Write a lab report with: 1)Abstract2)introduction 3)Experiment /Procedures4)Discussion and Results5)Conclusionmust have pictures of eqiupment used and equations in the sections 3 and 4Lab handout is attached along with the powerpoint and data..the lab conducted is in the powerpoint in a YouTube link.THERMAL/FLUID SCIENCE LAB

MEEG-423

Evaluation of Heat Transfer Coefficient of a Row of Tubes in Forced Convection

Equipment: HT10XC Heat Transfer Service Unit, HT19 Free and Force Convection Heat

Transfer Module, Computer.

Introduction

A heated surface dissipates heat primarily through a process called convection. Air in

contact with a hot surface is heated by the surface and rises due to reduction in density.

The heated air is replaced by cooler air which in turn is heated by the surface and rises.

This process is called free convection.

In free convection, the heat transfer rate from the surface is limited by the small

movements of air generated by the heat. More heat is transferred if the air velocity is

increased over the heated surface. This process of assisting the movement of air over the

heated surface is called forced convection. Therefore, a heated surface experiencing forced

convection will have a lower surface temperature than that of the same surface in free

convection for the same power input.

Theory

In the study of thermodynamics, the average heat transfer coefficient, h, is used in

calculating the convection heat transfer between a moving fluid and a solid. Knowledge of

h is necessary for heat transfer design and the heat transfer coefficient is critical for

designing and developing better flow process control resulting in reduced energy

consumption and enhanced energy conservation. Heat transfer through a bank of tubes has

several applications in industry and can be used in many applications from the design of

heat exchangers to the study of forced convection over pipes [1].

When tube banks are used in heat exchangers, two arrangements of the tubes, aligned and

staggered, can be considered as shown in Figure 1 and there are many correlations that can

be used to predict the heat transfer coefficient from cross flow over a bank of tubes in both

Figure 1: Arrangements of the tubes (a) in-line arrangement, (b) staggered arrangement

forced and natural convection situations. The correlation proposed by Zukaukas [2] will be

used in this analysis. In this correlation, dimensionless parameters, such as Nusselt number

(Nu), Reynold’s number (Re) and Prandtl number (Pr), for different geometries, can be

used to calculate values of h.

The arrangement of the tubes in the HT-19 pinned heater is staggered in the direction of

flow as shown in Figure 1b. The arrangement of the tubes is characterized by a transverse

pitch ST, a longitudinal pitch SL and a diagonal pitch SD, where SD can be determined from

√

= + ( )

For the HT-19, these values are ST = 28mm, SL = 17mm and SD = 22mm respectively.

In Zukaukas correlation, the Nusselt number for cross flow over a bank of tubes is

expressed as

=

= ( / ) .

where the values of the constants C, m and n depends on the Reynolds number, h is the

average heat transfer coefficient, D the diameter of one tube and k the thermal

conductivity of the flow. Values of the constants C, m, and n for the staggered arrangement

is given in the Table 1 below.

Table 1 represents Nusselt number correlations for crossflow over tube banks with more

than 16 rows (Nr). Since the HT-19 has less than 16 rows, a correction factor needs to be

applied to the Nusselt number of Equation 2. Thus

Nu = f Nu (Nr < 16)
3
For the HT-19 this correction factor is f=0.93.
Table 1: Average Nusselt Number Correlation [2]
Range of Re
Correlation
.
0 – 500
. . ( / ) .
500 – 1000
. . . ( / ) .
1000 – 2x105
. ( / ) . . . ( / ) .
2x105 – 2x106
. ( / ) . . . ( / ) .
The Reynolds number can be determined from
=
where and are the density and dynamic viscosity of the fluid (air) and VMAX is the
maximum flow velocity respectively.
The maximum average velocity, VMAX, between tubes is used in calculating Re (Equation 4).
For the staggered arrangement, if
>

+

Then

=

−

If not, then

=

( − )

In Equations 2 and 4 above, all properties are to be evaluated at the arithmetic mean of the

inlet and exit temperatures of the fluid (T1 + T2)/2, except PrS which is to be evaluated at

the surface temperature TS (the average temperature of T3 – T6). Table 2 below can be used

to obtain these properties.

Table 2: Properties of Air at 1atm Pressure

Heat Transfer Rate

Once the heat transfer coefficient is determined from the above analysis, the heat transfer

rate can be numerically obtained from application of Newtons Law of cooling as

̇ = ∆

where AS is the heat transfer surface area and ∆ is called the mean logarithmic

temperature difference. These values can be determined from

AS = DLPN

9

where LP is the length of the tubes (82mm), D the tube diameter (12mm) and N the number

of tubes (17) in the heater and

( − ) − ( − )

∆ =

[( − )/( − )]

Experimental Procedure

Place the pinned heater into the duct of the HT-19 and connect the HT-19 to the HT-10XC

service unit as shown in Figure 2. The heater is fitted with thermocouples that can be read

from the HT10XC console. The HT10XC provides the necessary measurement facilities

and power control for the module.

Set the heater power control to 60 watts and allow sufficient time to achieve steady state

conditions before noting and recording the heated plate temperature (T3). Also note and

record the upstream air temperature T1 and the temperatures T4, T5 and T6 of the pinned

heater. The distance of the three access holes on the pinner heater are given in Table 3

below.

Set the fan speed control to give air speed Ua of 1m/s using the air velocity sensor. When

the temperatures are stable (monitor the temperatures on the PC display screen), record

and save the displayed data. Repeat the procedure at 1.5 and 2.0 m/s.

