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INVESTIGATING THE EFFECT OF HEATING METHOD ON
POOL BOILING HEAT TRANSFER
Satish G. Kandlikar, Professor, Mauro Lombardo, Graduate Student, and Surendra K. Gupta, Professor
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY, USA
Phone: (716) 475-6728; Fax: (716) 475-7710
E-mail: [email protected]
ABSTRACT
Pool boiling experiments are generally conducted with electrically heated surfaces in laboratories to
obtain the heat transfer coefficient data. In many process applications however, a fluid stream is employed
as the heating medium. The heat transfer data generated with the electrically heated test sections therefore
raises the question of their applicability to practical equipment design. Similar concerns have been
expressed in literature for flow boiling heat transfer.
The present investigation focuses on generating experimental data using two identical stainless steel
tubes in pool boiling with water at atmospheric pressure. The tubes are made of stainless steel, 3.2 mm outer
diameter, 0.1 mm wall thickness, and 152 mm long. One of the tubes is heated electrically using direct current
from a power supply, while the other is heated by circulating pure ethylene glycol. Under comparable
conditions, the heat transfer coefficients are seen to be considerably different for the two heating methods.
A numerical analysis is also performed in the region of the wall in the vicinity of a bubble for both heating
methods. The numerical analysis shows the temperature profiles of the surface under and around a bubble
being considerably different for the two heating methods. The mechanism causing a localized reduction of
temperature in the wall underneath the bubble seems to be the primary reason for the differences in the heat
transfer coefficients for the two heating methods.
1. INTRODUCTION
Boiling mechanism offers a very efficient mode of
heat transfer involving a change of phase. The
presence of nucleating bubbles on the heating surface
leads to dramatic increases in the heat transfer rates.
The enhancement is caused by a combination of
mechanisms, including micro-layer evaporation,
increased micro-convection in the regions surrounding
the bubble, vapor liquid exchange mechanisms, etc.
The heat flux supplied by the surface is taken as the
convection heat transfer in the uninfluenced region far
from the nucleation site and the convective and latent
heat transport in the region covered by bubbles.
The effects of the heating methods on the pool
boiling performance is the focal point of this study. In
the present study, experimental data is obtained with
the two heating methods and a numerical work is
presented to identify the mechanisms responsible for
the differences.
2. LITERATURE SURVEY
In the past, some researchers have indicated that
the heating method could affect the heat transfer rate
in pool boiling. However, previous experimental work
that demonstrates a direct comparison on the same test
surface is rather limited. One experimental study by
Khanpara, Bergles, and Pate (1987) performed a
comparison of the in-tube evaporation of R-113 in
electrically heated and fluid-heated smooth and
microfin tubes. The results of this study focus mostly
on the heat transfer coefficients between the two
heating methods. The data was comparable for both
sets of tubes under certain sets of conditions of low
and medium mass velocities. However, the electrically
heated smooth tube at a high mass velocity had higher
local heat transfer coefficients that were about 20 to
40% higher than the average heat transfer coefficients
for the fluid heated tubes.
Another theoretical study conducted by Unal and
Pasamehmetoglu (1994) predicted some very
interesting characteristics. First, the nucleate pool
boiling curves for a fluid heated (constant temperature)
and electrically heated (constant heat flux) conditions
are different. Second, the position or magnitude of the
nucleate pool boiling curves depends on the thickness
of the heater. Third, the difference between the
constant temperature and constant heat flux boundary
conditions becomes smaller as the heater thickness is
increased. The results of this work were further
investigated by Kedzierski (1995) by conducting
experiments of pool boiling effects of R-123 on four
commercial enhanced surfaces. Kedzierski showed
much more extensively, the differences between
electrically and fluid heating methods. His work
provided results of the fluid heating condition
resulting in heat fluxes that are as much as 32 %
greater than those obtained by an electrically heated
surface.
From Kedzierski’s study, it has been
speculated that an interaction between the fluctuating
wall temperature and the fixed electrical heat flux
induces a higher degree of superheated liquid on the
electrically heated surface than on the fluid heated
surface. However, the heating boundary condition
may affect re-entrant and natural cavity surfaces
differently.
3. OBJECTIVES OF THE PRESENT WORK
The objectives of the experimental work is to
study the pool boiling heat transfer characteristics of
pool boiling of de-ionized water over two identical
stainless steel tubes which are heated by the two
methods respectively. The two methods employ a
fluid heated and an electrically heated test sections.
