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Welcome to lecture 3 of module 7, in this module we have been discussing on heat exchanger,
and in this lecture we are now we will briefly discuss on a various types of the compact
heat exchanges. Previously we have discussed about that various types of shell and tube
heat exchangers and different other types of heat exchangers like double pipe heat exchanger
on all. At first we will start with various type of compact heat exchanger, and then we
will try to see some important issues related to heat exchangers shell and tube or double
pipe heat exchangers. So, first when we say about that compact heat exchanger, the idea
behind is that heat exchanger is compact means that surface density is very high that means
that surface area per unit volume will be very high.
And it is usually we can say that large surface area per, so we can say that for compact heat
exchanger per unit volume, and it could be as high as 1800 meter square per meter cube.
And then the typical compact heat exchangers are examples plate type heat exchangers.
Then spiral heat exchangers it can have two divisions one is called spiral plate and spiral tube. And also we have seen previously
also there is that finned tube heat exchanger and so on, it can continue like that now importantly
with most importantly.
We should say that plate type heat exchanger has become very important nowadays I will
refer to as P H E plate type heat exchanger has become very important nowadays. Because
it is now we can say that it is the most widely used and as an alternative to the shell and
tube heat exchanger I will tell as S H E shell and tube heat exchanger.
And what happens is if you see there this here you can see that this is a typical diagram
of a plate type heat exchanger. You can see that there are these are the plates of heat
and there are four holes in each plate. There are four holes and tubes are some fluid is
coming like you can say that there are two type of fluids, this is the one fluid that
is going like this and then this is the other fluid that is coming out like this. So, this
is the way the heat exchanger takes place. So, it is a typical arrangement of this we
can see here that the fluid is coming, it is passing into the once it is passing through
this and then going to this as coming near and then it is then corrected back. And this
is the hot fluid is going and flowing off and then collected back.
So, this plate is acting as a barrier there can be different kinds of flow arrangements
in case of plate type heat exchanges we cannot go in so, details of this. But it is a typical
example you can see that in this case this is one liquid, it is a liquid one it is going
like this through this hole. And this is coming through this side and again it is another
one like this it is coming like this and then it is going. It is exchanging through the
plates the plate acts as a barrier between the two plates and through the plates the
heat exchange takes place between the two liquids and then they are collected back.
And mostly the flow is counter current you can see that this is the one fluid and this
is the other fluid so, this is there will be a counter current action so always.
But in plate heat exchange the flow action will be counter current in nature.
So, that way if we can say that thin cold pressed corrugated metal plates are heated sorry into a frame as we have shown
it. And the question is, that why this is corrugated? That corrugation this metal surface
is corrugated this is to increase the turbulence again this corrugation is to increase turbulence.
And there by the heat transfer rate that is what is being then so, this corrugation is because of that reason. And then we can
see that each plate has four holes so, two as inlet and outlet of one fluid and the other
two sorry for the other liquid so, this is used for that.
And then in addition to this there are some more information that we can say that this
plate acts as barrier between the fluids and the heat transfer as I told takes place through
the plate. And individual plates can have area as high as three meter square or higher. This the corrugation determines
the pressure drop and the heat transfer coefficient as I told the kind of corrugation. It increases
the turbulence and as you know that increasing turbulence increases the heat transfer coefficient
but at the same time it increases the pressure loss. Materials of construction for these
kind of plates are usually it is at least the these are little costly materials are
used lowest cost material is stainless steel. Others which can be used as material of construction
are Hastelloy this is to have some information about what type of material is used Hastelloy,
then Incoloy, then Aluminium, Brass, Titanium, Tantalum, Inconel etcetera. So, this these
materials are petty costly and these are many times used as material construction for the
plates for the plate type heat exchanger.
