P2 theory

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EG2010 P2 pressure Lab

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Theory

COMPARISON BETWEEN PARALLEL FLOW AND COUNTER FLOW HEAT

EXCHANGER

The heat exchanger that had the possibility of functioning in two separate ways, with four

valves controlling the flow direction in the heat exchanger, as shown in picture 1. In this

experiment the counter flow heat exchanger was analyzed, with valves 2 and 3 open and 1

and 4 closed, but a short discussion about the two systems will help to better understand the

differences, the advantages and disadvantages of both systems.

First of all the differences between parallel flow and counter flow are shown on the graphs

below:

Figure 3

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The main thing that can be seen is the difference of exit temperature of the cold fluid.

In the counter flow exchanger it's possible to reach a final temperature of the cold fluidhigher than the final temperature of the hot fluid, that's because the fluids will never converge

to the equilibrium temperature, which could theoretically be reached in the parallel exchanger

with enough contact between the two liquids. So if a higher heat exchange is required the

counter flow exchanger is more efficient and effective.

Although the counter flow heat exchanger is more efficient and can cool the fluid down more

than the parallel flow over a longer contact distance, the parallel heat exchange system has

advantages such as being able to cool the fluid faster at the initial phase of contact due to a

greater T at the entry point between the fluids. This may be advantages in certain

requirements in which a large overall drop in temperature is not needed but a fast initial drop

is.

Flow measurementair

The equation below gives the mass flow rate of air through the nozzle, which is situated

before the heat exchanger. This nozzle increases the velocity of air, thus increasing the mass

flow rate. This is given in the BS1571 pt2.

the temperature downstream of the nozzle (K)

gh =differential pressure across the nozzle (Pa)

(Eq 1)

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Absolute pressure downstream of the nozzlegh+atmospheric pressure=gh (Pa)Flow measurementwater

The Mass flow rate of water is simply measured by catching the exiting water in a beaker and

recording the time, the water is then weighed. The units of mass flow rate is mass of time,

hence to calculate the mass flow rate the mass of the water in Kilograms is divided by the

number of seconds it took to collect the water giving Kg/s.

Heat transfer rates

(

)

The steady flow energy equation as seen above is used to calculate the heat transfer rates.

That is the energy lost by the air and the energy gained by the water.

=mass flow rate

h=enthalpy

c=velocity

gz=potential energy

Q=rate of heat transfer

W=rate of work transfer

However for these equations the work done (W) is zero, gz is zero,and c is zero,

Leaving only Q=

(Eq 2)

This equation can be applied to both the water and the air to give the rate of heat transfer rate

between the air and the water in watts. it is assumed that the exchange is 100% efficient

however this is not the case as shown in the calculations in results for the measured values

taken from the heat exchanger, heat is lost to the atmosphere as well as to the instrument.

Film heat transfer coefficient (air to tube)

=ALMTD (Eq 3)

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A=surface area of tube through which heat is transferred

LMTD=log mean temperature difference, this is the average temperature difference between

the air and the wall and is required because the temperature varies at any given point along

the system.

This formula is important, it allows the coefficient of the heat transfer between to fluids of

different temperature and a certain surface area to be calculated.

This formula is equated using the measured values taken from the heat exchanger.

Correlation of heat transfer

where Nusselts numberh = the film heat transfer coefficient

d=equivalent diameter of air annulus

k=thermal conductivity of fluid

This formula can be rearranged to find the film heat transfer coefficient, using a calculated

analytical method rather than a measured practical answer. The h value can be compared to

the film heat transfer found using the log mean temperature difference.

using dimensional analysis and similarity techniques it may be shown that for heat transfer

in horizontal pipes of circular cross section when the flow is turbulent, data may be correlated

using the equation (Eastop & McConkey)

Within a heat exchanger Nusselts number is the ratio between conductive and convective heat

transfer between the boundaries of the two fluids. In this case the piping of the air annulus

which seperates the two fluids. It is a dimensionless number as it is simply a ratio. It looks at

the ratio of the conduction currents which are given off by a first fluid and then create

convection currents heating a second fluid.

(Eq 4)

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The temperature exchange done by these two fluids is a forced convection heat exchange, the

hot air gives of heat energy to the outer edge of the air annulus which in turn passes that

energy to the water being forced along the pipe in a counter flow direction to the air. In this

instance both conduction and fluid motion are working to cool the air inside the annulus. As

the water heats up from the heat new water is pushed in its place, cooling the annulus at a

very fast rate.

Ideally the energy lost by the air will be represented by the energy gained by the water, we

will in this experiment be able to see if this is true. We will be able to determine if this

system is 100% efficient with its insulation or if energy is lost to the atmosphere and to the

instrument pipe running inside the air annulus.

P2 theory

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