Micro Scale Heat Transfer - Part 2
Welcome to the course heat exchangers fundamentals and design analysis. If you recall we were discussing the special topic on micro heat exchangers. So micro heat exchangers you have seen that it is a special class of heat exchangers where the heat exchangers passages are very small. Basically these channels, the channels of a micro heat exchangers can be called as microchannels and also the micro heat exchangers if they handle this amount of weed so in that way they’re slightly different from competitive changes to their lot of similarities and as the channel channels are of small dimension so we find that the physics of the flow phenomena and physics of heat transfer that is different and in that respect to different muscle to special effects due to the small size of the channel that has been already discussed one is asleep at the wall that mean the actual the velocity of the fluid and the velocity of the solid they are not the same for most of the cases Diwali stationery but the velocity isin case of conventional conventional heat exchangers are conventional passages like a passage is metropcs we find that the temperature of the wall and the temperature of this week at listen to while they’re the same but in microchannel there is a temperature that means temperature of the fluidity wall and temperature of all their different route these two phenomena has been has been discussed in our last lecture and the boundary conditions then they are different for micro channel and macro channel withparallel plate channel we get q is equal to 3 by 200 m and then one minus y by the whole square + 40 in ÷ 1 + 8 KN upon 1 + 8 KS so most of the symbol see if you can understand but it’s for your benefit let me explain it you is the velocity at any point supposed to be considered a channel let me dry it here itself that it will be clear supposed and the thickness of the channel or width of the channel that is deep and in this direction we have got wife show at anyway if the velocity is given by this particular formula and then you when is the average velocity why is the distance from the bottom world CD is the width of the channel and cayenne is in knots and number already we have define what is nuts and number so then we will get this formula I mean get the situation now you see me in this expression if not say number is equal to zero then the floor is your flow through conventional channel and it becomes the origin of the expression which we have derived fourth plain porcelain floor or floor two parallel plates earlier from English similarly for succulent that we will get the next equation here for the circular dust again if we draw the figure this is your capital r and any dimensions that is your smaller and then act any radius r the velocity is given by his formula and obviously it depends on nothing number if it is macro if it is a floor to micro sized bike lynott you then what will happen then she will have your key in is equal to zero and then our equation is you is equal to twice um-1 - smaller by capital are all squares open one that meanscontinuity equation has been for flip-flop continuous equation has been considered only boundary condition different to this is just an example how in case of micro channel flow the analysis is slightly different of course if we go to transitional region or free molecular medium there will be a larger amount of difference so with this latest move to another important aspect of micro channel flow we go to the next line if we go to the next slide let me go to the next life so we find another number other another aspect becomes important in case of micro channel flow as I have already mentioned that in my coaching through as the surface area is large compared to the volume at the wall there is viscous viscous registered there will be lot of registered and that’s why I ultimately what we will get we will get a viscous dissipation which cannot be neglected business dissertation is there always going a fluid flows through some sort of attention whether it is a macro channel or microcalcification that means you love and that class that loss of energy what does the surface-to-volume ratio is large we introduce a number bring number which is also a non dimensional number represents the definition of differentthen we will have been into un Square / qw into TT is the characteristic length of the channel should be here gives the relative importance of discussing generation to heat transfer in history this is our brinkman number and brings my number is often associated when we we do because election analysis of micro channel flow or flow through microchannel because discuss the situation we cannot neglect in case of microchannel at least we should try to see how much is the contribution dissipation we cannot be ignorant of this classification microchannel showing this next light what I have done after we have seen what is our temperature what is our velocity and what is the number I have taken just an example when simple example just to give some idea and this is the problem or example in an air flow at it mean temperature of 40 degree celsius to a heated my profile with diameter of .224 mm knutson and bring PIN numbers are .06 and .0 so we have got treatment number and not same number that has been in calculate the fully developed heat transfer position for years of years for constant while temperature and constant working class boundary conditions for these two conditions we have to calculate the transfer case number is calculated to 640 degree Celsius is 67 what productivity of the flu equals to 1.912 into 10 to the power – 5 Newton second per metre square is the dynamic viscosity and PR equals 2.71 additionally14240 conviction and flood situation in such cases either one has to do an analysis and come out with some sort of its expiration for nusselt number and from there one can calculate heat transfer coefficient for such type of problem one has to look for a suitable correlation and the coalition will be in terms of let’s say nusselt number Reynolds number pencil number and in that equation putting the angel number and Reynolds number 1 King number and then the next day one can get here we will dojust let us see the property table show property table the national number actually it is not a property tablet is table of the non dimensional number the national number for developed laminate floor is tabulated so it can be taken like this that the way we get nusselt number in case of large sizes so there it is a function of Reynolds number and angle number many of the cases functional relationship is not but in this case at least there is effect of Reynolds number triangle number and also bring my number is important and not say number is also you see depending on the lesson number and brinkmann number we will have some correlations which again will be dependent on Reynolds number and pendulum let me repeat it again so basically for getting the heat transfer coefficient one has to know the number 4 large sides passage the number 4 large size passage the Silk number is given by the function of Reynolds number and frontal number it is a small size passage show the transport phenomena which depend on nursing number plus there will be discussed the situation so there will be effective ring PIN numbers depending on Knudsen number and brings number in a cell number we have a functional relationship with number and PIN number to it is a complex kind of correlationlike this that we have got enough but we have got different values of big band number for 12345 brinkman number have been considered and based on this