Sizing a Heat Exchanger: Counter Flow Video Lecture | Heat Transfer - Mechanical Engineering

In this screencast, we're going to look at
a concentric, counter-flow heat exchanger,
which means that the hot fluid (in our case
is oil) enters the heat exchanger in a different
direction, or counter direction, to the cooling
fluid (which in this case is water). The water
will enter the heat exchanger at the other
end while the oil will exit it again counter-flow
to the water. So we're going to do a similar
analysis here, finding the length of a heat
exchanger, as we did with parallel-flow. The
only difference again is going to be that
this heat exchanger is counter-flow. We're
still going to use our governing equation,
q equals U times A times delta T log mean,
as we did with parallel-flow. And again we're
going to rewrite it in terms of our length.
If we look at our properties and our equation,
what we'll see is that everything is exactly
the same in a counter-flow heat exchanger
as it is in a parallel-flow heat exchanger
except for one term. And that term is this
delta T log mean. Delta T log mean is going
to be our delta T 1 (which refers to the difference
in temperature at the entrance of the heat
exchanger) minus our delta T 2 (which is the
delta T at the end of the heat exchanger)
divided by the natural log of delta T 1 over
delta T 2. What's different in this particular
heat exchanger is, because the fluids are
going in the opposite direction, our delta T 1
and our delta T 2 are going to be different
for a counter-flow versus a parallel-flow.
So let's take a look and see what our delta
T 1 is going to be. And looking at this picture,
we can see that our delta T 1 is going to
equal the temperature of the oil that's entering
the system minus the temperature of the water
that's exiting the system. So that means that
our delta T 1 is going to equal 100 degrees
C minus 50 degrees C, or 50 degrees. Delta
T 2 is going to be the temperature of the
oil exiting the system minus the temperature
of the water entering the system. So our delta
T 2 is going to equal 60 degrees C minus 25
degrees, or 35 degrees C. And now let's find,
using these, our delta T log mean. So this
is going to be delta T 1, which is 50 degrees
C, minus delta T 2, which is 35 degrees C,
all divided by the natural log of 50 degrees
C divided by 35 degrees C. And when we calculate
this, we find that our delta T log mean is
equal to 42 degrees Celsius. And now let's
put in numbers for our length. And for sizing
a heat exchanger using parallel-flow, we found
that our heat transfer rate was 12,786 watts,
our overall heat transfer coefficient was
38.1 watts per meter squared degrees C, our
diameter was equal to 0.03 meters, and again
our delta T log mean is 42 degrees C. L is
going to equal our heat transfer rate, divided
by our overall heat transfer coefficient times
pi times this diameter times our delta T log
mean. And when we calculate this, we find
that the needed length for our heat exchanger
is 84.8 meters. We compare this for the length
of a parallel-flow heat exchanger, which is
a 110.6 meters. Why is there a difference?
Well because the delta T, or the difference
in temperature, is greater along the tube,
you need less surface area for the same amount
of heat transfer. Therefore, we would need
a shorter length for the counter-flow heat
exchanger.