HT 209HEAT TRANSFER IN TURBULENT FLOW

Experiment : 5/03/2012 Presentation : 12/03/2012

Group B1/B

100020012- Vartak Shankul Shisheer      10D020013- Abhishek Mathur                 10D020006- Kunal Bhoyar                      10D020021- Monika Kanwat

     

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OBJECTIVES

To determine the overall heat transfer coefficient.

To find the heat transfer coefficient for inner pipe with hot fluid from overall heat transfer coefficient.

To verify the Dittus-Boelter equation for turbulent flow heat transfer.

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MOTIVATION

• A wide variety of chemical processes involve heat transfer during one or more o the basic steps of mixing, reaction and purification.

• Dimensionless variables like Reynolds number and Nusselt number characterize the heat transfer processes and are used for scaling an experimental condition to the pilot scale and the plant scale.

• Thus determination of the nature of fluid flow in various regimes becomes essential from an industrial point of view.

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THEORY

Heat exchanger is a process device used to effect heat transfer between fluids. Here, we are using a double tube heat exchanger, in which hot fluid flows in a smaller diameter tube and cold fluid flows around these smaller tubes.

The flows is anti-parallel for efficient heat transfer. Heat transfer on both sides of the wall (in the fluid) is

generally by convection and by conduction inside the metal.

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THEORY (contd.) The system is equivalent to the system of three

resistances connected in series so the net resistance will be the summation of individual resistance.

(1) Ai, A0= Inner and outer surface area of the inner

pipe, hi, ho =Heat transfer coefficient between hot fluid

and inner pipe and inner pipe and cold fluid respectively,

Ui =Overall heat transfer coefficient for the inner pipe.

Alm is the logarithmic mean surface area given by

(2)

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THEORY (contd.)

The thermal conductivity of metal is very high. Hence for all practical purposes the resistance offered by the metal is neglected as compared to that offered by convection.

(3)

The heat transfer rate from the hot fluid is given by

Q = ρVCp(T1 - T2) (4) Also, from the definition of the overall heat transfer

coefficient (U), we have Q = U1A1ΔTlmtd (5)

i.e., U1 = Q/A1ΔTlmtd (6)

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THEORY (contd.)

where log mean temperature difference, Tlmtd is given by

(7)

Where, Q = Heat transfer rate (W) ρ = Density of hot fluid (monoethylene glycol) (kg/m3) V = Volumetric flow rate (m3/s) Cp = Specific heat capacity (J/kg-K) T1 = Inlet temperature of hot fluid (K) T2 = Outlet temperature (K) t1 = Inlet temperature of cold fluid (K) t2 = Outlet temperature of cold fluid (K)

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THEORY (contd.)

Heat transfer coefficient of fluid in the inner tube can be found using Dittus-Boelter equation

For different flow rates, if the mean temperature of the inner fluid does not differ much, then all physical properties remain almost constant. Hence,

Or equivalently,

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EXPERIMENTAL PROCEDURE

Switch temperature

indicator. Check for zero error for zero flow rate.

Set the flow rate of cold fluid at

constant value of 240 LPH. Start the

heating of hot fluid & set the

flow rate at 800 LPH initially.

Note the inlet & outlet

temperatures of hot & cold fluid

for particular flow rate of cold fluid.

Repeat for 6 reading of flow

rate till 300 LPH.

Measure length of the heat

exchanger, radius of the inner and outer diameters

of pipes.

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SCHEMATIC DIAGRAM OF APPARATUS

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CALCULATION PROCEDURE

Calculate Prandtl number

for the hot fluid.

Calculate LMTD

from the inlet &

outlet of hot & cold

fluids.

Calculate the

velocity of hot fluid

flow.

Calculate the heat transferred from the hot

fluid & overall heat transfer coefficient.

Calculate Re from flow rate & Nu from U &

LMTD.

Plot the curve between 1/U and 1/v0.8 &

use the intercept to calculate hi.

Plot curve between ln(Nu) & ln(Re) and

compare the coefficient of ln(Re)

with theoretical value.

OBSERVATIONS Table 4.3.1 Temperatures and flow rates

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S. No.

