CENG 176B, Spring 2016
Drews, Zhang, Yang, Xu, and Vazquez-Mena
Section B01 (W/F), Team 07: Double-O Seven
Nusselt Correlation Analysis of Single Phase
Steady-State Flow through a Chevron Type
Plate Heat Exchanger
Part I:
Part II:
Part III:
Part IV:
Thomas Arnold
Kimberly Nguyen
John Fukuyama
Renee Parker
Abstract
Chevron type plate heat exchangers are widely used in a variety of industries due to their large
surface area and corrugations that improve flow characteristics for heat transfer . We perform Nusselt correlation analysis to parametrize the single phase hydrodynamic conditions to improve heat
transfer within these heat exchangers. We determine a unique Nusselt correlation for the turbulent
regime of Reynolds numbers (2000 <Re <7500), Prandtl number from 3 <Pr <5, and chevron
angle of 60 degrees. Several novel trends are observed including linear increase in overall heat
transfer with increasing water flow rate and increasing dominance of convective heat transfer with
increasing reynolds number. The proposed Nusselt correlation closely aligns with correlations in
literature over the same chevron angle and Reynold’s number range. The results confirm superior heat transfer in corrugated plates over flat plates, however further investigation is required to
determine optimal corrugation spacing and angle for greater heat transfer coefficients.
1
Introduction
Heat exchangers are an essential part of nearly every chemical processing industry large and small,
from oil and gas refineries to local dairy producers.1 A heat exchanger is employed to re-use excess
heat from hot effluent fluids to heat other streams in a given process a practice which began in
the early 1920s with the advent of steam jet ejectors and vacuum condensers and evolved rapidly
in the 1980s with the boom of vacuum engineering technology that revolutionized petrochemical
processing.2
Today, there are two broad categories of heat exchangers: shell and tube exchangers, and plate
exchangers. Shell and tube exchangers find the most use in the oil and gas industry, as they are low
cost, and suited for high pressure applications, with tube leaks easily identifiable.3 Alternatively,
plate heat exchangers present higher efficiencies, easier cleaning and maintenance, and better capability for increased capacity, making them more viable for food processing and pharmaceutical
applications.4
Due to their easy disassembly and high efficiency, Plate Heat Exchangers (PHEs) are of greatest
interest to examine with experimental models. There are four common arrangements of plate
heat exchangers: plate and frame, plate fin, lamella, and spiral, each with different heat transfer
characteristics which are of most importance in any process. Plate and frame often presents the
highest efficiency, with heat transfer coefficients, U, in the range of 1000 <U <4000 W /m2 K.
Spiral and lamella follow closely in the range 700 <U <2500 W /m2 K.5
For a single exchanger, the values for heat transfer coefficient depend on the stream temperature
gradient and the flow rate of fluid in each hot and cold channel. When optimizing heat transfer, it
becomes important to parametrize how convective and conductive heat transfer interplay with flow
characteristics, often referred to as the Nusselt correlation.
1 Nikhil,
J.; Shailendra, L. M. Heat Transfer Analysis of Corrugated Plate Heat Exchanger of Different Plate
Geometry: A Review. International Journal of Emerging Technology and Advanced Engineering 2012, 2.
2 Athey, R. Graham Corporation: Evolution of a Heat Transfer Company. Heat Transfer Engineering 1999, 20.
3 Singh, A.; Sehgal, S. Thermohydraulic Analysis of Shell-and-Tube Heat Exchanger with Segmental Baffles. ISRN
Chemical Engineering 2013, 2013.
4 APV-Corporation In APV Heat Transfer Handbook: A History of Excellence; SPX: Getzville, 2008.
5 Ibid.
1
2
Background
Of the four common arrangements of PHEs, plate and frame exchangers typically have the highest
heat transfer efficiencies.6 While smaller plate and frame exchangers are generally joined through
brazing, larger commercial plate and frame exchangers employ gaskets to confine flow.7 These are
known as gasketed plate heat exchangers (G. PHEs).
G. PHEs engage several corrugated metal plates with multiple portholes and elastomeric gaskets to confine fluid flow through the channels, optimizing heat transfer.8 The corrugated design of
G. PHEs provides for high turbulence and shear stress, enhancing mixing and heat transfer.9
G.PHEs may be operated with co-current flow, cross-flow, or counter-current flow. Flow
schematics of co-current, top, and counter-current, bottom, G. PHEs are depicted in Fig. 5. Counter
current flow generally is preferred, as it allows for maximum heat transfer.10
A commercial G. PHE with water as its hot and cold fluid streams was used in this study. The
overall heat transfer coefficient was experimentally determined and evaluated alongside respective
hot and cold stream flow rates.