Table 3: Thermocouple Identification

T1

Input air temperature in duct

T2

Output air temperature in duct

T3

Heater temperature

T4

Surface temperature at root of pin

T5

Surface temperature at mid height of pin

T6

Surface temperature at tip of pin

Distance of nearest hole in pinned heater 10mm

Distance of middle hole in pinned heater 36mm

Distance of farthest hole in pinned heater 62mm

Figure 2; Armfield HT-19 Convective Heat Transfer Module

Results

Plot graphs of surface temperature against distance from the back plate of the heater at the

various flow velocities and comment on your results.

Determine the average heat transfer coefficient h and the heat transfer rate Q using the

properties in the attached table and compare your result to the actual power input applied

to the pinned heater. Address any differences in results and comment on your findings.

References

1. Manohar, K. and Ramroop, K.,“A Comparison of Correlations for Heat Transfer

from Inclined Pipes,” International Journal of Engineering (IJE), Volume: 4, Issue:

4, 268.

2. Zukauskas, A. “Heat Transfer from Tubes in Crossflow,” Advances in Heat

Transfer, 8:87-159, 1987.

CONVECTIVE HEAT TRANSFER

FREE & FORCED CONVECTION OVER A BANK OF TUBES

Convection

Convective heat transfer, often referred to simply as convection,

is the transfer of heat from one place to another by the

movement of fluids. Occurs by the mixing of one portion of the

fluid with another portion due to gross movements of the mass

of fluid.

Can be subdivided into free convection and forced convection.

Natural or Free Convection:

Caused by buoyancy forces due to density differences caused

by temperature variations in the fluid. At heating the

density change in the boundary layer will cause the fluid to

rise and be replaced by cooler fluid that also will heat and

rise.

Forced or Assisted Convection:

Forced convection occurs when a fluid flow is induced by an

external force, such as a pump or fan.

Free and Forced Convection

Air in contact with the hot surface is heated by the surface

and rises due to a reduction in density. The heated air is

replaced by cooler air which is in turn heated by the surface

and rises.

More heat is transferred if the air velocity is increased over

the heated surface. This process of assisting the movement of

air over the heated surface is called forced convection.

Therefore, a heated surface experiencing forced convection

will have a lower surface temperature than that of the same

surface in free convection for the same power input.

Heat transfer to or from

a bank (or bundle) of

tubes in cross flow

• Flow around the tubes in the first

row of a tube bank is like that for a

single (isolated) cylinder in cross

flow.

• Correspondingly, the heat transfer

coefficient for a tube in the first row

is approximately equal to that for a

single tube in cross flow.

• However, we wish to know the

average heat transfer coefficient for

the entire tube bank.

For tube banks, two arrangements of the tubes can

be considered

in-line arrangement

staggered arrangement

Zukaukas Correlation

Zukaukas proposed the following equation for the cross flow

of air over a bank or bundle of tubes.

=

= Τ

Range of Re

0.25

Correlation

0 – 500

. . . /

.

500 – 1000

. . . /

.

1000 – 2×105

. /

2×105 – 2×106

. /

.

. . /

.

. . /

.

.

All properties above except Prs (Prandtl Number at the surface

temperature) are to be evaluated at the arithmetic mean of the

fluid inlet (Ti=T1) and outlet (To = T2) temperatures.

The need to evaluate fluid properties at the arithmetic mean

of the inlet and outlet temperatures is dictated by the fact

that the fluid temperature will decrease or increase,

respectively, due to heat transfer to or from the tubes.

If the change of the mean fluid temperature, │Ti -To│, is

large, significant error could result from the evaluation of

the properties at the inlet temperature.

=

For the staggered configuration, the maximum velocity may

occur at either the transverse plane AT or the diagonal plane

AD.

It will occur at AD if the rows are spaced such that

2( − ) < ( − )
Hence Vmax occurs at AD if
=
+
<
+
in which case it is given by
= −
If Vmax occurs at AT then it may be computed from
=
−
If:
>

:

+

2

=

−

: =

2 −

Heat Transfer Rate

Newton’s law of cooling

ሶ = ∆

AS = DLPN

− 1 − − 2

∆ =

− 2 Τ − 1

Since the fluid may experience a large change in temperature

as it moves through the tube bank, the heat transfer rate could

be significantly overpredicted by using ΔT= Ts – T∞ as the

temperature difference in Newton’s law of cooling.

As the fluid moves through the bank, its temperature approaches

Ts and │ΔT│ decreases. Thus, the appropriate form of ΔT is

shown to be a log-mean temperature difference.

Experimental Apparatus

In free convection the heat transfer rate from the surface is

limited by the small movements of air generated by this

heat.

More heat can be transferred if the air velocity is increased

over the heated surface.

This process of assisting the movement of air over the heated

surface is called Forced Convection.

Therefore a heated surface experiencing forced convection,

for the same power input, will have a lower surface

temperature than that of the same surface in free convection.

Experiment

LAB #4 DATA

Air

Upstream Output Heater

Pin Root

Mid Pin

Pin Tip

Heater Heater Heater

Velocity

Temp

Temp

Temp Surface Temp Surface Temp Surface Temp Voltage Current Power

Ua

T1

T2

T3

T4

T5

T6

V

I

P

[m/s]

[°C]

[°C]

[°C]

[°C]

[°C]

[°C]

[V]

[A]

[W]

0.0

1.0

1.5

2.0

27.5

27.5

28.5

29.1

38.5

40.4

37.8

35.8

92.2

76.6

65.0

57.8

88.5

67.6

57.6

51.3

88.2

66.8

56.4

49.8

84.7

61.5

52.3

46.4

13.1

13.1

13.1

13.2

4.57

4.58

4.58

4.58

60.09

60.15

60.21

60.33

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