Now, the gaskets there are gaskets as I discussed in case of shell and tube heat exchanger of
gaskets are used for two as a liquid material. And in this case of plate and plate type heat
exchanger the gaskets are usually elastomeric materials these are used. And typical examples are Nitrile rubber then Ethylene,
Propylene, Diene, Monomer, Neoprene rubber, Silicone rubber, Ethylene, Propylene, Diene,
Monomer, etcetera. These are
the material of construction which made of this and then applications we can say that
there is a wide applications. Therefore, particularly for as a replacement wide application replacement
as I told for shell and tube heat exchanger in case of liquid heat transfer.
And in addition to that this is P H E plate type heat exchanger are also used for evaporation,
reboiling etcetera. And it allows maximum solid loading in the fluid as 40 percent.
Now, in this case there are similar to this there are some fouling phenomena, fouling
just as similar to shell and tube heat exchanger as discussed the as discussed in lecture two
we have discussed already. That how the fouling takes place and it is by depositions by area
of methods in addition to that there will be a collision also which is also important
phenomena. Therefore, here in this case the fouling will be relatively less because of
some cost as we have seen the material of construction is related to the cost of the
materials are being used and therefore, the fouling is relatively less.
And this is the figure that gives us or shows us some flow arrangements in case of shell
and plate type heat exchangers, we can see that this is the series flow. That means that
from one plate it is going to the other plate and this going to the other plate that hot
and cold fluid. There the two different fluids this is a one fluid, one if we say that fluid
one and this is say fluid two. So, hot and cold fluid they are going if this is anti
parallel their counter current flow is there in this case and if we see that from one plate
to the this is the diagram for the one plate. So, this is this consist of one plate this
is another plate and this is another plate so these are the based on the different plates.
So, here so, they are in series arrangement, therefore it is called series flow and then
in this case we can see looped or parallel flow. You can see that it is here there is
a fluid there is a one fluid and it is going like this way and then the another plate this
is another plate and they are meeting over here and they are going out. So, this is looped
and parallel flow this is parallel flow similarly, the other fluid is also coming as a parallel
flow. And they are looped they are finally, put into in the same loop they are coming
into the same loop so, this is looped on the parallel flow arrangement. So, this is a series
flow means this is the parallel flow arrangement, there are two different arrangements as I
told you in the plate type heat exchanger than can be of different types.
And this is a typical more little bit complicated arrangements that we can see that this is
two two pass 5 channels per pass counter flow arrangement. There are this is 5 channels
we can see 1 2 3 4 5 channels see here also 1 2 3 4 5 so, 5 channels per pass this is
one pass, this is another pass, you can see here. So, this is called therefore, it is
called two two pass arrangement, so at first it is coming like this and then again whole
things after it is margin here then it is again distributed. Then so fall this is the
first pass, but we can say the pass one and this pass becomes the pass two. You can say
this is pass one and this is pass two because it starts from here, so the way you can see
it is a anti parallel flow or counter flow that has been happening.
And this is very important in case of plate type heat exchanger we should understand the
full pattern. So, the first diagram whatever I have give shown here also a similar such
kind of behavior is taking, you can see that this is a we can say this the parallel things
are happening like this. So, it is a parallel flow and they are looped into this and they
are coming out similarly, this is coming upward and then it is looped and going into this
side. This is what is called your this is called parallel flow arrangement between the
two liquids fine. Now, we will see here that some advantages why the plate type heat exchangers
are becoming nowadays very much useful.
So, we will write here some advantages of plate type heat exchangers the typical advantages
are and because of that reason it is growing in use because of the following advantages what are these. So, high heat transfer coefficient
can be achieved and as I told you that it is by changing the corrugation, we can increase
the heat transfer coefficient. And it is said that about three to five times higher than
shell and tube heat exchanger, the heat transfer coefficient can be achieved. Then second part
is that it is suitable for P H E plate type heat exchanger, is suitable for a close approach
temperature. And this is as low as 2 degree centigrade,
which is 5 degree centigrade for shell type heat shell and tube type heat exchanger, we
try, we should try to understand the close approach temperature. Means and we know that
thermal equilibrium when the two fluids are under thermal equilibrium then there will
be a heat transfer. Thermal equilibrium means the temperatures are same so, there should
be a different shell temperature between the two fluids. When they are present towards
the same directions so, this is called approach temperature so, approach temperature should
be substantial amount of difference. In the approach temperature will be there
in case of heat exchanger shell and tube heat exchanger it is usually 5 will be and it should
be at least 5 degree it could be more than that, then only it will get a good performance.
