3 Dynamic Microscopic Study of Wax Deposition Particulate

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Dynamic Microscopic Study of Wax Deposition: Particulate
Deposition
Gabriel Santos, Nagu Daraboina,* and Cem Sarica
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ABSTRACT: This study presents a continuing effort to unravel the
wax deposition mechanisms using a state-of-the-art microscopic in
situ visualization technique. The investigation focuses on under-
standing the effect of the flow rate on the particulate deposition
mechanism. The existence of the particulate deposition mechanism is
proven by the presence of wax crystals at a distance more significant
than the mass transfer boundary layer thickness calculated from the
film mass transfer theory, reinforcing that molecular diffusion is not
the only one responsible for wax deposition. The flow rate study
presents a direct relation between the flow regime and the particulate
deposition mechanism. The lower the Reynolds number, the stronger
this mechanism is observed. Under laminar and transition flow
regimes, the deposit thickness and growth rate of the deposit are
considerably greater than those calculated under the turbulent flow regime. The number of available crystals at the boundary layer
for different flow rates is qualitatively analyzed. It is concluded that, under laminar and transition conditions, a larger number of
crystals is available for deposition compared to turbulent cases. This effect can be explained by the larger induced shear forces on the
flow at higher Reynolds numbers.
■ INTRODUCTION
The wax deposition is one of the costly and challenging flow
assurance issues during oil and gas production as a result of the
complex behavior of the liquid−solid interaction. Wax
deposition requires a negative radial temperature gradient, an
interface temperature less than the wax appearance temper-
ature (WAT), and an affinity of wax to the pipe surface.1 The
severity of this wax deposition problem depends upon the
environmental and operational conditions of the pipeline.
Under severe conditions, wax deposition can lead to a
complete pipeline blockage if not adequately addressed. In
those circumstances, expensive procedures are employed to
reestablish the regular operation of the production system.
Once the deposition of wax takes place in a pipeline,
mitigation and removal techniques need to be employed to
reduce or eliminate the problem. The most used treatments are
classified as mechanical2 (pigging and scrapping), chemical3,4
(paraffin inhibitors and pour point depressant injection), and
thermal5 (active heating) removal methods. It has been
documented in the literature that the cost of a wax remediation
operation on deep-water pipelines can cost up to $20−25
million, not including the cost associated with deferred
production.6 In more severe cases, the entire production field
has been abandoned as a result of wax deposition, implying
total losses of more than $100 million.7 Reliable wax
deposition models are required to deploy suitable mechanical
and chemical treatments safely and timely.
Unfortunately, the current models used to predict the
deposition of wax in pipelines have limited applicability as a
result of the lack of mechanistic understanding of the process.
Such deficiency leads to models with general fitting parameters
and implying predictions with uncertainty up to 100%.8 It is
fundamental to understand the mechanisms governing wax
deposition at different operational conditions to address this
problem.
Molecular diffusion of wax molecules from the bulk to the
deposition surface under a negative thermal gradient is widely
accepted as the deposition mechanism in the available
literature.7 The models based on this theory tend to
overpredict the wax deposition. The possible reason for that
lies in the fact that these models do not consider mechanistic
aspects, such as shear effects, deposit morphology evolution,
and supersaturation in the mass transfer boundary layer,9 that
Received: May 28, 2021
Revised: June 29, 2021
Published: July 13, 2021
Articlepubs.acs.org/EF
© 2021 American Chemical Society
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Energy Fuels 2021, 35, 12065−12074
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may play essential roles in the deposition process. Attempts to
incorporate the mechanistic aspects based on conventional
deposition flow-loop results did not provide the means for a
complete understanding of the deposition phenomenon.8
Some researchers used a static microscope to elucidate the
wax deposition process. Paso et al.10 studied the morphologies
of wax−oil gel with a wax content of 0.5 wt % using cross-
polarized microscopy, indicating that the sizes of crystals are in
the range of ∼10−20 μm. The authors concluded that the gel
point of the model oil in use is dependent upon the
morphologies and surface characteristics of the paraffin
crystals. Venkatesan et al.11 studied the yield stress of a
wax−oil gel and its relation with the cooling rate. The authors
also used a three-dimensional (3D) cross-polarized light
microscope to study the crystal structure of the wax−oil gel
under quiescent conditions. The observed structures of the
crystals are platelet structures that grow in two directions. The
yield stress of the platelet structures is dependent upon both
the cooling rate and shear rate. Soedarmo et al.9 studied the
two-dimensional aspect ratio and size distribution of crystals
under static conditions and concluded that the aspect ratio
distribution resembles a log-normal pattern, while the crystal
size has a distribution mode of 20−40 μm.