The fluid heated method uses pure ethylene-glycol
circulating through the tube. The electrically heated
method uses a power supply generating very high
amperes at low voltages. Using the same dimensional
and comparative parameters between the two methods,
the heat transfer characteristics will be compared. A
numerical analysis has been developed to complement
the experimental work. This numerical program uses a
finite difference method to develop a temperature
distribution in a radial plate element with a bubble on
the heating element. The results of the numerical work
will be used to identify the mechanisms responsible for
the differences due to the two heating methods.
4.
THEORETICAL MODELING
Mathematical Modeling
A steady-state bubble-plate system of radius R
and thickness t is modeled in a cylindrical coordinate
system with r-θ lying in the bottom surface of the
plate, and the z-axis passing through the center of the
circular bubble. The steady state heat conduction
equation for the plate in cylindrical coordinates is
1 ∂  ∂T  1 ∂  ∂T  ∂  ∂T 
 kr  +
k  +  k  + q& = 0 (1)
r ∂r  ∂r  r 2 ∂θ  ∂θ  ∂z  ∂z 
where k is the thermal conductivity and
q& is the heat
generated per unit volume per time. The temperature
T(r, θ, z) can be normalized with respect to a reference
temperature Tref such that u = T/Tref. Cylindrical
symmetry (i.e., ∂T/∂θ = 0) and isotropic k reduces (1) to
∂ 2 u 1 ∂u ∂ 2u
q&
+
+ 2 +
=0
2
r ∂r ∂ z
kTref
∂r
(2)
where the dimensionless temperature is given by u
= u(r, z) over the domain (0 ≤ r ≤ R; 0 ≤ z ≤ t). The
domain is discretized with grid lines spaced equally at
∆r = ∆z = δ. Replacing the partial derivatives in eq. (2)
by their appropriate central-difference O(δ2)
equivalents, it becomes
 ui +1, j − 2ui , j + ui − 1, j   ui +1, j − ui −1, j 

+


 

δ2
2iδ 2
 ui , j +1 − 2ui , j + ui , j −1 
q&
+
=0
+
2

 kTref
δ
(3)
where u i,j is the dimensionless temperature at the
node (ri, zj ).
ri = i δ, i = 0, K, n;
nδ = R
z j = jδ , j = 0,K , m; mδ = t
(4)
Figure 1 The heating methods for a plate element under a bubble of a circular tube in boiling conditions.
Due to the cylindrical symmetry, ∂u/∂r = 0 at r = 0
(left boundary) and at r = R (right boundary)
respectively.
At the top surface z = t, the boundary condition is
given by
∂u
h
= − bubble ( u − utop );
0 ≤ r ≤ Rbubble
∂z
k
∂u
h
= − ( u − utop );
rbubble ≤ r ≤ R
∂z
k
(5)
where Rbubble is the radius of the bubble, h bubble is the
heat transfer coefficient between the plate and the
region covered by the bubble, h is the heat transfer
coefficient between the plate surface not covered by
the bubble and the fluid, and u top is the dimensionless
temperature of the fluid at the top surface.
When the plate is heated by the hot fluid at
temperature u bottom at the bottom surface, the boundary
condition at z = 0 is given by
∂u
h
= − ( ubottom − u);
∂z
k
time
0≤r≤ R
(6)
Thus, the heat generated per unit volume per unit
q& can be calculated from
R
q& =
hTref ∫ ( u bottom − u )rdr
0
R
(7)
t ∫ rdr
0
Numerical Techniques
The difference equation (3) when prescribed at
each node where u is not explicitly known, and
coupled with appropriate boundary conditions
represents a linear system of algebraic equations. The
linear system is solved in double precision using overrelaxation method where the relaxation parameter ω ≥ 1
is re-computed after every 50 iterations. The solution is
validated by comparing it to that obtained by reducing
the grid size δ by a factor of two. In equation (7), the
integral in the numerator is numerically evaluated
using Simpson’s one-third rule to compute q& . This q&
value is used for the case when the plate is being
electrically heated.
