Monday, 5 September 2016

STEADY FLOW ENERGY EQUATION FOR HEAT EXCHANGER

STEADY FLOW ENERGY EQUATION FOR HEAT EXCHANGER


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.
mC and mH 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.

mC h1 + mH h2 = mC h3 + mH h4

mH (h2 - h4) =  mC (h3 – h1)

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

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