model number and this brings my number we have got the let me explain it once again sorry we have got nuts in number of tabulated on on the particular on particular column so we have got nuts in number starting from zero 2.1 and then we have got brinkman number two different values of Brisbane number we have conceded 0 and .01 so we have considered 2 cases one is constant while temperature and another is constant while because so let’s say we are trying to consider one situation that nonsense number is .02 and bring pin number is .001 and what temperature is constant so we will have this is we will have this value of nusselt number 0.74 270 and in between falling between values beautiful this is not very difficult to understand howso now we have understood then of course the solving the problem does not take much time because from the table we can pick up a value and that will be there so if we go to the next slide then you can find that from the table or 14 giving Manson number and bring pin number national number for council constantly class condition can be obtained muscle number is equal to 3.45984 heat transfer coefficient we can calculate and that is 390.66 what form it is likely that is your heat transfer coefficient and let us complete the problem complete the solution for the other place that is the constant while temperature case parcel number is equal to .50651 from the table given table and the coefficient for the transfer just like before we can calculate and it is 571.93 what is to be noted in this exercise is that that nusselt number depends on a large number of Aaron Reynolds number prime number in case of large or conventional channels but in case of small channels or microchannel it also depends on knutson number and thinking number just to impress upon this fact we have taken this example ok so you can understand that there will be different correlations are tables like this and we have to pick up the nusselt number of her work number and from there we can get the heat transfer coefficient microchannel latest first consider gas becausewe have you have noticed that we have discussed neck number compressibility of the fluid does a more relevant in case of blue Legacy what are the attributes of what are the specialities of gas flow through microchannel application is for high heat flux cooling problem ok so microchannel obviously they are adopted for high heat flux cooling problems conventional with exchanges are used where the dissipation of heat is not that challenging not that high the fabrication and design technology is chelate effect of active research so we will be fabricated this kind of heat exchanger so newer techniques are being adopted and so that is one way fabrication but analysis also you see the way we have got very well established correlations for macro channel flow for micro channel flow we do not have those established correlations theory is also difficult because you see there are so many interlink phenomena from our Aguilar example even understand that new and dimensions are coming because not same number and bring pin number are being important different geometries of channels are possible so actually let me tell you we will elaborate it in our in the next life on not only not in the next life but coming in coming some slide in some coming slide we will explain this that you see in different type of techniques are adopted different type of techniques for fabrication of my question answer right now play depending on the method certification we had Court different geometries of the channel and obviously the way we get very standard channels in case of conventional heat exchanger in conventional heat exchanger we get circular passages in many cases so those kind of procedures are not very common there could be circular passage that there could be a suggestion of other geometry which are very specific to micro heat exchangers countries are dependent on the method of irrigation they had the following advantages the micro heat exchanger or microchannel we have the following Avanti compact size low weight high surface area density so most of them are compacted exchanges no competitive senior and micro heat exchangers are not the same this this statement I use time and again to impress upon you that this to heat exchanger 70 just listen enhanced heat transfer coefficient due to this passage geometry etc we will have in most of the cases a high heat transfer coefficient it is not mandatory to have always higher transfer coefficient for handling low volume of fluid low volume flow rate of which we may have unique design of heat exchangers that did not have a very it is not always possible to have a very high transfer coefficient but most of the cases we transfer coefficient is also high there are certain limitations what are the limitations unique manufacturing techniques and tips we are going to spend some time on manufacturing techniques so you will find that the techniques of manufacturers that is not as common as in case of conventional channels are conventional exchange we have to have some unique technique for fabrication of the city because it is also high material of this heat exchangers are unique so that's why the cost is also high design method is not as tender as for it should be microskill passage microskill hit extempore macroscale Pacific launch messages we have got design methods very standard but in this case it is not sure please note down the type of in the line which I have just read it just rained that conventional size of the passages or conventional heat exchangers the passages at large so we have gotshuffle electronic component cooling let’s say that they’re there is heat generation and that he is to be dissipated so from that hot surface are heated surface or below Earth’s surface or below Earth’s surface we can put this kind of a module in this module we can see that there are channels and these channels are of small size truth to this channel so how the channels are defined or Dare let’s see how their dimensions are it’s length is equal to one particular channel link is e l l b Lodge comparable to the conventional linkshere you see there is some sort of bww this is the channel way so there will be less friction 2ww and HCL job w.w. and he basically it provides some sort of a rectangular channel okay if there is a top cover then it becomes some sort of a rectangular channel and this rectangular challenges of meru cross-sections her height is at which is small and quit the WWE which is also small this could be one design on a well-designed here we can see another design should this is only metallic surface and you can see that maybe with a special manufacturing techniques these channels have been made and one can see the fluid in Layton Creed out play so this is a micro channel reactor for gas with partial oxidation of storing a typical example like we have given some sort of a source it is from a paper to the source that has also been given to this is your micro channel and obviously keep separate exchanger there will be number of channels like this probably there will be stacking let’s say on one take this kind of channel is coming show at the top of this there will be another play so there will be stacking and ultimately we will have the heat transfer with thisgas flow to microchannel some of the special attributes. We will proceed with this, we have started gas flow through micro channel. Some of the special attributes we have discussed and some example of microchannel I have shown. In the next lecture we will proceed from this point. Thank you.
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