Most recently, Cabanillas et al.12 studied the particulate
deposition phenomenon in a laminar channel flow for three
different conditions: negative, zero, and positive heat flux. The
authors observed the deposition of particles only for the
condition of negative heat flux. They concluded that
particulate deposition plays a vital role in the deposition
mechanism for fluids flowing at temperatures below the WAT.
Particulate deposition is defined as the aggregation of wax
crystals, one to another, forming a paraffin deposit. On the
basis of flow characteristics, this deposit can continue to grow,
leading to a reduction of the flowing cross-sectional area of the
pipe.13 Similarly, Soedarmo et al.14 studied the in situ wax
deposition on a microscopic scale focusing on the mass transfer
boundary layer, deposit morphology, and shear effects during
the deposition under laminarconditions. The authors
concluded that the observed boundary layer is greater than
the boundary layer predicted by the heat−mass transfer
analogy. They also reported that the crystal aspect ratio
distribution is similar to the static conditions, resembling a log-
normal distribution.
To objectively validate wax deposition models, Soedarmo et
al.8 compared experimental data for deposition rate at various
conditions to molecular-diffusion-based models. It was
observed that the film mass transfer (FMT) theory over-
predicts the deposition rate of wax. The FMT theory considers
complete supersaturation of wax molecules in the boundary
layer, meaning that wax molecules cannot precipitate at a
distance further away from the pipe wall than the theoretical
mass transfer boundary layer (δC,FMT).
15 However, visual-
ization studies showed precipitated wax crystals at a further
distance from the wall than δC,FMT.
8 These observations
support the necessity of more mechanistically based wax
deposition models.
Visual observations of flow dynamics and deposition with a
microscope proved to provide a basis for validating the
mechanisms involved in the deposition process. The current
study encompasses visualizations of the boundary layer at
different flow rates (ranging from laminar to turbulent) at
similar temperature conditions. Understanding this wax crystal
precipitation and interaction between particles and the wall
surface at different flow rates provides the basis for improving
or developing models to predict wax deposition accurately.
■ EXPERIMENTAL DETAILS
The experimental study details, describing the fluid, facility, operating
procedures, test matrix, and data analysis process, were provided.
Test Fluid. The fluid used in the experimental campaign is a
mixture of Exssol D-60 mineral oil and CSP-165 food-grade wax at a
weight ratio of 95:5. The precipitation curve for this oil is presented in
Figure 1.
Physical properties, including viscosity, solubility, density, heat
capacity, thermal conductivity, molecular weight, and molar volume of
the oil, are presented in Table 1.
Facility Description. A bench-scale microscopic flow loop is used
in this experimental campaign for the dynamic study of wax
deposition. A piping and instrumentation diagram (P&ID) of the
facility with both the oil system and cooling system is presented in
Figure 2. The isometric drawing of the flowing test cell (a) and
positions of temperature probes (b) is presented in Figure 3.14 This
facility has two decoupled systems for oil and coolant. The oil system
is composed of an airtight oil tank with a capacity of 50 gallons and
operates using a centrifugal pump with a maximum flow rate of 35
gallons/min. The coolant system is composed of a refrigerator/heater
circulator operating with water. The circulator has a capacity of 3.4
gallons and a maximum flow rate of 4 gallons/min. A precision heater
controls the oil temperature, and the flow rate is measured by a
Coriolis flowmeter (Micro Motion model F100S). The Coriolis
flowmeter has an uncertainty of ±0.2%. This embedded flow meter is
also able to measure the density of the fluid.