Additionally, a brief analysis of the correlation between the Nusselt, Prandtl, and Reynolds
number was conducted. The Nusselt number characterizes the intensity of the convective heat
exchange between surface of an object and the flow of a fluid.11 The Prandtl number is an exclusive
characteristic of fluids, and determines whether the momentum diffusivity or thermal diffusivity
of a liquid dominates.12 Gases generally possess low Prandtl numbers, while oils possess high
Prandtl numbers.13 The Reynolds number is a ratio of inertial force and viscous force, with a high
Reynolds number indicating turbulent flow.14
6 Heat
Exchangers Information., IEEE Global Spec, 2011.
of Gasketed/Brazed Plate heat Exchangers., Graham Corporation, 2016.
8 R. Shilling, e. a. In Chemical Engineers’ Handbook, Perry, R., Chilton, C., Eds., 8th ed.; McGraw Hill: New
York, 2008, Ch. 11.
9 Heat Exchangers., Encyclopedia of Chemical Engineering Equipment, University of Michigan, 2014.
10 Hewitt, G. F., Barbosa, J. R., Eds. Heat Exchangers., Thermopedia.
11 Condon, E., Heat transfer. In Handbook of Physics, Condon, E., Odishaw, H., Eds., 7th ed.; McGraw-Hill: 1967,
5.5.7–5.8.
12 Hewitt and Barbosa, Heat Exchangers.
13 Weisstein, E., Ed. Prandtl Number., Wolfram Research, 1996.
14 GRC Database Reynolds Number., NASA Glenn Research Center, 2016.
7 Advantages
2
3
Theory
3.1
Overall Heat Transfer Coefficient
The heat equation relates the amount of heat transferred at any given time, dq, to the overall heat
transfer coefficient, U, the difference between the temperature of the hot stream, Th , that of the
cold stream, Tc , and the differential area available for heat transfer, dA, by the following equation,
dq = U(Th − Tc )dA.
(1)
The temperature difference between hot and cold streams may be defined as ∆T1 = Thout − Tcin and
∆T2 = Thin − Tcout , where Thin is the temperature of hot stream entering the heat exchanger, Thout
is the temperature of hot stream exiting the heat exchanger, Tcin is the temperature of hot stream
entering the heat exchanger, and Tcout is the temperature of cold stream exiting the heat exchanger.
Under steady state, counter-current flow operation, ∆T1 and ∆T2 may be approximated as linear.
Through integration, the total amount of heat transferred, qT , is given by
qT = UA∆Tlmtd = UA
∆T1 − ∆T2
1
ln( ∆T
∆T2 )
,
(2)
where ∆Tlmtd is the log-mean temperature difference.
If the overall heat transfer coefficient is unknown, qT may be alternatively defined as,
qT = ωhC ph (Thout − Thin ) = ωcC pc (Tcout − Tcin ).
(3)
where ωh is the mass flow rate of the hot stream, ωc is the mass flow rate of the cold stream, C ph
is the specific heat of hot fluid at Thavg =
Tcavg =
(Thin +Thout )
,
2
and C pc is the specific heat of cold fluid at
(Tcout +Tcin )
.
2
The overall heat coefficient, U, may be determined from equating equations 2 and 3.
3
3.2
Correlation Between Nusselt, Prandtl, and Reynolds numbers
The Nusselt numbers, Nuh and Nuc , for hot and cold streams respectively are defined as
Nuh =
hh Dh
kh
(4)
Nuc =
hc Dh
,
kc
(5)
and
where hh and hc are the convective heat transfer coefficients of hot and cold streams, kh and kc are
the thermal conductivity coefficients of hot and cold streams, and Dh is the hydraulic diameter. For
a plate heat exchanger, Dh is determined by,
Dh =
4α
,
Φ
(6)
where α is the amplitude of plate corrugation and Φ is the surface enlargement factor. Heat exchanger plates have an approximate sinusoidal profile,15 resulting in an area increase factor of
1
Φ = (1 +
6
s
r
1+(
2
( 2πα
2πα 2
P )
) + 4 1 + c ),
Pc
2
(7)
where Pc is the plate corrugation pitch, as shown in Fig. 6 of the Appendix.
