Design and Simulation of Heat Exchangers - Numerical Problem
 
In continuation to our earlier discussion on the design and simulation of heat exchangers, today will try to do some numerical problems and in that problem. Before going into that a problem let us see what we have learnt so far a summary of the problems that we have learnt in the last class we have talked about the NFL and relations well in case of a counter-current exchange as we have seen that this is the expression for the heat exchanger effectiveness either it can be expressed in terms of the heart rate it capacity or it can also be expressed in terms of The bakul Priya Bangla minimum capacity fluid we will either have this expression of these expressions and this may be cancelling out on me not cancel now in continuation to that we have also said that if we make an energy balance between these two freight trains we can get a relation something like this which will involve the Epsilon and then she went with the help of this expression of the sea are all the heat capacity ratio which is defined as seeming by C-Max we can also find that we will have expressions like this one which has been in in the last class we tried to and I got this expression so this is he had the mind that this situation is for the counter flow heat exchanger element we have tried at in case of palatial obviously the expression will change and even in case of counterflow wort fluid is getting mixed are all mixed also will try to solve this problem later on when we discuss about the mixed and re-mixed fluid problem we will find that there are series of expressions for the excellent and the interview and obviously the heat capacity weight ratio and for all exchanges will see her because 20 what is mean by cl equals to 0 + I mean by sin x equal to zero or this is particularly you will find that this corresponds to commencing of evaporative heater so in that case we will have a simple relation and equals to 11 by 1 – 10 depending on our situation we may also had it will be such that we may be knowing the hair salon and in that case we can find out the n2 from this relation but in case if it happens that information on we’re trying to find outback silence in that case we will have a slightly different relation given by say that in case of corresponding over-the-counter current exchange of the following expression look like this it is same as before except that the NTU and CR is on the right hand side as known and 1 – Epsilon is on the left hand side so if the influencia is known we can drive regular calculatorwe have professional and chill with you and all exchanges this is the corresponding equations so this background if we know someone dies but we have lunch so far is basically we have talked about the electrical we have also looked for the assignment you one and two excellent relations based on these relations we now can try to sell some example we have taken this example from intro prayer and David Guetta most on Facebook and it is basically dealing with the industrial gas turbine heat exchangers what the lubricating oil is getting cold using the water in a concentrated area so basically it is a tube and tube heat exchanger where the internal diameter of the tube is 25mm where is the outer diameter is 45mm the thickness of the inner tube has been neglected and the oil is flowing through the Alley in the space where is water is flowing through the internal TV the flow rate of water and that of the oil is given the English temperature is known so the entry temperature of water we can see that it is 30 degree centigrade whereas that of the oil is 100% to get the water flow rate is .2 kg per second the oil flow rate is .1 kg per second now what we’re supposed to find out is the length of the tube so that the exact temperature of the oil is 60 degree centigrade so there’s only centre 100 centre in it and we are trying to find out the length of the skills so that this all will come out at 60° intriguing now we have to determine the length of theand we intend to find out the length of the exchanges are The dimension of the heat exchangers so basically it is a typing problem now let's try to see how we can find the stop acceptable if we had to find out the size and problem if we want to apply the lnp matter what we need to know is the exact temperature of all the salt Lake city what are the things that we had to find out or assume it’s like we have been given this inflated or deflated entry temperature of one entry temperature of the water and now we need to find out the exact temperature of water because already we have been told that we intend to find out I mean measure the length of the exchanges so that the exact temperature of the oil will become 60° centric it so we know what is expected from is equals to MC CPC and then TC out wireless PC and that is equals to m dark-age CPA and the9th out so if we had to find out this heat transfer later see what are the balance those are known to us we know this last product of the complete what is the full free the water is the qualifying of the mass product of the heart rate that is also known this tco is known the cold entry temperature that is entering a 30 degree centigrade we have no idea about TC I’m sorry this is TC in is known this PC out is to be find out and he hopped in his lone the hot out is expected to be 60% sure yet so we have this is 60° c hot in 100-degree sanctuary TCI is 30° entry Gate so what we do not know is TC of the heart called example and this purpose of the house and called it a supposed to be known to us now the hat-trick againstthat is not known would not have an idea about the average temperature of the cold so we will make an assumption say here in this case we are making an assumption that the exact temperature would be at least until it’s about the phone fluid is 35% because we won’t be able to find outset up the code for 8 and then we’ll try to find out the exact temperature of the cold flu and then we’ll find out whether it is a good assumption or not so I took your advicethe conductivity and the phone number of the water is given here is not this one because we find that it is not I mean it is not needed in the proper way to that is equal to .1 then we have to 2131 x park in the difficult 200° centigrade and it is coming out at 60 degree centigrade so this is the amount of heat getting transferred through the heart through it so it is 8524 what now if this is the first fluid getting transferred from this is the in this age of and this is an annular space through which the oil was flowing out and this is the 6th this is also thi and this is true for HTC eye and PCR call exoctic 12.2 * what is the specific heat that specific heat was for 178 and x PC -3 cm is 38 South to BBC exit 2B 13.2 sonam we have been able to estimate the cold exit temperature so this is