The flowing test cell comprises two rectangular channels for oil and
water flow and the copper plate in between both. The copper plate
connects the two channels, providing the means for heat transfer
Figure 1. MO-20 wax precipitation curve determined using
differential scanning calorimetry (DSC).
Table 1. MO-20 Fluid Properties
parameter value method
viscosity at 37.8 °C (cP) 1.23 rheometer
viscosity range from 15 to 60 °C
(cP)
0.9−7.9 rheometer
WAT (°C) 32.9 ± 0.1 differential scanning
calorimeter
wax content (%) 5 weighting scale
density at 37.8 °C (g/cm3) 0.78 Coriolis flowmeter
thermal capacity (J kg−1 K−1) 2019.64 PVTsim simulation
thermal conductivity
(W m−1 K−1)
0.11 PVTsim simulation
molecular weight (g/mol) 260.6 fluid composition
molar volume (cm3/mol) 334.1 fluid composition
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between them. The complete specifications of the test cell are
presented in Table 2. Furthermore, the test cell is equipped with a
perpendicular view window, equipped with four thermistors, used for
wall temperature measurement.
The wax deposition process under different flow rate conditions
was recorded with an optical magnification of 1.5×, a recording speed
of 60 frames per second (fps), and a resolution of 1920 × 1440.
Operating Procedure. Before testing, the oil is circulated
through the test section at a temperature of 48.9 °C, 16.0 °C above
the WAT, at a flow rate of 5 gallons/min for 24 h to ensure that no
wax crystals are present in the system prior to the experiment. All
experiments were conducted under the same oil temperature (Toil) of
37.8 °C, which is 4.9 °C above the WAT. Once the desired oil
temperature is reached, the coolant is allowed in the test section and
set as time zero for that test. The water at the coolant system is kept
under room temperature conditions (Troom = 32.2 °C) before the
initiation of the experiment. The coolant temperature was adjusted to
Figure 2. P&ID of the microscopic flow loop, where solid red lines represent the oil system and blue dashed lines represent the coolant system.
Figure 3. (a) Isometric view of the flowing test cell and (b) thermal probe locations, T1, T2, T3, and T4, and their location on the test section Δx1 =
Δx2 = 2.54 cm and Δy1−2 = Δy3−4 = 1.27 cm. This figure was reproduced with permission from ref 14. Copyright 2016 American Chemical Society.
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maintain the same wall temperature in all experiments, as presented in
Table 3.
Text Matrix. The test matrix presented in Table 3 was chosen to
study particulate deposition under different flow rate conditions.
Data Analysis. The evolution of thickness over time is determined
by the direct measurement of the deposit using representative pictures
at a chosen time from the recorded videos. The technique employed
uses the pixel quantity of the picture to determine the actual size of
the deposit observed (Figure 4). Micrometric graduated glass beads of
known size were used to calibrate the system.
The average deposit thickness of the deposit is obtained by the
direct measurement of equally spaced points (N), represented as
yellow arrows in Figure 4. Equation 1 summarizes the procedure
described above.
δ
δ
=
∑
Navg
deposit
(1)
■ RESULTS AND DISCUSSION
The average thickness of the wax deposit observed using a
microscope and deposit images at various time steps for Toil =
37.8 °C, Twall = 31.3 ± 0.2 °C, and flow rate of 4.4 kg/min are
presented in Figure 5.
From Figure 5, it is evident that the formation of a wax
deposit does not start at thesame time as the cooling process
(time = 0 min). However, once the coolant is flowing, the
appearance of crystals above the wall is observed. Crystals
flowing at the boundary layer begin attaching to the surface of
the wall after 7−13 min of cooling, depending upon the flow
rate. However, these crystals can detach and reattach based on
the flow rate. To be experimentally consistent measuring the
deposition layer thickness for all experimental observations, a
full deposit layer was considered as the starting point of
measurement. A continuous layer of wax is visible approx-
imately 30 min after the cooling, as seen in Figure 5A. In
addition, the crystals flowing in the observed boundary layer
were also contributing to the deposit growth, as seen in panels
B−F of Figure 5. Deposits formed as a result of wax crystals
flowing in the boundary layer are attributed to the particulate
deposition.