Program Input Structure
The program has an input structure in which
parameters can be varied between the two cases as
seen in Figure 1. The input parameters that can be
varied are as followed:
• Dimensions − t plate , rout ,
rbubble
rout
• Pr operties − material conduction ( k )
h
• Boundary Conditions − htop , hbottom , bubble
htop
• Methods Conditions − Ttop , Tbottom , q&
• NumericalParameters − δ grid , ε convergence
Upon inputting the parameters, the program will
first create a temperature distribution for the plate
element under fluid heating conditions. The program
will then calculate the total heat flux from the fluid
case. The next stage uses that heat generation and
calculates the temperature distribution for the
electrically heated plate element. The program outputs
from both heating methods are calculated in one cycle
run and the computing time on a VMS V6.2 system is
1-3 minutes depending on the grid size. The program
was validated, by comparing the numerical results with
the analytical solution, using a radial element with two
different convection coefficients at the top and bottom
surfaces.
First, both surface temperatures were
calculated along with the heat flux. Second, the
electric method case was simulated with the bottom
surface insulated and the top surface exposed to water.
Using the heat generation from the fluid case, the
temperatures at the top surface were calculated along
with those at the insulated surface. The temperatures
at the top and bottom surfaces compared exactly with
the analytical solutions for each of the two heating
methods.
5.
EXPERIMENTAL SETUP
The experimental setup was to be constructed in
such a way that a valid comparison could be made
between the heating methods using the same test
section. The fluid heated system had to accommodate
tube dimensions to achieve a heat flux ranging from 104
to 106 W/m2 with a controllable temperature drop within
1.0 degree Celsius. For the electrically heated system,
the tube dimensions must produce an acceptable
electrical resistance. Numerous dimensions were
analyzed by varying the flow rates, temperature drops,
and heat flux values to give a set of optimal
parameters. The test section was a stainless steel tube
that was cut to a working length of 177.8 mm , but the
actual length of the tube exposed to the bath is 152.4
mm. The tube has an outer diameter of 3.2 mm, with a
wall thickness of .1 mm.
The tank holding the de-ionized water was a clear,
poly-carbonate tank with a maximum temperature rating
of 135 °C. The outside dimensions of the tank were
21.6 cm x 24.1 cm x 39.4 cm. The tank was placed inside
another plastic tank which was insulated on the inner
walls with fiberglass insulation. The purpose of the
insulation was to minimize the heat loss from the deionized bath to the surrounding. An immersible
auxiliary heater was then mounted on the tank, keeping
the de-ionized water near its saturation temperature
during the experiments.
Fluid Heated Setup
Figure 2A shows the fluid heated setup which
uses pure ethylene glycol as the heating medium. The
heating fluid’s temperature was controlled by the
circulation tank and the flow rate was monitored by the
flow meters. The heating fluid flows from the
circulation tank through a 12.7 mm inner diameter
insulated rubber hose. The hose ran through an
auxiliary pump to overcome the pressure drop in the
test section. The heating fluid then ran through the
fittings on the insulating tank and then into the
stainless steel tube test section. Figure 2B shows a
detailed cross-section of the fluid heated test section.
Both ends of the test section are connected to a
phenolic bushing and sealed with a high temperature
epoxy. The rubber hose clamps onto the bushings on
both ends to ensure a proper seal. A thermocouple
was placed at each end of the tube to give inlet and
outlet temperatures. At the outlet of the tube, the hose
runs out of the tank and back to the circulation tank in
which the heating fluid gets re-circulated into the
system.
Electrically Heated Setup
The electrical test setup uses the same insulated
water tank as in the fluid heated apparatus. However,
the only difference was that just a power supply and
thermocouples were needed. The immersible auxiliary
heater was used to bring the water bath to its
saturation temperature. Figure 3 shows a detailed
cross-section of the electrically heated test section. A
wooden rod was fabricated to fit closely inside of the
tube with grooves milled into the rod. The grooves
hold the thermocouples against the inner wall of the
steel tube. The two thermocouples on each side were
placed at 3.1 and 6.1 cm from the edge of the steel tube.
Also shown in Fig. 3 are the copper clamps which are
tightly fitted over the stainless steel tube and sealed
with an epoxy. The clamps provided the connections
for the power supply leads.
Figure 2A Fluid Heated Experimental Apparatus
Figure 2B Steel Tube Test Section From The Fluid Heated Apparatus
Figure 3 Steel Tube Test Section For The Electrically Heated Apparatus
6.
RESULTS AND DISCUSSION
60
q"fluid
50
q" (kW/m2°C)
q"electric
40
30
20
10
0
1
2
3
4
5
Wall Superheat (°C)
Figure 4 Comparison of the experimental heat flux
between the fluid and electrically heated
method.
