# Heat Transfer

Published: Last Edited:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

### Abstract

The objective of the experiment was to investigate heat transfer between the inner surface of a pipe maintained at uniform temperature and a fluid flowing along the pipe. Results were obtained for all the four orifices. Air flow rates were measured for the different diameter orifices and the pressure of air flow was measured. From, the results obtained we were able to show the relation between Stanton and Reynolds number and compare it with the Dittus Boelter correlation

### Introduction

Heat transfer in industrial heat exchangers usually occurs between the surface of the pipe and a fluid flowing inside it. It is therefore important to be able to calculate the heat-transfer coefficients for flow inside pipes so that the total heat transfer rate and size of the equipment can be calculated. [1] In the experiment, an investigation on the heat transfer to air flowing through a pipe with a constant wall temperature was carried out.

### Background and Theory

Convection heat transfer between the inner surface of a pipe and a fluid is proportional to the velocity of the fluid. The higher the velocity, the larger the flow rate and the higher the heat transfer rate (Cengel, 2003).

As the fluid enters the pipe with uniform velocity, the fluid adjacent to the wall is brought to rest. The boundary layer increases in thickness until it fills the whole pipe and from this point the velocity profile along the duct remains unchanged. If the turbulence in the entering fluid is high, the boundary layer will become turbulent. Forced convection in the pipe increases the heat transfer rate. [3]

The heat transfer coefficient in the entrance region of the pipe will tend to be higher than the rest of the duct. When a fluid with uniform velocity enters the pipe a velocity boundary layer, (also a thermal boundary layer if heated) starts developing along the surface of the pipe. The heat transfer through a pipe is dependent on the thickness of the pipe and isolation layers it contains.

The flow beyond the entrance region of the pipe is termed “fully developed flow”. The transition from laminar to turbulent flow is likely to occur in the entrance region.

For a fluid, such as air flowing through a pipe, the heat transfer coefficient and hence the Nusselt number depend primarily on the Reynolds number. For Re=2000, flow is said to be laminar, heat transfer is by conduction only, and heat-transfer coefficients are relatively low. For Re ~ 10 000, the flow is turbulent and the mixing of hot and cold eddy fluids leads to higher heat-transfer coefficients than in the laminar region.

(1)Heat transfer coefficient is expressed in terms of the dimensionless Nusselt number, Nu as:

(2)Dimensional analysis indicates the existence of the following relationship for forced convection heat transfer for flow in pipes.

Dittus Boelter correlation is applicable when forced convection is the only mode of heat transfer.

Dittus Boelter correlation:

(3) Apparatus

* Numbers indicate thermocouples

The apparatus shown in Fig.2 consists of a steel pipe with a fun to draw air through it. The pipe is fitted with five electric heaters, maintained at a constant wall temperature over a section of 1.5 m long. Thermocouples are used to measure the wall temperatures at ten points along the heated section and the inlet and outlet temperatures of the air. The insulated mixing chamber insures that the measured outlet temperature is close to the true “bulk” mean temperature. The pipe is divided into five sections along its heated length, so that the variation in heat-transfer coefficient along the pipe can be investigated. A venturi meter, with a water manometer, is used to measure the mass flow rate of the air.

### Experimental Procedure

· Atmospheric pressure and the ambient temperature were recorded.

· Manometer reading was recorded when connected between the inlet and throat of the venturi meter and when connected between venturi inlet and atmosphere.

· Temperatures were recorded for each of the five heaters in the pipe.

· The power dissipated was recorded from the selector switch, in each of the five heaters as a percentage of their total rated power of 1200 W.

· From the second selector switch, the inlet and outlet air temperatures were obtained.

· The orifice on the fan exit was removed, after a sufficient time (~20 minutes), when all the wall temperatures and heater powers became steady, to allow a second set of observations to obtained.

· In total, results for four flow rates were obtained (one with fully open orifice, the other three with different orifice plates).