Flow rate

Temperatures (°C)    ΔTlmtd

(K)

  (LPH) Cold Fluid   Hot Fluid    

    Inlet Outlet Inlet Outlet  

1 800 28.5 36 64.5 58.5 28.80

2 740 28.5 35.9 64.7 58.5 28.95

3 680 28.4 35.6 64.8 58.5 32.00

4 620 28.4 35.5 64.6 58.2 29.00

5 560 28.4 35.5 64.5 57.9 28.80

6 500 28.4 35.1 64.5 57.8 28.95

OBSERVATIONS Table 4.3.2 Heat Transfer Rate (Qhot), Heat Transfer Coefficient

(U) and Velocity (v)

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S. No.Flow

rate VLMTD Qhot Ui vi

1/vi^0.8

1/Ui

  (lph) (K) (W) (W/m2K) (m/s)   (10-4 m2K/W)

1 800 28.8015799.

520555.04 2.83 0.435 0.4865

2 740 28.9515038.

219462.63 2.62 0.463 0.5138

3 680 32.0014013.

516407.69 2.41 0.495 0.6095

4 620 29.0012954.

516736.87 2.19 0.534 0.5975

5 560 28.8012021.

415639.39 1.98 0.579 0.6394

6 500 28.9510876.

514077.51 1.77 0.633 0.7104

OBSERVATIONS Table 4.1.3 Inner Heat Transfer Coefficient (hi), Nusselt Number

(Nu), Reynolds Number (Re)

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S. No. hi (W/m2 K) Nu =hidi/k ln(Nu) Re= diui / ln(Re)

1 6191.02 240.07 5.48 5904.90 8.68

2 5835.85 226.30 5.42 5466.73 8.61

3 4859.23 188.43 5.24 5028.56 8.52

4 4963.30 192.47 5.26 4569.52 8.43

5 4617.38 179.05 5.19 4131.35 8.33

6 4130.32 160.16 5.08 3693.17 8.21

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WILSON PLOT

0.4 0.45 0.5 0.55 0.6 0.650

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

f(x) = 1.06086757554995 x + 0.037821679526148

1/Ui Vs 1/u^0.8

Series1Linear (Series1)

1/u^0.8

1/U

iE-0

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GRAPH OF LN(NU) VS LN(RE)

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.84.8

4.9

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5.1

5.2

5.3

5.4

5.5

5.6

f(x) = 0.816329956666415 x − 1.6314027744446

Ln(Nu) Vs ln(Re)

Series1Linear (Series1)

Ln(Re)

Ln

(N

u)

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RESULTS AND CONCLUSION

Overall Heat Transfer Coefficient= 20555.04 W/m2K

Outside fluid heat transfer coefficient ho=45491 W/m2K

Thus the value of the constant c1 in the Dittus- Boelter Equation (1.9) is 0.816.

Expected (theoretical) Value is 0.8. Relative error is (0.816-0.8)/0.8*100= 2%.

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CONCLUSIONS (CONTD.) On decreasing the volumetric flow rate, and hence the velocity,

of hot fluid, Reynolds number (Re) decreases, while, Prandtl number (Pr) remains almost constant as it primarily depends on the fluid properties and is not sensitive to flow rates.

If the heat transferred from hot fluid, Q decreases, Nusselt number decreases as overall heat transfer coefficient, U decreases.

As the velocity, i.e. volumetric flow rate decreases, total heat transferred, Q & overall heat transfer coefficient U decrease. This is because of the relationship between Reynolds number & Nusselt number.

The Dittus-Boelter Equation for heat transfer in turbulent flow is verified with an error of 2 %.

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SOURCES OF ERROR

Fluctuation in flow rate of cold and hot fluid by +/-10 l/hr.

Some heat is lost from water to the surroundings while undergoing heating in the heat exchanger, so to remove this error, consider only the change in temperature of the hot fluid for calculation of amount of heat transferred and not of the cold fluid.

Proper insulation of the pipes is required to ensure no heat is lost to the surroundings.

Voltage fluctuations lead unsteady flow rates. At high flow rates, the measurement of temperature of

the hot liquid can be inconsistent.

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PRECAUTIONS

Arrange for appreciable difference between the flow rates of two readings.

Flow rate of the cold fluid should be kept constant throughout the experiment.

Readings should be taken only when the inlet and outlet temperatures stabilize.

Minimize the parallax error in noting the flow rates.

The volume flow rate of hot fluid should be in the turbulent regime.