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:
𝑅𝑒𝐷 ≡
𝜌 𝑢𝑚 𝐷
(1)
𝜇
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
𝑅𝑒𝐷.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;
𝑚̇ = 𝜌 𝑢𝑚 𝐴𝑐
(3)
For steady, incompressible flow in a tube of uniform cross-sectional area, 𝑚̇ and um are constants
independent of x. From Equations 1 and 3 it is evident that, for flow in a circular tube (𝐴𝑐 =
𝜋𝐷2 /4), the Reynolds number reduces to
𝑅𝑒𝐷 =
4 𝑚̇
𝜋𝐷𝜇
(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(𝑇𝑠 − 𝑇𝑚 )
(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 ≡
ℎ𝐷
= 4.36
𝑘
𝑞 ′′ 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 =
ℎ𝐷
= 3.66
𝑘
𝑇𝑠 = 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
Voltage
L/min
V
Current
T1
T2
T3
T4
T5
T6
T7
T8
Tin
A
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 = 𝑚̇ 𝐶𝑝 (𝑇𝑚,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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Tout
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 = 𝑚̇𝑐𝑝 (𝑇𝑜 − 𝑇𝑖 )
(12)
Also, a form of Newton’s law of cooling for the entire tube at fixed surface temperature is as
follows:
𝑞𝑐𝑜𝑛𝑣 = ℎ̅ 𝐴𝑠 ∆𝑇𝑙𝑚
𝑇𝑠 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(13)
Where As is the tube surface area (𝐴𝑠 = 𝑃. 𝐿) and ∆𝑇𝑙𝑚 is the log mean temperature difference.
In fact, ∆𝑇𝑙𝑚 is the appropriate average of the temperature difference over the tube length:
∆𝑇𝑙𝑚 ≡
∆𝑇𝑜 − ∆𝑇𝑖
∆𝑇
ln ( ∆𝑇𝑜 )
𝑖
(14)
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Where
∆𝑇𝑜 = 𝑇𝑠 − 𝑇𝑚,𝑜
(15)
∆𝑇𝑖 = 𝑇𝑠 − 𝑇𝑚,𝑖
(16)
Combining the energy balance, Equation 12, with the rate equation, Equation 13, the average
convection coefficient is given by:
ℎ̅ =
𝑚̇𝐶𝑝 (𝑇𝑜 − 𝑇𝑖 )
𝜋 𝐷 𝐿 ∆𝑇𝑙𝑚
(17)
By considering different mass flow rate (𝑚̇) 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 0.10.2 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
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?
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References
[1] Incropera, F. P., and DeWitt, D. P., Fundamentals of Heat and Mass Transfer,Fourth edition.,
John Wiley & Sons.
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