But in case of plate type heat exchanger this can be as low as 2 degree centigrade that
is what is very important point and then plate heat exchanger as we have seen that is the
simple plates of being placed over there. So, in case of plate type heat exchanger easy inspection cleaning and maintenance possible,
then we have some more important that heat transfer area can be adjusted by changing
the number of plates. So, if we require more heat transfer area
we will put more number of plates, if we require less heat transfer area we will put less number
of plates or also we can change the plate area also. This is one very important and
this adjustment can be I should say that it can be easily done and then sometimes it is
possible that two or more streams can be handled at the same time, at the same instant. So,
it can be so, designed that two or more streams can be heated or cooled in the different sections. So, by changing
the sections we can use even more than two fluids should be heated or cooled so, this
is one uniqueness of this particular plate type heat exchanger.
In addition to that there are some more advantages that it is a less floor space is needed naturally
it is a vertical upwards or less. It is a compact one less floor space is required and
then we have plate type heat exchanger offers low hold off volume of fluids. And then the
costs are that are cost is less even though costly materials are used and this is with
respect to shell and tube heat exchanger. Now, so this is all about a plate type heat
exchanger so ,we can understand that plate type heat exchangers are nowadays people are
using and because of certain advantages. And we have seen that the various advantages that
it can have. Now, in addition to this plate type heat exchanger
there are some more compact heat exchangers, which are being used and I will just briefly
tell a few things about those heat exchangers.
And like for typical one is that as I told that the spiral plate or spiral tube heat
exchanger this is also a typical compact heat exchanger. In this case what happens there
are this is also the flow is in this case also it is a compact heat exchanger, then
the suitable for handling viscous fluids and slurries. Then it is reduced fouling rate,
fouling is less then it can be cleaned easily so, we have to see the operational point of
view also this fouling is less that cleaning easy maintenance. This are basically operational
ease we have to see the operational ease also we have to see the construction point of view
the spiral heat exchanger is in difficult to construct. But it is operational there
could be some operational ease, but they are some difficult in construction.
In case of spiral heat exchanger what happens is, it is like that two plates spiral when
you have consider the tubes to concentrate tubes and they all making coils like this.
And show two concentric channels and they are coiled so this so, the one fluid is just
adjacent to the others and that that it continues in the form of the coil like a centrifuge.
So, it is it is like a coil and this continues, but so, this maintenance may be easy some
cleaning may be easy. But the difficulty is in fabrication of spiral T plate or spiral
tube heat exchanger, in comparison to shell and tube heat exchanger or even plate and
frame heat exchanger. But spiral tube or spiral plate heat exchanger
would be much more compact heat exchanger we should say. So, what happens in this case
is that pair of particular per spiral rate pair of concentric passages are coiled and
one is for hot fluid and the other one is for cold fluid. There will be some concentric
passages of the fluids so, first hot cold, hot cold like that the same fluid will first
to take hot fluid then it will take a passage and will go to the cold next then the next
resume and then it will be accompanied by the cold fluid also. And similarly, that pair
of concentric in place of concentric passages in case of spiral tube it will be pair of
concentric tubes, those will be of used for flow of this fluids in the spiral tube heat
exchanger. And in case of spiral tube heat exchanger
that the it has got some advantages as I told you that it can the advantages of this is
that, in the case of spiral tube heat exchanger that it gives the fouling is less. Fouling
sorry fouling is less as we have discussed and then discontinues the viscous fluids and
this always been done in case of it can use viscous fluids. And it can be designed for
low flow rates also and designed for low rates and the spiral the tube or spiral plate heat
exchangers are always they are always counter current in nature. The two fluids are counter
current in nature of flow so, their flow nature will be counter current.