The Prandtl numbers, Prh and Prc , for hot and cold streams respectively are defined as
Prh =
µhC ph
kh
(8)
Prc =
µcC pc
,
kc
(9)
and
where µh and µc are the dynamic viscosities of the hot and cold streams.
15 Plate
Heat Exchanger., ACHP Component Models, 2011.
4
The Reynold numbers, Reh and Rec , for hot and cold streams respectively are defined as
Reh =
vh ρh Dh
µh
(10)
Rec =
vc ρc Dh
µc
(11)
and
where ρh and ρc are the densities of the hot and cold streams and vh and vc are the maximum
velocities of the hot and cold streams.
The correlation between Nu, Pr, and Re may be generally defined as,
Nuh = ah Reh bh Prh ch ,
(12)
Nuc = ac Rec bc Prc cc ,
(13)
and
where ah , ac , bh , bc , ch , and cc are experimentally determined coefficients.16
Since Re and Pr values are constant a given flow rate and temperature, empirical Re and Pr
values may be used alongside a, b, and c coefficients from literature to provide a plot for calculated
Nu values (Table 1).17
,18 ,19 ,20 ,21
To determine the coefficients with the best fit, the plot of
calculated Nu values may then be juxtaposed with a plot of empirically determined Nu values for
comparison.
16 McCabe,
W. et al. In Unit Operations of Chemical Engineering, 7th ed.; McGraw Hill: Boston, 2004, Ch. 15.
E.; Hossfeld, L. Effect of rounding of protruding edges on heat transfer and pressure drop in a duct. Int
J. Heat Mass Transfer 1984, 27.
18 Okada, B. et al. Design and Heat Transfer Characteristics of a New Plate Heat Exchanger. Heat Transfer Japanese
Research 1972, 1.
19 Talik, A. et al. In Heat Transfer and Pressure Drop Characteristics of a Plate Heat Exchanger; ASME: New York
(1995).
20 Focke, W.; Oliver, I. The Effect of the Corrugation Inclination Angle on the Thermohydraulic Performance of
Plate Heat Exchangers. Int J. Heat Mass Transfer 1985, 28.
21 Thonon, B. et al. Recent Research and Developments in Plate Heat Exchangers. Journal of Enhanced Heat Transfer 1995, 2.
17 Sparrow,
5
Author
Correlation
Sparrow Nu = 0.491Pr0.3 Re0.632
Okada
Nu = 0.317Pr0.4 Re0.65
Talik
Nu = 0.248Pr0.4 Re0.7
Focke
Nu = 0.440Pr0.5 Re0.64
Thonon Nu = 0.227Pr0.333 Re0.631
Chevron Angle
Re
60
2000 < Re < 30000
60
700 < Re < 20000
60
1450 < Re < 11460
60
45 < Re < 300
60
50 < Re < 15000
Table 1: Nusselt number correlations: comparisons in literature
4
4.1
Methods
Experimental Setup
The experimental apparatus was set up in accordance with Fig. 1. The PHE consisted of 6 channels
(3 hot, 3 cold) between corrugated plates in counter-current orientation. The flow in each channel
was directed by symmetric gaskets, which caused flow to travel diagonally across corrugations and
is depicted in Fig. 1 with flow inlets diagonally across from their corresponding outlet. Specifications for individual plate geometry are given in Table 2. Flow from each of the 65 gallon capacity
water tanks was controlled by Blue-White Industries F-450 polysulfone molded flowmeters and
pumped by 0.5 horsepower Dayton 6K580A pumps. Hot water was heated by Bradford White 50
gallon water heater, and allowed to heat for at least 30 minutes before beginning experimentation.
All piping elbow connections were Teflon wrapped and all PVC piping was insulated with 0.5
in K-Flex insulation. When the system began flowing, temperature of each stream was recorded
by Pt-100 resistance temperature detectors (RTDs) and output to a custom Labview VI, which
recorded time and temperature data.
Figure 1: Basic process flow diagram of experimental apparatus
6
Table 2: Geometric characteristics of chevron plate
Parameter
Symbol
Plate Width
Lw
Channel Spacing Dg
Chevron Angle
β
4.2
Value
Parameter
10.8 cm Plate Length
5.3 mm Plate Area
60 ◦
Corrugation Pitch
Symbol
Value
Lp
A
Pc
32.9 cm
323 cm2
92.7 mm
Procedure
The water heater was switched on to begin hot water generation at least 30 minutes before trials
were run. During heating, cold water valves were configured to facilitate flow from the higher
volume cold tank (generally tank 1), through the PHE, and out to the lower volume cold tank. After
sufficient hot water has been generated, hot and cold water pumps were switched on individually
to adjust the flow meters to the proper flow rate, always matching equal hot and cold flow rates.