The results obtained in this investigation as seen
in Fig. 4 are in agreement with the pool boiling results
reported by Kedzierski (1995) with R-123 as the
working fluid. They obtained similar results with
enhanced GEWA-T or “T-fin” surfaces. From these
results, it can be concluded that for the range of
parameters tested, the electrically heated method
yields a lower heat transfer coefficient compared to the
fluid heated method.
Another observation made during the experiments
was that the nucleate boiling was initiated as the wall
temperature exceeded the saturation temperature. The
absence of any hysteresis effect may be attributed to
the dissolved gases present in the water. Although
the system was allowed to boil for a couple of hours
prior to experiments, the water bath was open to
atmosphere thereby allowing air to dissolve in it.
In order to find the reasons for the differences in
the thermal performance with the two heating methods,
a numerical work was undertaken as described in the
earlier section. A bubble of radius rbub was considered.
The region of the plate affected by this bubble was
assumed to be twice the bubble radius. The heat
transfer coefficient under the bubble was assumed to
be a factor of n times its value in the surrounding
region. The numerical analysis was performed under
the following conditions.
Ttop =100 C, Tbottom =120 C, rout =2 mm, t=.12 mm,
k=13.4 W/mK, brub /rout=.5, qgen =5.65e+9 W/m3
htop=70,000 W/m2 K, hbottom =100,000 W/m2K
The purpose of the numerical analysis is to
identify the differences in the temperature profile in the
wall adjacent to a growing bubble. Although the
boiling process is a transient one, the present analysis
is expected to give a qualitative nature of the
temperature distribution under the two cases.
110
109
108
107
106
105
104
103
102
101
100
Fluid
Temperature (°C)
Figure 4 shows the results of the experiments
conducted with the two heating methods. The range
of the wall superheat was limited by the highest
temperature that could be employed in the constant
temperature bath employing ethylene glycol as the
heating fluid.
The results for the fluid heating method are shown
by the diamond symbols and electrically heated
method are shown by the square symbols in Fig. 4. It
can be seen that over the entire range, the electrically
heated test section yielded a lower heat transfer rate
compared to the fluid heated test section.
n=6
n= n=
n
n
=
0
n=
6
0.0005
0.001
0.0015
Plate Radius
0.002
Figure 5 Numerical comparison of the temperature
profiles between heating methods varying the
convection coefficient ratio ‘n’.
Figure 5 shows the temperature profile for the
above conditions for different values of the parameter
n (ratio of heat transfer coefficients under the bubble
and the surrounding region). The solid line represent
the fluid heated case while the dashed lines are for the
electrically heated case. In both cases, the overall heat
flux is the same.
The temperature profiles in Fig. 5 indicate that
the temperature of the surface under the bubble is
lower for the electrically heated case, while in the outer
region, the fluid heated case yielded lower temperature
values. For the electrically heated case, as the ratio n
decreases, the results come closer to the fluid heated
case in the outer region.
Figure 6A and 6B represent the top surface and
adiabatic surface temperatures for an electrical case
respectively. A constant heat generation was applied
and the thickness of the plate was varied at 008, 012,
and 020 mm. The following parameters were used:
Ttop=100 C, Tbottom =0 C, rout =2 mm, t=varied,
k=13.4 W/mK, brub /rout =.5, qgen =5.65e+9 W/m3
htop=70,000 W/m2 K, hbottom =0 W/m2 K
130
0.00008
Temperature °C
125
0.00012
0.0002
120
115
110
105
100
0
0.0005
0.001
0.0015
0.002
Plate Radius (meters)
Temperature (°C)
Figure 6A
145
140
135
130
125
120
115
110
105
100
Numerical comparison of the plate’s top
surface temperatures with a constant heat
generation with varied ‘t’.
0.00008
0.00012
0.0002
0
0.0005
0.001
0.0015
Plate Radius (meters)
0.002
Figure 6B Numerical comparison of the plate’s bottom
insulated surface temperatures with a constant
heat generation with varied ‘t’.
Both figures, Figs. 6A and 6B, indicate that the
plate height or wall thickness have no significant effect
at the top convective surface. However, the adiabatic
surface reaches a higher wall temperature as the plate
thickness is increased. The inflection point of the
profiles still represent where the bubble’s radius ends
from the center line of the plate. In a practical
experimental setup with electrically heated unit, the
temperature is measured at the adiabatic surface. As
can be seen, as the heater thickness increases, the
temperature profile gets flatter in the plate and
approaches the fluid heated case with increasing
heater thickness. In other words, the differences
between the two heating methods will become
significant for thin heaters, whereas thick heaters will
exhibit similar behavior to the fluid heated method.
