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Forced-Convective Heat Transfer To A Water-Cooled Pipe Lab

March 24 2003


1.0 Introduction

1.1 Background

In 1821, the thermoelectric effect was discovered which forms the basis of modern thermocouple technology. An electric current flows in a closed circuit of two dissimilar metals if their two junctions are at different temperatures. The voltage produced depends on the metals used and on the temperature relationship between the junctions. If the same temperature exists at the two junctions, the voltage produced at each junction cancel each other out and no current flows in the circuit. With different temperatures at each junction, different voltages are produced and current flows in the circuit. A thermocouple can therefore only measure temperature differences between the two junctions, a fact which dictates how a practical thermocouple can be utilised. [1]

In this lab, the Type T - Copper-Constantan thermocouple is used. This thermocouple is used less frequently in industry; its temperature range is limited to -200C up to +350C. It is however very useful in food, environmental and refrigeration applications. Tolerance class is superior to other base metal types and close tolerance versions are readily obtainable [1].


Figure  1: Cu-CuNi Thermocouple

1.2 Scope

1.   To determine how heat transfer rates from a fluid flowing inside a pipe to the tube wall can be measured and compared to results obtained from existing heat transfer correlations. [2]

2        To investigate the factors that can cause significant errors when thermocouples are used to measure gas temperatures. [2]

2.0 Data Analysis

2.1 Temperature and Velocity Profile

For this experiment temperature readings were taken from three prescribed locations along the pipe.  From this data, temperature profiles of the flows were created, as shown in figure 1. 


Figure  2: Temperature profile from pipe centerline at various pipe lengths

 It is apparent from figure 1 that the temperature profile gets smaller with increasing distance from the entry point, which is due to the continual heat transfer from warm air to the cold pipe.  Since the pipe wall is kept at a constant temperature the heat transfer rate is not constant, as the difference between the flow temperature and the wall temperature decreases.  The mechanism of this heat transfer is through convection and advection.  In convection heat transfer, energy is transferred due to random molecular motion (diffusion), and is also transferred by the bulk motion of the fluid over a surface.

 The temperature profile at the center of the pipe has a flat region, which shows that the flow is fully developed.  Moving towards the pipe wall, the flow temperature decreases, and as the profile edges closer to the pipe wall, the temperature decrease rapidly, until both the flow temperate and the wall temperature are the same.  The reason for the gradient is as follows.  When the flow enters the pipe, the fluid particles that come in contact with the surface achieve thermal equilibrium.  In turn these particles exchange energy with those in the adjoining fluid layer, and the temperature gradient develops.  The region of the fluid in which these temperature gradient exist is the thermal boundary layer [3]. 

 Figure 3 shows the velocity profile of the air flow at the exit of the pipe.  The velocity profile develops as it comes in contact with the surface, where viscous effects and shear stresses slow down the flow as it approaches the wall of the pipe, and stops it at the wall because of the no slip condition.  Since the profile peaks, and doesnt flatten out at the center, the velocity profile is fully developed.  Both the velocity profile and the temperature profile share the same curve shape


Figure  3: Velocity profile

2.2 Experimental Convective Heat Transfer

Using the mean temperature and the mass flow rate, at convective heat transfer between station 1 and station 2 was calculated based on experimental data.  Details of this calculation is presented in Appendix 1.  The convective heat transfer was calculated to be 819.42 Watts using the following equation: 

2.3 Theoretical Convective Heat Transfer

The theoretical value of the convective heat transfer from section 1 to section 2 can be calculated as briefed below and detailed in appendix 1.  The convective heat transfer obtained from this method was 931.55 Watts.  The correlation used to calculate this result is based on:



Using linear interpolation, property values based on an average temperature between Tm1 and Tm2, were obtained from standard heat transfer tables.  The Reynolds number was calculated using.  Since the Reynolds number was found to be greater than 20000 the following equation was used to calculate the Nusselt number  where was the friction factor.  Finally  was calculated and applied to the correlation to obtain a result.


2.4 Experimental versus Theoretical

The percent difference between the experimental and the theoretical results was 12.036%.  This difference between the two results can be due to the many assumptions made, such as constant properties, fully developed flow, and no convection from outer surface, and negligible radiation, which are not the case in reality.  Furthermore there could have been numerous experimental errors such as calibration and other human factors.

3.0 Thermocouple Error Analysis

Temperature measurements by thermocouples are subject to three major sources of error [2]:

1.         Calibration error of the thermocouple itself, which introduce a statistical uncertainty to the results.

2.         Conduction heat losses down the length of the thermocouple wires to the supporting structure.

3.         Radiation heat exchange from the thermocouple to the surroundings.


The conduction and radiation heat losses introduce a bias error to the results in the form of a temperature offset in one direction [2].   

The following analysis was conducted with the following general assumptions: steady state conditions; constant material properties, fully developed hydrodynamic and thermal conditions.


3.1 Error Analysis Short Thermocouple TCL1


Figure  4: Control volume for thermocouple junction

 The junction energy balance equation was developed from Figure 2:

    [Appendix 2]

The convection term of the energy balance was simplified to:

  [Appendix 2]

The junction was modelled as a sphere in external flow; hence the heat transfer coefficient was determined using the Whitaker correlation for spheres where (υ/υs) was assumed to be unity.

 [Appendix 2]

The effects of radiation heat loss were investigated by modelling the thermocouple junction and wire as small objects in a large isothermal enclosure.

