrication of materials we have to make sure that the material does not shrink more material shrink under heat it shows that the solution to observe will be the upper solution branch which we need one to take note of in the issue of cooling of the surface and for stressing surfaces there is a unique solution we obtained here which there is no problem about that and finally to enhance the cooling rates at heat surface using nanofluid it is advisable to regulate the value of ferrous embedded parameters with respect to engineering and tertiary applications so this is what the model produced and we have worked with people for instance here in South Africa we have a laboratory called in Tambala where we have a big study of a fabrication of nanofluid some of the results are similarly useful in terms of modeling and to confirm what they are getting in the experimental many papers have been published on this type of issues but there was a paper published with that engineering laboratory that we were able to confirm some of these results that when you when you add nanoparticle or the magnetic field the heat enhancement rate the cooling rate is higher than when you use ordinary nanofluid without the application of magnetism and the only reason is because of Lorentz force we decreases the flow therefore enhances the rate at which the heat can be taken from the surface so that is what we which solve the thesis of the problem as well that is what is agreeing able with the thesis of the concept of application of magnetic field in the direction of the flow thank you very much the technology that that go down and so on but during question time we can we can deliberate and probably I will throw more light on the model thank you very much thank you professor for your very detailed so there is the question that I can read from the forum and then it's from Atmasu okay saying that the result from the result which graphically comes from experimental or numerical solution okay he is asking if the result is coming from experimental or numerical solution of the primitive equation oh sorry the result is coming from numerical solution what result this is not from experimental it is purely numerical and this numerical solution which you observe is confirmed to agree with experimental observation okay so have you done an experiment or a group did a group carry on this that is a group that is a group I have looked at the results in South Africa call it intemper lab is a lab which is based on UNESCO funding professor Malik Massa they work on issue of nanoparticles and fabrication of nanoparticles and so on and the issue of nanofreed as well so when we look at the heat transfer enhancement in terms of the of what they do you can see the result producing here confirm some of the we had the paper in 2018 we joined paper together on the issue of nanofreed and and the issue of nanofreed and the experimental work in fabrication and so on and it confirms some of the results and also in the literature the experimental literature some of the results are also confirmed which are compared some of the other papers are published thereafter in 2019-2020 okay i think that your talk was interesting for many people because i see many people who want to ask questions but now we have there's a question Robinson who wanted but i don't know i think maybe you talk privately you can give one or two maybe allow at least one Robinson just quickly it's okay thank you prof like in your formulation consider the incomprehensible fluid okay what of a model for this if that's comprehensible because of a constant equation you say that you didn't include rho this one is incompressible density it has to be averagely constant okay yes it's comprehensible the density will be very yes i know i know is it possible to consider a fluid that's comprehensible that's compressible yes it's like gas like gas like air air is a compressible fluid we can look at that in that case our fluid here our base fluid the base fluid here is water which is which is compressible i mean which is incompressible incompressible yes but when you talk of like that what can be air or gas you are using okay i think i have to stop the session right okay please ask one question i think it's better to ask the professor directly in private because maybe the discussion because now we are out of the schedule right okay please let me give my address we collaborate with several people in India Pakistan in Africa also please you can contact me i can formulate so many for compressible where you can use gas and all those things and the equation will change and get a better result we can be tested to understand so okay professor i think the meeting is also the equation the location for people so you people can be