Heat Transfer Laboratory

Forced Convection (Liquid Flow)

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Table of Contents

Introduction ……………………………………………………………….………………………3

Description …………………………………………………………..……………………………3

Equipment ……………………………………………………………...…………………………7

Procedure …………………………………………………………………………………………7

Analysis……………………………………………………………………………………………8

Calculation …………………………………………………………………..……………………9

References ………………………………………………………………….……………………10

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Introduction

Convective heat transfer is the conduction of heat into a moving fluid. The lab will examine the

convection transfer problem for internal flow in a tube. An internal flow, such as a flow in a

pipe, is one for which the fluid is confined by a surface. Hence the boundary layer is unable to

develop without eventually being constrained. In our lab setup we have a very long tube, which

is sandwiched between two plates.

In this lab, the model of internal convection heat transfer is investigated experimentally

and laminar and turbulent theory will be investigated.

Description

When considering external flows, it is necessary to only understand whether the flow is laminar

or turbulent. However, for an internal flow we must also be concerned with the existence of

boundary layer (entrance) and fully developed regions.

Consider laminar flow in a circular tube of radius r0 (Figure 1), where fluid enters the

tube with a uniform velocity. We know that when the fluid makes contact with the surface,

viscous effects become important and a boundary layer develops with increasing x. Viscous

effects extend over the entire cross section and the velocity profile no longer changes with

increasing distance downstream. The flow, is then said to be fully developed.

In laminar fully developed flows the velocity profile is parabolic in a circular tube. For

turbulent flow, the profile is much flatter due to turbulent mixing in the radial direction.

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Figure 1. Laminar, hydrodynamic boundary layer development in a circular tube

To first understand whether the flow is laminar or turbulent we must calculate the Reynolds

number. The Reynolds number for flow in a circular tube is defined as:

ℜD≡ρum D

μ(1)

Where um is the mean fluid velocity over the tube cross section and D is the tube diameter. In a

fully developed flow, the critical Reynolds number corresponding to the onset of turbulence is

ℜD.C≈2300(2)

The mean velocity when multiplied by the fluid density ρ and the cross-sectional area of the tube

Ac provides the rate of mass flow through the tube. Hence;

m=ρ um Ac (3)

For steady, incompressible flow in a tube of uniform cross-sectional area, m and um are constants

independent of x. From Equations 1 and 3 it is evident that, for flow in a circular tube (

Ac=π D2 /4), the Reynolds number reduces to

ℜD=4 mπ D μ

(4)

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If fluid enters the tube of Figure 2 at a uniform temperature T(r,0) that is less than the surface

temperature, convection heat transfer occurs and a thermal boundary layer begins to develop.

Moreover, if the tube surface condition is fixed by imposing either a uniform temperature (Ts is

constant) or a uniform heat flux (q ' ' is constant), a thermally fully developed condition is

eventually reached.

Figure 2. Thermal boundary layer development in a heated circular tube.

The mean temperature Tm is a convenient reference temperature for internal flows, playing much

the same role as the free stream temperature T∞ for external flows. Accordingly, Newton’s law

of cooling may be expressed as

q ' ' s=h (T s−T m )(5)

Where h is the local convection heat transfer coefficient. However, there is an essential

difference between Tm and T∞.

Also, we know that in a circular tube characterized by uniform surface heat flux and laminar,

fully developed conditions, the Nusselt number is a constant, independent of ReD, Pr, and axial

location.

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NuD≡hDk

=4.36q' 's=constant (6)

For laminar, fully developed conditions with a constant surface temperature, the Nusselt number

may be shown to be of the form

NuD=hDk

=3.66T s=constant (7)

Note that in using Equation 6 or 7 to determine h, the thermal conductivity should be evaluated

at average value of Tm . If the flow is turbulent we may use either the Dittus-Boelter correlation

or the Gnielinski correlation (see the text). The effect of thermal boundary condition is much less

and we assume the heat transfer coefficient is approximately the same.

The overall objectives of this experiment are to:

1) Determine the experimental internal flow forced convection heat transfer

co-efficient for a heated tube.

2) Compare these results with results generated from appropriate correlations in your

text.

Equipment

The equipment for this lab is as follows:

1. A large liquid cooled heat sink (cold plate) that is made up of a long copper tube,

which makes ten passes in an aluminum plate. The tube is 5.79 m in length and

has an inner diameter of 7.75 mm.

