forced convection heat transfer from a circular cylinder embedded in ...

FORCED CONVECTION HEAT TRANSFER FROM A
CIRCULAR CYLINDER EMBEDDED IN POROUS MEDIA
MIRLATIFI A.M., GHAZAL M.
Mechanical Engineering Department, EMU, Via Mersin 10, Turkey
ABSTRACT
In this study an experimental work was performed to examine the effect of porous media on
the heat transfer from a cylindrical heater in the case of steady-state forced convection.
Porous media consisted of Spherical glasses of diameter 0.6 cm and air was used as the
cooling fluid. The bulk temperature was approximated by the inlet temperature and
Properties of the air were found at the film temperature. Mean Nusselt number of a cylinder
is found both for clear fluid and porous media and the results were illustrated in
dimensionless form. It was clearly pointed out that porous media enhanced the heat transfer
rate compared to the clear fluid.
1. INTRODUCTION
The usage of porous media in engineering
applications is considerable; flows through
packed beds, filters, perforated plates, flow
distributors, and tube banks are only few
examples. In this work heat transfer from a
vertical cylinder placed in a saturated porous
medium was considered. It was assumed that
flows about the cylinder were driven by the
imposed pressure drop. Buoyancy effects
were neglected with a high accuracy. The
cylinder was subjected to different air flow
rates and different input power to create
constant heat fluxes with respect to times.
The surface of the cylinder was raised to a
higher temperature than the surrounding
medium and maintained at that temperature
thereafter; heat from the cylinder uniformly
diffuse in the radial direction. Analysis of
the influence of the porous medium on the
mean Nusselt number with different Peclet
number was performed in various heat
fluxes. For comprehension some results
were compared to those of the clear flow
case. The experiment shows a great
increase of heat transfer from the cylinder
when the porous medium was used.
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NOMENCLATURE
L
Diameter of the porous
Diameter of the cylinder (16 mm)
Darcy Number,
Permeability
Thermal conductivity of Spheres
Thermal conductivity of air
Thermal conductivity,
( )
Length of the bed
Prandtl number
Q Heat flux ( )
Heat flux per unit area ( )
Reynolds number
Inlet temperature
Surface temperature of the cylinder
Average velocity
Diffusivity
Porosity
Nu Nusselt number (( – ) )
P Pressure
Pe Peclet number,
Kinematic viscosity
ρ Density of air
µ Viscosity
3. EXPERIMENTAL METHOD
The experiment includes a bed of porous
media in an insulated duct. Inlet velocity
was measured by hot wire transducer and
pressure drop was measured before and
after the porous bed using a monometer. A
power supply was connected to a
cylindrical heater embedded in the porous
media to generate heat ( ). T-type
thermocouples were used to measure the
surface temperature of the cylinder ( ) as
well as the flow temperature in the
downstream, (figures 1 & 2). The porosity
( ) was found to be 0.388. Subsequently,
permeability was obtained by using
Kozeny-Carman equation:
( )
where is the diameter of the spheres, (6
mm). Thermal conductivity of the porous
material was taken as 1.3 W/m °C.
Permeability was found to be
and Darcy number was calculated
as .
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Figure 1 : Experimental Setup (Front
View)
each air flow five different heat fluxes
were supplied to the element. By changing
the heat flux and waiting for a while to
reach to a steady state surface temperature,
all temperatures were automatically
recorded by the means of a data acquisition
system. The whole process was done for
both the clear flow and flow in the porous
medium. To compare the heat transfer rate
for each medium, Nusselt number versus
Reynolds number were plotted for all the
cases.
4. RESULTS AND DISCUSSION
Figure 2 : Experimental Setup (top view)
The air flow was supplied by the use of a
suction type wind tunnel. The inlet
temperature, the surface temperature of the
cylindrical heater, and downstream
temperature in the porous media, were
recorded through the data acquisition
system. The experiment was carried out for
three different air velocities, which were
measured using the hot wire transducer.
Pressure drop before and after the porous
bed was measures using a manometer. For
Table 1 shows different heat fluxes and
their corresponding steady state surface
temperature for various numbers. The
difference between the surface temperature
of the cylindrical heater and inlet
temperature in the case of porous media is
much lower than the case of clear fluid.
For example, in the case of Re = 1800 and
Q=15.9 W the difference between the inlet
temperature and the surface temperature is
17.2 ºc in the porous medium case and
50.1 ºc in the case of clear flow. One of the
main aims of such setup is to enhance the
heat transfer and to decrease the
temperature of the element to the lowest
degree possible. Here, we can see the
difference in the heat transfer
effectiveness. That is, the temperature of
the surface of the cylinder recorded 35.7 ºc
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in the porous medium case and 70 ºc in the
case of clear flow. This advantage can be
implemented in heat exchangers; if our
element is to be considered as a part of
heat exchanger, the surface temperature of
the fin or the pipe is going to be less in the
case of porous medium than that of the
clear flow.