Pumps were switched off after each flow rate was adjusted to prevent unnecessary and unrecorded
heat transfer. Once configured, the hot and cold pumps, as well as the data recording software,
were started simultaneously. The system took an average of 1 minute to reach steady state, at
which point pumps were shut off and recording concluded. Experiments were conducted with the
following flow rates, which were kept equal between hot and cold sides for each trial: 1.5, 2, 2.5,
3, 4, and 5.5 gallons per second.
5
Results and Discussion
A few types of measurements were made in order to determine relevant heat transfer data - inlet
and outlet temperatures of the water leaving and entering the heat exchanger, the flow rates of the
cold and hot streams, and the hydraulic diameter of the plates, given by Eq. (6). The overall heat
transfer coefficient, U was determined by first calculating qT using Eq. (3) and then equating qT
to Eq. (2) to find U. By determining U at different flow rates, it was demonstrated that the heat
transfer coefficient increases with increasing flow rate, ω, as seen in Fig. 2.
7
Figure 2: Hot and cold heat transfer coefficients increase with flow
rate
The Prandtl number was shown to be between 3 and 5, indicating that momentum diffusivity
was slightly more dominant than thermal diffusivity in terms of the energy transferred by water.
The Reynolds number, which was shown to be between 2000 and 7500, indicates turbulent
conditions in the heat exchanger.22 These conditions are desirable for convective heat transfer
since more turbulence allows for heat to be distributed more readily through convection. This is
why the plates used to exchange heat are often corrugated since corrugation helps induce turbulent
flow and thus higher rates of heat transfer.
Using Eq. (4), the Nusselt number was shown to be between 70 and 170, indicating that heat
transfer through convection was more dominant than through conduction of heat through the plates
and water. It was also observed that for increasing Reynolds number, Nusselt number also increased as seen in Fig. 3. This is to be expected due to the fact that greater bulk motion of fluid
22 Gradeck,
M. et al. Local analysis of heat transfer inside corrugated channel. Int J. Heat Mass Transfer 2005, 48.
8
will give rise to higher Reynolds numbers and convective flow will dominate in the numerator of
the Nusselt number. Our data shows a similar trend to others seen in literature, and most closely
with that of Thonon,23 as seen in Fig. 3.
There are a couple of considerations to take into account when designing a plate heat exchanger
that will most effectively cool a fluid. The most important are those that will increase convection
and result in higher Reynolds numbers. Higher flow rates as well as chevron corrugations all serve
to induce turbulent flow in the fluid, and thus transfer heat more readily. Plate heat exchangers are
of particular interest due to their ability to move fluid over a large surface area in a relatively small
volume of space. All of these features are present in the heat exchanger under consideration and
its similarity to industry standards is seen in Fig. 3.
Figure 3: Comparison of Nusselt number for similar heat exchangers. Experimental data most closely matches Thonon.
23 Thonon
et al., “Recent Research and Developments in Plate Heat Exchangers”.
9
6
Conclusions
We determine by varying flow rates and recording each inlet and outlet temperature that overall
heat transfer coefficients increase linearly with mass flow rate of water. Using mean temperatures
of each hot and cold stream to tabulate material properties of water, coupled with the flow rate and
hydraulic diameter of the plate, we solve for the Prandtl, Reynolds, and Nusselt numbers for each
trial of continuous, equal hot and cold flow. The Nusselt correlation is concluded to be consistent
with literature and most similar to results published by Thonon, et. al,24 with deviations most likely
arising due to differences in surface enlargement factor and the limited range of Reynolds numbers
tested in this experiment. Nevertheless, the agreement of the reported Nusselt correlation with
literature provides confidence that our simplified model is an accurate representation of industry
equipment.
To improve this work, we recommend that alternative chevron angles and surface enlargement
factors be tested, via the use of different plates. Such an analysis would provide greater comparison
to literature for the nusselt correlation and allow analysis for the effects of these parameters on
overall heat transfer coefficient.
24 Thonon
et al., “Recent Research and Developments in Plate Heat Exchangers”.
10
7
Appendix
Figure 4: A Gasketed plate heat exchanger.25
11
Figure 5: Co-current and counter-current flow configurations in a
plate heat exchanger.26
Figure 6: Plate geometry and nomenclature for a corrugated plate.27
12