Now, in addition to this spiral tube heat exchanger there is another one which already
we have discussed previously there is the finned tube heat exchangers are also there.
In this case the tubes are having some fins and this fins can be these are called and
this is we can see these lateral fins and this is the circumferential fins. And these
are circumferential fins, we can see that it is a radial or it is also radial or circumferential
whatever you say. This is these are rectangular profile and these are circular tube heat transverse,
these are transverse fins or longitudinal fins sorry fins. So, longitudinal fins are
used there in case of shell and tube heat exchangers that of certain aspects that has
to be taken into consideration and while using this kind of fin.
So, the aspects of that fin height fin efficiency already we have discussed these issues, then
spacing between fins so, this is basically the overall design of fin tube this is again
that fin orientation. So, overall design of the fin tube will decide, it will decide that
pressure drop, it will decide a heat transfer coefficient. And then depending upon that
we can use this as we have discussed that rate of heat transfer Q is equal to Q dot
is equal to U A delta T. And this as I told in the last class also last lecture, last
two last lecture, that U is the overall heat transfer coefficient. Delta T is a temperature,
A is the area of heat transfer, when the fluids particularly that airy substances air say
in case of say. If we have to extract energy from air heat
energy or if we have to cool somebody then and then what happens is that air to metal
surface heat transfer coefficient is air or vapor or any glacier substance to metal surface.
Heat transfer coefficient is very small compared to the liquid side one and therefore, what
happens is that rate of heat transfer becomes less. Because if you see that rate of heat
transfer depends upon the area U and delta T, delta T as I told that previously also
that it cannot be it cannot be independent. It is decided by the standard world there
is a maximum value of U, that can be obtained by changing flow ratio. And making the very
high flow also you can make some maximum amount of U, that can be obtained and also there
is a flow rate limitations. That we have to the cost of pumping and cost
of compressor all these things has to be taken into considerations. And then what staging
now hand is that area, by increasing the area we can increase in the heat transfer rate
and which has been done in case of heat transfer between the airy substances and surface as
I was telling. And these fin tube heat exchanger is normally being done for this kind of applications,
where the surface area of the tube surface area or heat exchange surface area is drastically
and dramatically improved, increased. And, but then heat transfer rate accordingly gets
increased so, this is about the different types of compact heat exchangers, which are
usually being used. And now, we will come to one more type of
heat exchanger heat exchange or heat exchanger that is called regenerator.
So, what is being done in this case is that it is basically heat transfer between two
streams passing by passing the hot and cold fluids alternatively through bed of solids.
so we have a bed of solids it is like this
So say this is we have to say bed of solids here you can say bed of solids and then the streams
are passed it can be counter current it can be co current usually it is a counter current.
So, from one side one flow say if this is if I say the fluid 1 and then other fluid
is coming like this is a fluid 2 so, this is fluid 2. So, in fluid 1 is coming if I
draw in the other rounded to be like this say so, it is like this if I say this is F
1 and this is F 2 in that case it will go like this. And then here also exactly the
similar way if we draw it will look like this say this one and this and this say F 1 and
this is say F 2 I am sorry both cannot be like that.
So, here I will make little changes so, it is like this F 1 is going this side and say
this is F 2 as F 2 has to come from this side so this is F 2 and this is say F 1. So, if
F 1 is hot fluid F 2 is cold fluid so, hot fluid is coming in and is becoming colder
and it is here it is leaving the energy and this becoming warmer. And then once it is
done then that from the other end this fluid is F 2 is coming which is a cold fluid is
coming in and then it is taking the energy and going out like this way. So, this kind
of utilization of the energy particularly for the cases of says extracting thermal energy
from flue gas. So, flue gas it comes out at a high temperature so, what it can be done
it is placed through this packed bed. And so, the packing material should have some
substantial amount of the heat storage capacity that should be property of the packing material,
so good heat storage capacity. The packing material should have appreciable heat storage
capacity and what happens if that then what advantage we are going to, but what advantage.