entering at 30° central it going out at 40.2 degree celsius what is the average temperature then it will come out to be 35.1 degree celsius and this is supposed to be a very good approximation that we have taken for the average temperature of the poultry so now we have both the inlet and exit temple is known for both hot and cold feet so that means we had along with the floor it’s this other products then we have the entry temperature now we know also the exact temperature and the fluid properties like the specifics thermal conductivity etc and the panel number so with this information we can now try to calculate the Delta to love me delta-t long will how do 30 degree centigrade and it is moving out at 40 point to disintegrate this is what is the purpose of profile now we will try to find out the delta-t Ellen so she is this is the did it say the smaller we can understand this is a smaller one so this is nothing but 60 - 30% so it is 30% what song is this please come talk to me 59 point ABC clm is 39.8 – 30 ÷ 59.832 8524 so in the expression q is equals to you a delta tlm so out of which we have already been able to calculate the density Helen we have been able to find out that you don’t we need to know is the overall heat transfer coefficient and from there we’ll be able to find out the area now this is basically one by you is equals to 1 by hi-5 one by h o r if you look at ourthis heat transfer surface area is our power main concern here this is the day that has been given and this is this is you what we're trying to find out is the heat transfer coefficient between these two reasons why is the internal heat transfer coefficient and other one is the heat transfer coefficient of this annular space so far internal heat transfer coefficient this is the place to the fine and we know how to estimate the heat transfer coefficient 04 Nissan universal or we need to find out how to estimate the heat transfer coefficient in the analysis and what is the heat transfer area in for this is the internal surface area is the area of which is involved when this heat is getting transferred from the halfway to the Coldplay and please remember that we have neglected the thickness of this internal to you so bad and the heat transfers resistance offered by the wall is negligible in case of this internal floor we know that this kit result coefficient and you is given by the nurses number for the internal floor is given by .023 in to order to the power point 8in to PR2 the PowerPoint for so this early is the tenants number and how to find out the rules number corresponding to this water flow through this internal team this re is GTA buy new what is this GG stands for the month velocity is called the mass velocity this is nothing but the last product / the free flow area what is the free-flow area here this is the free flow area of 5 squared by 4 so Amber is m.com fluidmaster 8 / by t.i. Square by 4 so this is nothing but for end of the corporate / Idi Square so this can be obtained as we already removed them or spirit of the pulpit the culprit lost wallet is .2 and we can estimate it to be 101 4050 so the Reynolds number is more band the LED is more than 2300 that means the floor is in the total entries this is so we have this number is equals to this park is we can use the status filter equation for finding out the heat transfer coefficient this number we already know and we can try to find it out the heat by the bungalow number was how much was the panel number we have let’s go back and see how much is the point 8.48 58.85 is the phone number so if we put all these videos I mean values we can of paint we h I d I y k is equals to the nurses number and the classic number is nothing likefor now we know the internal heat transfer coefficient so when this knowledge now we have to go to the next parameter that is that patient of the annulus passage so what is the timing of passage the animals passage is just like this when we have the internal diameter is behind this is Di and this is the 0 so for this case we need to find out what is the heat transfer coefficient so before going into that one we need to find out what is the Renault number for this annular space so again if we trying to find out this is the chair of the heart rate and th of this and in the space what is the hydraulic diameter corresponding to the journalist is this is if we let us try to find out that value also and this annular space hydraulic permitted if we say from the basic dimension and basic definition of the heat transfer mean hydraulic diameter we know this is for a c by the weighted perimeter what is the AC this is the cross-sectional area through which the floor is taking place so this is just nothing but fall into pi tea or Square minus b square / the wetted perimeter is this is the wetted perimeter as well as this is also the wetted perimeter so we have five d05d I so in that case this comes out to be that would be of course and other 45 is there by 4 digital Square – 3 square service for will be cancelling out the spice getting cancelled so we have finally 20 – di as the hydraulic diameter this is g is how much tea is basically the cold fluid mass flow rate divided by the free flow area what is that if Larry the free-flow area you will be able to find out that as 5 by 4 520 Square minus b square and this conflict must flow rate is .1 kg per metre square so will this values if we try to if I try to estimate the canyons number corresponding to that value it becomes 56 for that annular space now for the zaniness space we have expression when we have an insulated out-of-boundary and the internal why temperature remains constant so for this type of configuration the heat transfer coefficientalmost to remain constant so we will have a corresponding value for the nurses number is equals to 5.56 this can also be obtained from the intrapreneur to and David school now this is nothing but 80 – di HD by the care of the fridge so we can find out the heat transfer coefficient of the annular space and this comes out to be 38.4 Watford Twitter Square so once we know the internal heat transfer coefficient and external transfer coefficient we can now try to find out the overall heat transfer coefficient one by is equals one day is equals to 1 by 85 + 1 by 80 and that would give you and you are overall heat transfer conductance to be 37.8 Watford to metre square this information will now be used to find out cubicles to buy di into you into delta glmv roanoke you already have estimated you we have already calculated delta tlm we can use this parameter is also known so we can find out this link to the 66.5 minute so in a nutshell it will look at this samadhi will find that this is what exactly has the internal I mean calculation solid you have discussed about and we have obtained the length of the heat exchanger to be 66.5 meters. Thank you.