The pressure drop measured during the
experiment was found to be 667, 588, and
379 ( ) for Reynolds numbers 1800,
1600, and 1200 respectively.
Calculating the corresponding Darcy
velocities by equation:
velocities. Therefore, this equation was
discarded in the further calculations.
Instead, the velocities, measured using the
hot wire transducer, were taken into
account as the real velocities.
Figure 3 shows versus Renolds
number. The more is the heat flux the
higher is the mean Nusselt number, which
is nearly constant for different Reynolds
numbers. The results show conformity
with the similarity solution, which is
in the porous media, [1].
( )
resulted in 4.4, 3.98, and 2.56
, which
is twice as higher as the measured
Table 1: inlet, element’s surface temperature, and the difference between them, for different
Re and heat flux for both of the cases.
With porous medium
Clear flow
Re Q(W)
1800 15.9 35.7 18.6 17.2 71.0 20.9 50.1
1800 13.3 32.2 17.5 14.7 63.4 20.0 43.4
1800 11.4 30.6 18.0 12.5 58.0 20.0 38.0
1800 9.6 28.3 17.6 10.7 52.0 19.9 32.1
1800 8.0 26.6 17.8 8.8 47.3 19.7 27.6
1600 15.9 35.7 17.4 18.3 73.9 19.6 54.2
1600 13.3 33.2 17.3 15.9 66.4 19.6 46.7
1600 11.4 30.4 17.1 13.3 59.8 19.6 40.2
1600 9.6 28.4 17.2 11.2 53.3 19.7 33.7
1600 8.0 26.6 17.1 9.5 47.4 19.5 27.9
1200 15.9 39.1 17.1 22.0 74.0 19.2 54.8
1200 13.3 36.1 17.3 18.8 66.0 19.3 46.8
1200 11.4 33.1 17.0 16.1 59.3 19.3 40.0
1200 9.6 30.7 17.1 13.6 52.7 19.2 33.6
1200 8.0 28.2 17.0 11.2 46.9 19.2 27.7
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Variation of Nu in porous medium
using porous media for heat transfer
Nu/Pe^.5
14.4
14.2
14
13.8
13.6
q''=2.53 kw/m^2
q''=2.12 kw/m^2
q''=1.86 kw/m^2
q''=1.53 kw/m^2
q''=1.27 kw/m^2
problems is emphasized.
3.50
Comparison of Nu for both heat transfer in porous
medium and in a clear flow
13.4
3.00
13.2
2.50
13
1200 1610 1810
Re
Nu/pe^.5
2.00
1.50
1.00
With porous
Clear flow
Figure 3:
and heat fluxes
For the clear fluid
for various Reynolds
versus
Reynolds number is presented in figure 4.
In this case the results show conformity
with the similarity solution. That is, the
relation
exists in the clear fluid [2].
Figure 4: versus Reynolds
number in clear fluid.
0.50
0.00
Figure 5: Comparison of Nusselt number
for heat transfer in porous media and clear
fluid.
4. Conclusions
The steady state forced convection heat
transfer around the cylindrical heater
embedded in the porous media was
examined experimentally. The results
compared with the clear fluid case shows
that the porous media enhances the heat
transfer rate. The value of
porous media increases by increasing the
heat fluxes and it remains approximately
constant by increasing the Reynolds
number.
1200 1610 1800
Re
in
The comparison of Nusselt number is
plotted in figure 5. It is evident that porous
media enhance the heat transfer from the
embedded cylinder. Thus the superiority of
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5. REFERENCES
[1] D. A. Nield, A. Bejan, “Convection in
Porous Media”, Second Edition, Springer,
1998.
[2] Y. A. Cengel, Heat Transfer, A
Practical Approach”, McGraw-hill, 1998,
P. 367.
[3] L.B.Y. Aldabbagh, H.F. Manesh, and
A.A.Mohammad. Unsteady Natural
Convection inside a Porous Enclosure
Heated from the Side.
[4] S. Kımura, Transient forced and
natural convection heat transfer about a
vertical cylinder in a porous medium, In,.
J. Hear Mass Transfer. Vol. 32, No. 3, pp.
617-520, 1989.
[5] J. Thevenin, Transıent Forced
Convectıon Heat Transfer From A
Cırcular Cylınder Embedded In A Porous
Medıum, Int. Comm. Heat Mass Transfer,
Vol. 22, No. 4, Pp. 507-516, 1995.
[6] J. Thevenın And D. Sadaou, About
Enhancement Of Heat Transfer Over A
Cırcular Cylınder Embedded In A Porous
Medıum, International Communications İn
Heat And Mass Transfer, Vol. 22, No. 2,
pp. 295-304, 1995.
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