So, there are some advantages we are going to get and in this case is that high surface
area because final particle starting to be huge solid surface. That has been there in
packed bed so, high surface area for heat exchange and they are easy to clean and then
easy to replace also. That packing materials destroyed or if needed
can be easily replaced, why if needed? Because if we want to change the packing material
because of depending upon the amount of heat capacity storage, so this can be done.
Now, this is as I told you this is very good for use for the viscous substances particularly
it is a rotary it can be static or it can be rotator, rotary generator, regenerators
are widely used in electric power plant. But this is not suitable this is a very important
not suitable for liquids there are many reasons behind that, first of all the thermal conductivity
thermal conductivity of liquid in pores would be similar to that of solids that is one thing
therefore, the heat exchange could be a difficulty. And then the mixing that is the major problem
between two fluids
is always there. So, it is better if we can so, that cannot be mixing, cannot be avoided.
So, it can be so, this thus that regenerated heat exchanger could be good when that two
fluids can be separable and the mixing would not be a problem for cases. And the effectiveness
of such heat exchanger it is like a packed bed and it depends upon on a number of transfer unit and cycle time,
how many times it is being used so that is also very important thing. And the number
of transfer unit is. Defined as U over heat transfer coefficient
A is the area by C, C is the heat capacity it is M dot into C for M dot is heat capacity
into mass flow rate is the total heat capacity. And this is the specific heat capacity, this
is the total heat capacity, this is equal to C and this is for hot fluid or cold fluid.
So, this capital C we can say that is equal to M dot into C M dot is the mass flow rate.
And C is the heat capacity, specific heat capacity so; this is becoming the heat capacity
per unit time. So, and U A by U is the over heat transfer coefficient and A is the area
of heat transfer which is called a number of transfer units for such situations. So,
this is about the different types of some aspects on different types of heat exchangers
that are normally being used in case of heat transfer operations.
Some of them are very commonly used like double pipe it is not double pipe like say anti heat
exchanger, some of them are very important and upcoming like blade type heat exchangers,
spiral heat exchangers. These are very upcoming heat exchangers and they are replacing the
shell and tube heat exchangers in many situations. Now, some important aspects now related to
the driving force for heat exchange would like to discuss here.
So, some issues related to flow pattern and driving force, we will discuss this so, first
of all let us consider say a double pipe heat exchanger. In case of double pipe heat exchanger
that there can be a two type of flow pattern as you have discussed, this is the perfectly
co current and perfectly counter current over we have discussed. So, co current and counter
current already we have seen it, but if we say that this is the length and if we say
that this is the temperature. Here the profiles if we draw for co current the profiles appear
to be like this so, we can say this is the approx temperature. So, this is the maximum
possible approx temperature so, it can be at least 5 degree centigrade or even more
than that. This is the co current case and we can say
that in the double pipe there is a pipe co current or perfectly counter current situation.
So, this is the hot fluid, this is the cold fluid now, the question is that we know that
L M T D also we can find out what is the because we have seen that in both the cases, that
delta T gradually changes along the length of this. Delta T gradually changes, so here
it is delta T 1 if I say and this is delta T 2 in this case, this is delta T 1 and this
is delta T 2 as because they are gradually changing. And we have seen already this for
parallel flow and counter flow there will be some at both the cases, the driving force
is being given by L M T D log mean temperature difference.
And L M T D is nothing but delta T 1 minus delta T 2 by l n delta T 1 by delta T 2 so,
this is what is the driving force for that, but the question is it is a very common question
that we can have we all know that counter current is better performing and counter current
heat exchanger is preferable. The reason behind this is that, if you see first point is that
the in case of counter current the outlet temperature of the hot fluid does not decide
the outlet temperature of the cold fluid. So, we can increase the cold fluid temperature
even more than the outlet temperature of, we can increase the outlet temperature of
the cold even more than the outlet temperature of the hot fluid so that is not restricted
that is the first point. And second point is that if you see in case
of co current that delta T is gradually changing and initially it is very high and laterally
it is very low, so it is a non uniform. But in case of counter current heat exchanger
uniform distribution of the driving force is always there and that gives a better performance
of the heat exchanger. So, these are the two important aspects that we should keep in mind
and therefore, that counter current heat exchanger is always preferable in most of the situations,
it is preferable than the co current heat exchanger. Second point what I wanted to say
over here is that when we consider about the multi passes.