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2. The plate is equipped with a large flexible heater, which covers one surface of the

plate. The heat source is connected to a power supply, which you control.

3. The plate is equipped with eight thermocouples for measuring surface temperature

at the mid-plane of the two plates. An additional two thermocouples measure inlet

and exit fluid temperature.

4. A digital thermocouple reader.

5. Two voltmeters to measure the power input to the heater.

6. A liquid flow meter with digital display to read volumetric flow rate.

7. An insulated box to minimize heat losses to the surroundings.

Procedure

To start the lab, you must ensure that all required equipment is switched on. This includes: the

power supply for the heater (maximum power 700 W). Also, turn on the flow meter, the

thermocouple display, and voltmeter.

Establish a flow near around 2 L/min and wait for steady state conditions to be reached. This

may take some time. Once steady state is reached, record all the temperatures using the

thermocouple reader. You can read two at a time. You will have to switch plugs. When doing

this, be careful as the wires are delicate for the thermocouples attached to the heated plate. Make

sure you record the inlet/outlet temperatures separate from the surface temperatures so you don’t

mix them up. Record the power input and the flow rate. You will repeat the procedure for flows

around 2, 3, 4, 5, and 6 L/min. When steady state is reached, record the necessary data. Record

your data in the Table below. Also measure the ambient room temperature.

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Flow

L/min

Voltage

V

Current

A

T1 T2 T3 T4 T5 T6 T7 T8 Tin Tout

Table 1. Data Measurements

Analysis

In your analysis, you can use the following assumptions:

1. Steady-state conditions

2. Uniform surface temperature

3. Negligible potential energy, kinetic energy, and flow work changes

4. Constant properties using mean bulk temperature

5. Adiabatic outer surfaces

Test the heat balance (conservation of energy) for each line of data, i.e. is the heater power input

equal to the enthalpy balance or heat removed by water which can be calculated by using the

following equation:

q=m Cp (T m,o−Tm ,i )(9)

Compare your theoretical results with those measured in the experiment and comment on any

sources of error. How good is the heat balance? Estimate the heat losses through the insulated

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box. The heated plate has approximately 50 mm of high density Styrofoam insulation on each

side. It has dimensions of L = 24 in and W = 12 in.

Calculation

If conditions are fully developed over the entire tube, the local convection coefficient and the

temperature difference between the pipe and water inside the pipe are independent of x. In this

experiment for purposes of our analysis, we may assume that the tube surface has a constant

average temperature close to that measured. Since the outer surface of the plate is insulated, the

rate at which energy is supplied must equal the rate at which it is convected to the water barring

significant losses through the insulation. But consider your heat balance carefully. If losses are

significant then account for them. In general we should have:

˙Power=qconv(10)

By considering the equation:

qconv=m cp (T o−T i )(12)

Also, a form of Newton’s law of cooling for the entire tube at fixed surface temperature is as

follows:

qconv=h A s∆T lmT s=constant (13)

Where As is the tube surface area (A s=P .L) and ∆T lm is the log mean temperature difference. In

fact, ∆T lm is the appropriate average of the temperature difference over the tube length:

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∆T lm≡∆T o−∆T i

ln (∆To

∆T i)

(14)

Where

∆T o=T s−T m,o(15)

∆T i=T s−Tm, i(16)

Combining the energy balance, Equation 12, with the rate equation, Equation 13, the average

convection coefficient is given by:

h=mC p

π DL(T o−T i)∆T lm

(17)

By considering different mass flow rate (m) in your experiments, calculate the average

convective heat transfer coefficient and compare it with the appropriate convection correlations

for an isothermal tube. In the case of turbulent flow use at least two correlations.

For turbulent flow create a plot with the measured data (as points – no line) and the correlations

(as lines – no points). You will be plotting Nu versus Re.

Comment on sources of error. In general the temperature can be measured with an accuracy of

0.1 C. How does this error impact the log mean temperature difference? The flow measurement

is normally accurate to within 2 percent. But you only read a single value which fluctuated 0.1-

0.2 L/min. How good are the measurements? Estimate the errors in measured heat transfer

coefficient and Reynolds number. What could be done to improve measurements? In your plot if

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the data have a consistent error with the correlations, this is due to a bias error. What parameter

has the greatest impact on this error. Why?

References

[1] Incropera, F. P., and DeWitt, D. P., Fundamentals of Heat and Mass Transfer,Fourth edition.,

John Wiley & Sons.

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