### Raw Results

Atmospheric pressure = 772.50 mmHg = 102991.5 Pa

Ambient temperature = 21 oC = 294.15 K

Wall temperature (Heaters): H1=80, H2=81, H3=80, H4=80, H5=80 (constant)

Inlet Temp. = 19 oC

Outlet Temp. = 38 oC

### Table 1: Experimental Results

Orifice

/mm

Heater

Powers/%

Inlet

Temp./oC

Outlet

Temp./oC

Venturi inlet to throat/ mmH2O

Venturi

inlet to atm. /mmH2O

Venturi inlet to throat/Pa

Venturi

inlet to atm. /Pa

Fully open (62)

H1=26 H2=13 H3=15 H4=16 H5=16

19

38

145

320

1422.0

3138.1

40

H1=22 H2=12 H3=15 H4=15 H5=14

20

38

122

258

1196.4

2530.1

27

H1=17

H2=11 H3=13 H4=13 H5=13

20

40

62

140

608.0

1373.0

20

H1= 8

H2=11

H3= 9

H4=10

H5= 9

20

42

30

56

294.2

549.2

Sample Calculations and Results

CASE: Fully open orifice - 62 mm

Air mass flow rate

Heat-transfer rate

Heater powers / W

Heat-transfer rate

Calculated temperatures

Log-mean temperature differences

Surface heat-transfer coefficients

### Discussion

The objective of the experiment was to investigate heat transfer between the inner surface of a pipe maintained at uniform temperature and a fluid flowing along the pipe.

Reynolds number, Re was calculated for all the four orifices, and found that the range of values were between ~20 000 - 40 000, ensuring turbulent flow and validity of the Dittus Boelter correlation, since forced convection was present in the pipe. The heat transfer coefficient and the Nusselt Number depend primarily on the Reynolds number. Prandtl Number, Pr is only dependant on the fluid and the fluid state, unlike Reynolds number where it is subjected to length scale variable. The Pr for the air flow in the three cases was constant and small in value, allowing the heat to diffuse quickly. Variation in Pr would lead to different viscosities in the heaters and therefore affect the outcome of the results.

Fluid flow can be divided into three regions. Below Re=2000, the flow is laminar, heat transfer is by conduction only and heat transfer coefficients are relatively low. For Re~10 000, the flow is turbulent and mixing of hot and cold fluid by eddy motion leads to higher heat transfer coefficients than in the laminar region. Between the laminar and turbulent regions is a transition region where a small amount of mixing occurs. Entrance effects are not accounted for the Dittus Boelter correlation as it is only applicable for forced convections, i.e. turbulent flow.

The main errors carried out in the experiment were due to human errors and apparatus used. Parallax errors were one of the main factors in the experiment, where taking readings from the manometer contributed significantly to experimental errors.

The accuracy of the venturi meter, barometer, manometer and thermocouples also accounted for the possible errors in the experiment. Errors resulted in less accurate readings in calculating the heat-transfer rates, heat transfer coefficient, mass flow rate, air density etc. This is because there would have been errors in the ambient temperature, wall temperature, atmospheric temperature, heater powers (%) etc. Having more heaters along a greater region in the pipe would give better variations in the heat transfer coefficient.

Due to time constraints the experiment was only carried out once, errors could have been minimised by repeating the experiment 5 - 10 times. The outcome of the experiment turned out to be fairly accurate, although if errors were taken into account when calculating the results, the outcome would have been better.

### Conclusion

The outcome of the experiment turned out reasonably well. Results were obtained for all the four orifices. Air flow rates were measured for the different diameter orifices and the pressure of air flow was measured. From, the results obtained we were able to show the relation between Stanton and Reynolds number and compare it with the Dittus Boelter correlation, and found out that the values followed the correlation.

### References

[1] DEN208 - Assignment handout

[2] Cengel, Yunus A. (2003) Heat Transfer: A Practical Approach. 2nd ed. McGraw-Hill: New York.

[3] http://canteach.candu.org/library/20043905.pdf- accessed on 22nd Feb. 2009.

[4] DEN208 - Heat Transfer Assignment Handout.

[5]F P Incropera and D P DeWitt (2007) Introduction to Heat Transfer, 5th Ed. Wiley, Chapter 8.5.

[6] Fluid Mechanics by Douglas J F, Gasiorek J M, and Swaffield J A. Longman publishers. Pages 327-332.

[7]http://www.cartage.org.lb/en/themes/Sciences/Physics/Mechanics/FluidMechanics/RealFluids/Boun daryLayers/BoundaryLayers.htm-accessed on 22nd Feb. 2009