Then what happens? Say consider the two case one to pass it is shell and tube heat exchanger
first consider this case. So, what happens in this case if we just quickly draw
this is the shell and tube heat exchanger. So, this is say T h and this is T c a that
is the starting point and it is say one two pass so, it is like this. So, this is I am
sorry and then there should be a nozzle over here this is the hot fluid at start and hot
fluid out this is hot fluid in and this is T h b and this is say sorry T c b this is
T c b and this is T c in. And write it as T c a, so what happens is we can know that
it comes like this and then it goes like this and then it comes like this and then goes
out. So, this is the flow directions of the cold
fluid and the flow direction for the hot fluid is that will come like this and then it goes
like this. Therefore, in this region we can see in this region it is counter flow and
this region is parallel flow. So, in a one two heat exchanger and there in the two, that
the fluids the tube side fluid once it will encounter as a counter flow and another time
to encounter as a parallel flow. So that is very important to decide that where we should
put should we put the tube side here and then cold fluid empty here. And output here or
empty here or output that side that is very important say maximize the driving force for
the heat exchange. And if we draw it like this way we will find
that it is like this sorry and it does not exactly so, this is not correct we should
draw like this here it exactly matches. And then so, this is the case and this is becoming
T c i and here it is say T c a this is T c b cold fluid and this is T h a and this is
T h b. So, what we can see here that from T c a to T c i is the parallel, T c a-T c
i and T h a-T h b T h a-T h b T c a-T c i these are in parallel and this is encounter.
So, in the counter flow is the hot portion of the hotter side or hotter hot fluid of
the hotter part of the cold fluid and the this one is in counter flow and the other
side is in the parallel flow operations. Now, what we can say here in this case is
that it is neither a perfect so; in this case this is neither a perfect parallel flow or
not a perfect counter flow situations. So, under perfectly counter flow there can be
something L M T D or under perfect parallel flow there will be L M T D, but it is not
neither a perfect parallel flow neither a perfect counter flow. So, how to get the values
of the log mean temperature difference for this system, actually what is being done in
this case that, we have to find out this is the delta T maximum possible delta T and this
is the maximal possible delta T 1 and delta T 2. So, we have this we have and based on
that we will calculate L M T D will be delta T 1 minus delta T 2 by l n delta T 1 by delta
T 2. But this is not the actual scenario in the
heat exchanger there will be a lot of changes.
And that is taken care of by a factor or by a plot this is called a plot of correction
factor. That correction factor takes care of this issue and to give it and to give a
average value of L M T D log mean temperature difference. And this is obtained there is
correction factor versus some temperature ratio and that is plotted for some parameter.
So this temperature ratio correction factor versus temperature ratio for certain parameter,
in case of shell and tube heat exchanger that for this is for one, two heat exchanger. Similarly,
one, two shell and tube heat exchanger there can be for two four for different passes,
there can be different such plots, these plots are available in several literatures.
This can be followed, this can be used to find the values of the correction factor and
this must to find out the correction factor and correction factor is if I say here now.
Say I will say that correction factor is F T and so, it is maximum value is F T maximum
value of F T equals to one and so, actual average L M T D is F T into L M T D or I should
say average L M T D not actual average L M T D is this F T into L M T D actual based
on that configurations. Now, what happens is in this case that ratio there are two things
are being there temperature ratio that is the x axis. It is nothing but if I say that
it is equal to R and that is equal to T c b minus T c a so, this is the cold fluid higher
hot temperature, cold fluid inlet temperature, outlet temperature, cold fluid inlet temperature
by T h a minus T c a this is the maximum temperature difference between the cold and hot fluid.