Further evidence in support of the particulate deposition is
shown in Figure 6A; although wax crystals appeared in the
boundary layer, the interface remained clear (free from
crystals) for a stipulated time. Moreover, as seen in Figure
6B, particulate deposition occurs while crystals are flowing in
the boundary layer. For both points, the observed boundary
layer thickness (δC,m) is higher compared to the theoretical
mass transfer boundary layer proposed in the film mass transfer
theory (δC,FMT). δC,m is the observed concentration boundary
layer thickness based on microscopic observation, defined as
the distance between the cold wall and the furthest observed
wax crystals from the cold wall.14
The mass transfer boundary layer is obtained by calculating
the hydrodynamic boundary layer thickness (δv) using “law of
the wall” proposed by von Kaŕmań.16 Characteristic distance
from the wall and the shear stress at the wall are calculated
from eqs 2 and 3, respectively.
ρ
μ
= *+y
yv
(2)
τ
ρ*
= ̅v w,width
(3)
The hydrodynamic boundary layer (y = δv) is back-calculated
by assuming a value of 30 for y+.16
From the hydrodynamic boundary layer, the thickness of the
mass transfer boundary layer can be approximated by eq 4 by
assuming that mass transfer is analogous to momentum
transfer.17,18
Table 2. Specification of the Flowing Test Section
parameter value
copper layer thickness (m) 0.04
oil duct width (m) 0.013
oil duct height (m) 0.035
water duct width (m) 0.013
water duct height (m) 0.04
length (m) 0.565
observation window diameter (m) 0.04
Table 3. Experimental Matrix
experiment
Qoil
(kg/min)
Tb,o
(°C)
Tb,c
(°C)
Tavg,wall
(°C) NRe
flow
regime
PD-01 2.9 37.8 20.6 31.5 1325 laminar
PD-02 4.4 37.8 20.0 31.2 1987 transition
PD-03 8.8 37.8 19.4 31.5 3975 turbulent
PD-04 13.2 37.8 18.3 31.0 5963 turbulent
Figure 4. Example of the deposit thickness measurement with the microscope for deposit thickness determination.
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δ
δ
=
ScC,FMT
v
1/3 (4)
The calculated values for the hydrodynamic boundary layer
and mass transfer boundary layer for the flow rates studied are
presented in Table 4.
As seen from Figure 6, δC,m is much larger compared to
δC,FMT. Soedarmo et al.
14 observed the flow of wax particles on
the boundary layer and speculated partial supersaturation in
the boundary layer. Lee19 also assumed and incorporated this
partial supersaturation assumption in the transport equation
for wax deposition prediction.
On the basis of the FMT theory proposed by Singh et al.,7
the deposition of wax occurs as a result of the radial molecular
diffusion, where the deposition forms as a result of the
concentration difference (as a result of the temperature
gradient) of dissolved wax between the mass transfer boundary
layer and the pipe wall. However, recent studies showed that
the deposition could occur with no temperature gradient when
oil flowed below the WAT, which contradicts the prevailing
molecular diffusion theory.20,21 They speculated that the
Figure 5. Example of the average wax deposit thickness change and corresponding images (A−F) over time for Toil = 37.8 °C, Twall = 31.3 ± 0.2 °C,
and Reynolds number equal to 1987.
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deposits might be formed by a different mechanism other than
molecular diffusion. It is also reported that deposition
predicted using the molecular diffusion theory consistently
overpredicts the experimental deposition observed in different
flow loop studies.8,14,19,22,23 The clear experimental evidence of
particulate deposition provided here explains the over-
predictions of wax deposition using the FMT theory.8
On the basis of the new experimental evidence in the current
work, particulate deposition is possible along with molecular
diffusion. Thus, this mechanism should be given more
attention in model development and deserves further in-
depth investigation.
Influence of Operational Parameters on the Partic-
ulate Deposition Mechanism. In addition to the wax
deposition mechanisms, the effect of the flow rate on the
deposition process is still not fully understood.