The conduction term of the energy balance was determined by modelling each wire as finite length fins with prescribed tip temperatures. The fin equation was evaluated with htotal, which is the effective heat transfer coefficient including fin convection and radiation. Htotal was expressed using the average of the known tip temperature TCL1 and known base temperature TL [Appendix 2].

 The convection, radiation and conduction terms complete the junction energy balance. An iterative procedure was employed in Excel to determine the unknown value Tfl which exists within the conduction and convection terms. Tfl was determined to be 355C. Therefore the error was ∆T = 5C which is 2.3% higher than the correct temperature of 350C [Appendix 2].


3.2 Accuracy versus Immersion Length

Thermocouple can be used in surface and immersion applications depending on their construction. However, immersion types must be used carefully to avoid errors due to stem conduction.

When the effective length was reduced to 6mm, the measured temperature was 372C, which yields an error ∆T = 22C. This is 6.7% higher than the correct temperature of 350C. [Appendix 2]

This can be attributed to the fact as the effective length increase, decreases; the prescribed temperatures at each end of the fin remains the same but the distance x increases which lowers the temperature gradient. The lower temperature gradient results in lower conduction from the junction to the fin. This results in more accurate readings as the junction temperature is closer to the actual temperature.


3.3 Error Analysis Long Thermocouple TCL1

In examining the heat transfer of the long thermocouple at station one an energy balance was conducted using the thermocouple as the control volume as follows:

Where,  is heat transfer in W,  is surface area in m2,  is Stephan- Boltzman constant in W / m2*K4,  is emmisivity, and  is average heat transfer coefficient in W / m*K and  represents the indicated temperature in K.

Using the above equations the difference in temperature of the thermocouple (352.86 K) and the fluid (353.71 K) at the centreline was found to be 0.85 K. (Calculations in Appendix 3).  The difference is small because the Leff of this thermocouple is large, thus, the fin effect of the wires will be negligible and the temperature of thermocouple one will be similar to the fluid temperature. 


3.4 Error Analysis with Thin Radiation Shield

In determining the difference between the fluid temperature and thermocouple one when a thin radiation shield was introduced around the junction with emissivity of 0.1 two energy balances were considered.  The first energy balance was the same as in section 3.3 involving a control volume around thermocouple one.  The next energy balance was conducted using the radiation shield as the control volume as indicated:


Where,  is heat transfer in W,  is surface area in m2,  is Stephan- Boltzman constant in W / m2K4,  is emmisivity, and  is average heat transfer coefficient in W / m*K and  represents the indicated temperature in K.

The two equations from the energy balance with two unknowns were solved using an iterative technique in excel, the calculations are presented in the Appendix 3.  The fluid temperature was found to be 352.88 K and the difference between the fluid temperature and thermocouple one was 0.02 K.  The difference was even smaller when a radiation shield was present when compared to section 3.3 without a radiation shield.    

3.5 Error Analysis - TCL1  = 1000 K with and w/o Radiation Shield

The analysis in section 3.3 and 3.4 were repeated for the same conditions with only one change.  Thermocouple one temperature was assumed to be 1000 K in place of the measured value of 352.86 K.  The calculations were identical to the procedure for the above questions and are shown in Appendix 3.

It is shown that without a radiation shield the temperature difference between the fluid and the 1000 K thermocouple was 61.67 K.  With a radiation shield the temperature difference decreased to 26 K.  These errors were higher when compared to the lower temperature value of thermocouple one (352.86 K).  This is because at higher temperatures there are higher radiation losses which are not accounted for from the thermocouple.  With a radiation shield the difference decreased indicating that a radiation shield will reduce the error.  Thus, at higher temperatures it is important to control the error using a radiation shield. 


4.0 Conclusions

This lab demonstrated the various factors affecting convection through a pipe.  From the data analysis it was demonstrated that the temperature profile and the velocity profile had the same shape, and that the slope of the temperature profile was indicative of the heat transfer.  Calculations were done to study the different between the experimental and the theoretical results.  The difference between these values was due to the assumptions and the errors.  It was found that conduction and radiation heat losses introduced a bias in the error.  It was also presented that as the length of the thermocouple increased the temperature gradient decreased which increased the accuracy of the thermocouple.  The affect of radiation on the thermocouple was found to be negligible at low temperatures, but becomes a contributing factor as the temperature is increased.

5.0 References


1                    Thermocouple Theory and Practice, http://www.w-dhave.inet.co.th/Thermocouple.html, 2003

2                    J. L. Wright, ME 3B Lab Manual, University of Waterloo, Waterloo, 2003.

3                    F. P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer 5th Edition, John Wiley & Sons, Inc, New York, 2002.


Appendix 1: Data Analysis

Experimental Calculation of Convective Heat Transfer

The heat transfer from the hot air stream to the cold pipe, between station one and station 2 can be calculated from the following  simple relationship:


Theoretical Calculation of Convective Heat Transfer

 Calculation of a more accurate heat transfer coefficient as detailed in the 3B lab manual is as follows



Appendix 2: Thermocouple Error Analysis 1-2


Thermocouple Error Analysis Question 1


Energy Balance at Thermocouple Junction:





Energy Balance - Convection:



Air properties at , geometry of junction (Interpolation not required).


Since Re and Pr effectively falls within the acceptable limits of the Whitaker correlation, its use is permitted.


Energy Balance - Radiation:



Energy Balance Conduction:


Determine h rad:



Determine hconv:





Since Re and Pr effectively falls within the acceptable limits of the above correlation, its use is permitted.