Micro Scale Heat Transfer - Part 1
Welcome to everyone if you recall, we have started a new topic in our last lecture, we want to know regarding micro heat exchangers and for knowing regarding micro heat exchangers it is important to know that we should have some, it is important to know micro scale heat transfer we should have some idea regarding the convective heat transfer which takes place when the channel this is called micro scale heat transfer and we have started this I will go back to one slide which we have seen in our last lecture so here this year we have seen in our last lecture to hear we had to find a number contact number and this number is given by lamp given by the expression Lambda by 5 Lambda is the mean free path of molecule air condition and Haley is the characteristic length of the of the engineering system which we are constipated depending on that same number we can have continuum to when natural number is less than .001 we do not have any difficulty this is about conventional flow situation so we can have a very small channel but not say number is in this way so we can analyse it as we have analysed or what are the problems of heat transfer through it so then we can have a different value of lesson number or a range of nursing number that’s a number is greater than .001 but less than .1 then we will sleep at you while we will have we will have a temperature difference between the wall and the fluid which is called temperature and sleep so basically you use the navier-stokes equation we will use the electrocution boundary condition so you can seeyou have it can be operating in this transition ID number is greater than .1 but less than point so we will have we cannot have our conventional equation for fluid flow and heat transfer that is needed to situation etc we cannot have and we have to have either Monte Carlo simulation or the Baldwin transportation follicularkissing little bit so I think that would be good to let us go to the flight and in the Bible let me explain so let's say this is a solid surface conventionally if we see that the fluid that is made up of number of particles so what will happen all these particles they will help brand emotion from the from the physics widow that they will happeninstant of time as millions of particles are colliding with the wall and how to do deal with from the spectacle from the continuum in her lunch and basically when this kind of pictures are there we are not bothered what is happening at the particle particle level we are to meet until then where’s continuum label and we basically have different kind of floors etcetera like momentum equation of baby is two situation in equation we can apply there but what happens if the number of particles are small play happens like thisending number at numbers are small particle numbers are small then what will happen the mean free path quilling please who in the Channel dimension that is small but there are enough number of particles so in that case also been linked up the mean free path becomes comparable with The dimension of the chapter this is the second situation we have considered and now we will have different kind of different kind of physical phenomena which is not present in case of the conventional to so far what we have considered two situations one can think it is really fight that means there are very less number of particles so when one particle Travis is a large link which is comparable to be physical dimension of the system or the physical dimension of the system itself is very small so that it becomes comfortable with the free mean free path that the particles for condition today now that is one thing we can understand that why he fidgets are different and they it is very important though we are not concerned only time that energy transfer momentum transfer for this since it is very important to know that how the particles are interacting with the world the particles are interacting with the wall at a very large number at 1 instant of time there are millions of impacts of the particles with the wall then we get one period and we need them with one type of law in Phoenix type of laws in physics and when there are small number of interactions then weeding them with another law offices and other types of micro transfer we are concerned with the second problem here is the number of particles used show number of interaction and see how we can deal with that this is not the place to discuss in detail for kind of situation but scientists have developed laws in this condition condition matric and Claudialocal Sonic velocity that will be given by root over 2RT is the gas constant is the temperature and k is the ratio of the specific it’s okay to come kinetic theory of gases again new can be obtained by this particular formula and from there we can define knutson number again we’re coming back tonight same number but hearing see that too important online encinal number we have included that is one is your number and another this is this is very interesting and important to see initially define knudson lumber in terms ofjet Li one can define mass number and Reynolds number from where one can get the idea of the number number or rational number are associated with what kind ofreally we have got a heat exchanger in the microscale scales how we have to determine that I have give me some games so then yes and specific kind of more appropriate type of fluid flow equation and transportation we have to consider now to see what kind of question we have to take care I mean we have to consider and we will try to learn these things with some simple example simple problems so far I have told regarding your microscale heat transfer one is velocity and another is temperature significantly this is also one thing all the interaction is not like before when there are large number of molecules that the gas is not really fine order channel is not a small and dimension so large number of positions used to take place now number of conditions are reduced then what will happen the molecules name some of their momentum and create a CS trace only oneand let me read it and then I will explain the deflection and neglecting me brief summary balance at the wall if the process is the velocity or the velocity of weed at the wall ideally we should have got hereno husband let me explain that thing you do let me Show two types of two types of pollutions hambidge or other the particles let’s said this is our success and up until let's saythis kind of conditions are called speculate and hear more or less in the laws of laws of reflection so we can get some sort of momentum exchange also we can try to apply over here depending on how the direction of motion is changing changing as we can see that one particle came here and going back like this so when it comes when it came like this so there will be two component of momentum one is in this direction and another is in this direction when it is going back like this it will also help to component one is like this and another is like this so now you if you read that regarding specular reflection whatever I have told that that is or whatever I have been in this line so that can be related from the small figure which I have here is coming and then it is getting bounced back by 1 but is coming and then it is getting back by this is your specular reflection another kind ofit is kind of a technical service which is not totally smooth not totally laugh then we can have both type of reflection ok unfollowing specular reflectionmake a call to the next line and then it can be understood by a presidential momentum accommodation coefficient Lambda is the molecular mean free path for smoothwall reflection is specular and tangential momentum is conserved that we have and then diffuse reflection reflection and FM ranges between point-to-point a range is between .2 to .8 as expected there will be some sort of the valuewe will go to some other flight but so far whatever I have told let us try to record today it will be it will be it will be like what we have done so far now we have we want to do or we want to know regarding micro heat exchangers which is more heat exchanger different from the conventional heat exchangers and the difference comes that the channels which these heat exchangers news they are basically they are very small they are they are very small and due to the small size of the channels we will have different kind of different kind ofnumber gives a comparison between the mean free molecule apart and the characteristic length of these systems which we are using our which way you want to analyse what happened and then we go to the domain of microchannel are microbes microflow different kind of now we come should temperature difference between the temperature at the wall and wall temperature this is aobviously you can understand that this is some sort of issue and this is a function of ftft thermal accommodation position and is defined as if p is equal to q y -2 / - 4 on the wall you are that is the likely of the reflexForrest Gump is given by this part so you see where you can come and we got the and both of them they are dependent on the this is how we do we get there the product will be good listening. How one can get the expression for the friction factor and the heat transfer coefficient that will be giving us some idea on how to deal with convective heat transfer at micro scale. Thank you
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