A further explanation for the mechanism
responsible for the differences in the two methods can
be offered as follows. In the electrically heated
method, the temperature in the surrounding region is
seen to be higher. Under the boiling condition, the
area occupied by a bubble is quite small at lower heat
fluxes. The temperature measurement at the adiabatic
surface would be more representative of the nonboiling region of the heater surface which is at a higher
temperature than the corresponding region in the fluid
heated case. This would result in a lower value of the
heat transfer coefficient for the electrically heated case.
This would also imply that the differences between the
two methods would be smaller at higher heat fluxes
when large regions of the heater would be occupied by
bubbles.
The analysis and discussion presented in this
section are based on a steady-state heat conduction
model in the heater plate in the vicinity of a bubble.
Using the results, it is possible to qualitatively present
a mechanistic description for the effect of the heating
methods on the boiling heat transfer.
Further
refinements are recommended in the future work to
incorporate the transient heat conduction due to the
cyclic nature of bubble growth and departure. The
high frequencies of bubbles may however justify the
use of a steady state model as applied in the present
work.
7.
CONCLUSIONS
An experimental study is conducted to investigate
the effects of fluid heating and electrical heating on the
pool boiling heat transfer. In order to explain the
mechanism responsible for the differences in the two
methods, a numerical analysis is conducted in the
vicinity of a bubble in the heated wall. From the
present study, the following conclusions can be
drawn.
a) The experimental results indicate that
the heat transfer coefficient with the electrically
heated surface is lower than the fluid heated
surface for the same wall superheat.
b) The numerical analysis indicates that
the temperature profile in the heater plate under
the bubble is different with the two heating
methods. The higher temperature in the major
area of the heater surface not covered by bubbles
leads to a lower heat transfer with the electrical
heating method.
c) The difference between the heat transfer
rates for the two methods becomes smaller for
thicker heater walls.
d) At higher heat fluxes, larger portion of
the heater surface is covered by the bubbles and
the difference between the two heating methods
becomes smaller.
8. NOMENCLATURE
h top
h bot
k
q&
q”
rout
rbubble
t
L
Ttop
Tbot
Tref
u
u top
u bot
top convection coefficient for plate
element (W/m2°C)
bottom convection coefficient for plate
element (W/m2°C)
thermal conductivity (W/m°C)
heat generation rate per unit volume
(W/m3)
constant heat flux per unit area (W/m2)
outer radius of plate element (m)
radius of bubble on the plate element (m)
thickness of plate element (m)
length of experimental test section (m)
top fluid temperature of plate element (°C)
bottom. fluid temperature of the plate
element (°C)
reference temperature for numeric program
dimensionless parameter, T/Tref
dimensionless parameter, Ttop/Tref
dimensionless parameter, Tbot/Tref
Greek Symbols
δ
grid size for numerical program (m)
ε absolute numerical convergence factor
9. REFERENCES
Dalle Donne, M., and Ferranti, M. P., 1975,
“The Growth Of Vapor Bubbles In Superheated
Sodium,” International Journal of Heat and
Mass Transfer, vol. 18, pp. 477-493.
Kedzierski, M. A., 1995, “Calorimetric and
Visual Measurements of R-123 Pool Boiling on
Four Enhanced Surfaces,” National Institute of
Standards and Technology, Report No. NISTIR
5732.
Khanpara, J. C., Bergles, A. E., and Pate,
M. B., 1987, “A Comparison Of In-Tube
Evaporation Of R113 In Electrically Heated And
Fluid Heated Smooth And Inner-Fin Tubes,”
Paper presented at the ASME Heat Transfer
Conference, August, Advances in Enhanced
Heat Transfer 1987, HTD-Vol. 68, ASME, New
York, pp. 35-45.
Lee, R. C., 1987, “Investigation of the
Mechanism of Nucleate Boiling Through
Numerical Modeling,” Ph. D Dissertation,
Department of Mechanical Engineering Graduate
School, University of Wyoming.
Moore, F. D., and Mesler, R. B., 1961, “The
Measurements Of Rapid Surface Temperature
Fluctuations During The Nucleate Boiling Of
Water,” AICHE Journal, vol. 7, no. 4, pp. 620624.
Unal, C. and Pasamehmetoglu, K. O., 1994,
“A Numerical Investigation Of The Effect Of
Heating Methods On Saturated Nucleate Pool
Boiling”, International Communications in Heat
and Mass Transfer, vol. 21, no. 2, pp. 167-177.