Microscopic experiments at different flow rates ranging from
laminar to turbulent were conducted to understand the
influence of the flow rate on wax deposition. The critical
Reynolds number (Re) for the geometry of the test section was
calculated on the basis of the work of Tosun et al.24 and found
to be approximately equal to 1700. Four different flow rates
under both laminar and turbulent conditions were analyzed to
comprehensively study the effect of the flow rate on the
deposition mechanism (Table 3).
The changes in the deposition as a result of the flow rate
were analyzed quantitatively and qualitatively. The quantitative
analysis focused on the deposit thickness measurements and
growth rate of the deposit. The qualitative observations
concentrated on the number of available crystals at the
boundary layer of each flow rate under analysis.
As expected, changes in the flow rate directly affect the
average deposit thickness (Figure 7). Laminar conditions tend
to form a larger thickness, while turbulent conditions have a
considerably lower thickness. These observations were
consistent with several flow loop experimental results in the
literature.15,25,26 On the basis of the work proposed by Guha,27
Ravichandran15 correlated this observation by relating the
Reynolds number, deposition, and settling of particles. The
larger the Reynolds number, the higher the inertial force
provided by the fluid, meaning that the particles will acquire
more momentum, reducing their ability to settle at the pipe
wall and form the deposit.
Figure 6. Observed and calculated (FMT) boundary layer during wax deposition and corresponding images at (A) time = 19.7 min and (B) time =
38.9 min, for Toil = 37.8 °C, Twall = 31.3 ± 0.2 °C, and Reynolds number equal to 1987.
Table 4. Boundary Predictions
experiment Qoil (kg/min) δv (μm) δC,FMT (μm)
PD-01 2.9 14848 759
PD-02 4.4 12123 619
PD-03 8.8 8572 438
PD-04 13.2 6999 358
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From Figure 7, it is observed that the flow rate does
influence not only the average thickness but also the growth
rate of the deposit. This behavior can be observed on the
sharper changes in slope for the deposition curve of the PD-01
and PD-02 tests. The growth rate was quantified using the
gradient of the deposition thickness curve and presented in
Figure 8, along with screenshots of the deposit evolution.
Equation 5 shows the calculation procedure for the growth rate
using x1 and x2 as the points in time as deposition takes place.
δ δ
=
−
−t t
growth rate x x
x x
1 2
1 2 (5)
From Figure 8, it is observed that a higher growth rate was
achieved under the laminar flow and transition region
compared to turbulent flow conditions. Tests PD-01 and
PD-02 were performed at flow rates of 2.9 and 4.4 kg/min,
respectively. The number of crystals available at the boundary
layer and the shape of the deposit formed were similar.
However, the thickness formed at the test PD-02 is smaller.
Both turbulent cases presented a smaller number of crystals in
the boundary layer and a different deposit shape with
considerably thinner thickness. Tests PD-01 and PD-02 both
presented a peak in the growth rate between 17.7 and 26.5
min, and after that, the growth rate reduced considerably. For
tests PD-03 and PD-04, the peak of deposition happened
earlier, between 8.8 and 17.7 min. After that, the growth rate
reduced slowly until the end of the experiments.
For tests PD-01 and PD-02 under laminar and transition
conditions, respectively, it can be observed that particles of wax
crystals were flowing at the boundary layer contributing to the
formation of the wax deposit from the beginning to the end of
the process. With regard to the two turbulent flow conditions
(PD-03 and PD-04), particulate deposition is well-observed for
the early stages of the process and diminishes as time
progresses.
The deposit thickness and growth rate vary differently for
changes in the flow rate. For laminar and transition conditions,
the reduction in the growth rate and deposit thickness is
smaller when compared to a turbulent case. For test PD-02,
with Re equal to 1987, the final deposit thickness is 14.8%
smaller than the laminar test (PD-01). The reduction is even
more significant for fully turbulent cases when compared to the
laminar case. The PD-03 and PD-04 tests have a final average
thickness of 63.5 and 60.9%, respectively, smaller than the PD-
01 test. On the other hand, changes in the flow rate inside the
full turbulence range did not present significant changes at the
final average thicknesses of the deposits.
All experiments were conducted at the same temperature
conditions. Therefore, it was expected that the number of wax
crystals to precipitate out of the bulk oil would be similar.
