We were discussing various basic
concepts of thermodynamics in our previous post such as “

*Thermodynamic reversible cycle, reversible heat engine and reversible heat pump*”. We have also seen the concept of “*Steady flow energy equation for throttling process*” in our previous post.
Before writing and understanding the
concept of steady flow energy equation for a heat exchanger, let us first brief
here steady flow energy equation and after that we will analyze the steady flow
energy equation for a heat exchanger.

###
**Brief
introduction of steady flow energy equation**

For steady flow process, net
quantity of energy contained within the system will never change with respect
to time. Therefore according to the principle of conservation of energy, we
will have following statement and energy equation for a steady flow process.

Net quantity of energy entering to
the control volume = Net quantity of energy leaving the control volume

For more detail about steady flow
energy equation, please find the post “

*Mass balance and energy balance in steady flow process*”.###
**Let us see first the brief introduction of a heat exchanger**

Heat exchanger is basically defined
as one mechanical device where two moving streams of fluid exchanges heat
energy with each other without mixing.

###
**Steady flow energy equation for a heat exchanger**

During energy analysis of a heat exchanger,
we usually neglect the change in kinetic energy and also change in potential
energy because change in kinetic energy and change in potential energy will be negligible
for each fluid stream and therefore we will neglect the change in kinetic
energy and change in potential energy during writing the steady flow energy
equation for a heat exchanger.

Heat energy will be exchanged
between two moving streams of fluid and therefore there will no heat
interaction between system and surrounding. Therefore Q = 0

There will not be any work
interaction between system and surrounding and therefore, W= 0

Let us see here the following
figure, cold water enters at state 1 and leaves the heat exchanger at state 3.
Similarly, hot fluid enters at state 2 and leaves the heat exchanger at state 4
as displayed in figure. Cold water is flowing through the tubes of heat
exchanger and hot fluid is flowing over the surface of tubes in heat exchanger.

m

_{C}and m_{H}are the mass flow rate of cold fluid and hot fluid respectively through the heat exchanger.
Applying here the concept of steady
flow energy equation and we will have following energy equation for a heat
exchanger.

####
**m**_{C} h_{1} + m_{H} h_{2} = m_{C}
h_{3} + m_{H} h_{4}

_{C}h

_{1}+ m

_{H}h

_{2}= m

_{C}h

_{3}+ m

_{H}h

_{4}

####
**m**_{H} (h_{2} - h_{4}) = m_{C} (h_{3} – h_{1})

_{H}(h

_{2}- h

_{4}) = m

_{C}(h

_{3}– h

_{1})

We will see another topic i.e. “Concept of steady flow energy equation for turbine and compressor” in our next post.

Do you have any suggestions? Please write in comment
box.

####
**Reference**

Engineering thermodynamics by P.K Nag

Image Courtesy: Google