This is the cold fluid empty temperature the hot fluid empty temperature to this is the
maximum difference, temperature difference.
So, for multi pass heat exchanger we use correction factor and correction factor or F T is used
to get corrected L M T D. And so, L M T D corrected is equal to L M T D into F T and
L M T D is delta T 1 minus delta T 2 by l n delta T 1 by delta T 2. That is what as
we know and the this values of correction factor we have to calculate from the figure
as I said. And there are two parameters are there one is the temperature ratio that is
the x-axis, it is R and this is equal to T c b minus T c a by T h a minus T c a and you can see that
it is the cold fluid outlet temperature minus cold fluid inlet temperature.
So, there is a differential temperature between the cold fluid and this is the maximum temperature
difference in the heat exchanger, either there is the temperature difference between the
hot fluid inlet and the cold fluid inlet.
So, this is the temperature ratio and that parameter P and that is given by T h a minus
T h b by T c b minus T c a. So, it is that differential temperature of the hot fluid
by differential temperature of the cold fluid that is being achieved by the heat exchanger.
So, based on these parameter we have several values of the correction factor L M D T correction
factor so, like this way we have to use for even for two foot passes or one foot passes.
Different passes of heat exchangers we have to consult the respective charts and find
out the values of the L M D T correction factor and then go for the calculations of the heat
exchanger area we will take off some problems later on in some subsequent lecture.
And we will see how to use this and then I will ask only a simple question say that first
question is that, if the driving force delta 1 T 1 is equal to delta 2 whether it is a
parallel flow or counter flow does not matter, if the driving force delta 1 T 1 and delta
2 are same then what is L M T D or what would be the what would be the temperature difference?
That should be used even it is a very common question as we know what L M T D expression.
Why the question comes L M T D expression is delta T 1 by delta T 2 by I am sorry it
is delta T 1 minus delta T 2 by l n delta T 1 by delta T 2. So, when delta T 1 is equal
to delta T 2 though L M T D becomes 0 by 0 that is undefined so we need not bother about
this L M T D, because it is undefined. And we need not bother about what we can understand
is that when both sides driving force are same then, what we will say is? That the actual
driving force is delta T 1 is equal to delta T 2 is equal to delta T we will use the same
driving force for that. And second point is that when we have say in case of heat exchangers.
If we have say linear driving force exactly linear driving force say it is this is delta
T 1 and this is delta 2. And if it varies linearly there is no non linear variations,
if it is possible then our driving force will be delta T will be equal to delta T 1 plus
delta T 2 by 2. That is why it is a simple arithmetic mean we should use so, we should
use the arithmetic mean when there is a linear variations of the driving force we should
use the same driving force. When there is no more change in delta T both the sides of
the delta T is same then also there is a linear arithmetic mean also, we will do. And when
there is a non linear variation then we should take we should make use of L M T D or log
mean temperature difference. And another thing also I should point out
over here that when there is a condensing steam in a shell and tube heat exchanger condensing
steam means, that the hot fluid so steam is used to heat cold fluid. And steam is just
loosing the latent heat of vaporization to heat the cold fluid. So, condensing steam
when it is used on the shell side and tube side there will be a cold fluid which is used
off, which is taking off, that latent heat sensible latent heat. From the more sensible
heat only the latent heat from the fluid under that situation it remains the co current or
counter current remain the same. Because if you see the temperature profiles it will become
like this temperature profiles whether it is co current or countercurrent does not give
any difference it will remain the same. So, if I say this is the condensing steam
and say this or both the times both the cases that delta T remains the same, because this
is become the reference frame. And the reference frame is there is no change in the reference
frame therefore, whether it is a counter or co current that does not create any differences.
So, this is all for today I will stop over here and next class we will see to find out
some we will do some calculations, to find out the heat exchanger areas or design of
the heat exchanger thank you very much.