Tests under laminar and transition conditions imposed
lower shear forces on the process of deposition. Such a
characteristic leaves more crystals available per area in the
boundary layer, promoting deposition. On the other hand, the
turbulent cases will have those crystals swept away by the large
shear forces induced over the boundary layer close to the cold
wall, reducing the deposition. Figure 9 presents the proposed
mechanism explaining how different flow rates affect the
process of deposition.
These results stress the importance of the crystal density in
the boundary layer at different operational parameters to
develop models based on particulate deposition.
■ CONCLUSION
An experimental bench-scale facility was used to study
microscopic in situ visualization of wax deposition under
laminar and turbulent conditions. The experimental evidence
of particulate deposition was provided. On the basis of the new
experimental evidence in the current work, particulate
deposition is possible along with molecular diffusion. There-
Figure 7. Average deposition thickness at different flow rates. Temperature conditions were Toil = 37.8 °C and Twall = 31.3 ± 0.2 °C.
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fore, this mechanism should be given more attention in model
development and deserves further in-depth investigation.
The study of flow rate effects was analyzed quantitatively
and qualitatively. Changes in flow regimes have a direct impact
on the deposit thickness and growth rate. Turbulent flow
conditions present thinner wax deposits and lower growth rates
compared to laminar and transition regions. Under similar wall
temperature conditions, the wax deposit formed at turbulent
flow presented thickness up to 60% thinner than the laminar
flow.
Under laminar and transition flow regimes, the number of
crystals flowing at the boundary layer is more prominent in
comparison to turbulent flow regimes. The crystals are
observed at lower Re during the whole duration of the
Figure 8. Deposit growth rate under laminar and turbulent conditions: (a) PD-01, (b) PD-02, (c) PD-03, and (d) PD-04 experiments. Toil = 37.8
°C, and Twall = 31.3 ± 0.2 °C.
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deposition process, while for higher Re, the crystals are
observed at the beginning of the deposition process. The
number of crystals flowing at the boundary layer also changes
significantly when complete turbulence is reached. At this
condition, the lower number of crystals can be explained by the
higher shear forces induced on the flow.
■ AUTHOR INFORMATION
Corresponding Author
Nagu Daraboina − Tulsa University Paraffin Deposition
Projects, The University of Tulsa, Tulsa, Oklahoma 74104,
United States; orcid.org/0000-0002-6910-5295;
Email: nagu-daraboina@utulsa.edu
Authors
Gabriel Santos − Tulsa University Paraffin Deposition
Projects, The University of Tulsa, Tulsa, Oklahoma 74104,
United States
Cem Sarica − Tulsa University Paraffin Deposition Projects,
The University of Tulsa, Tulsa, Oklahoma 74104, United
States
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.energyfuels.1c01684
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
The authors thank the company members of Tulsa University
Paraffin Deposition Project (TUPDP) consortia for their
continuous support of this research effort.
■ NOMENCLATURE
Variables
NRe = Reynolds number
Figure 9. Illustration of the particle deposition mechanism for laminar and turbulent conditions: (a.1) PD-01 test, (a.2) PD-02 test, (b.1) PD-03
test, and (b.2) PD-04 test. Toil = 37.8 °C, and Twall = 31.3 ± 0.2 °C.
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δC,FMT = mass transfer boundary layer thickness calculated
with the film mass transfer analogy theory (μm)
δv = hydrodynamic boundary layer thickness (μm)
δC,m = mass transfer boundary layer observed thickness
observed from a microscope (μm)
δdeposit = pointwise deposit thickness measured from a
microscope (mm)
δcopper plate = thickness of the copper plate pipe (mm)
δavg = average deposit thickness (mm)
Qoil = oil mass flow rate (kg/min)
ρ = oil density
Sc = Schmidt number
Tb,o = temperature at oil bulk (°C)
Tb,c = temperature at water bulk (°C)
Tavg,wall = average temperature of the wall (°C)
y+ = dimensionless distance from the wall
v* = friction velocity (m/s)
μ = viscosity (Pa s)
τ̅w,width = shear stress acting on the width of the wall (Pa)
x = subsequent points for growth rate calculation
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