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Correction to Fluids 2024, 9(4), 94.
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Correction

Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94

by
Sudha Mahanthesh Sachhin
1,*,
Ulavathi Shettar Mahabaleshwar
1,*,
David Laroze
2 and
Dimitris Drikakis
3
1
Department of Studies in Mathematics, Shivagangothri, Davangere University, Davangere 577 007, India
2
Instituto de Alta Investigacion, Universidad de Tarapacá, Casilla 7 D, Arica 1000000, Chile
3
Institute for Advanced Modelling and Simulation, University of Nicosia, Nicosia CY-2417, Cyprus
*
Authors to whom correspondence should be addressed.
Fluids 2024, 9(10), 241; https://doi.org/10.3390/fluids9100241
Submission received: 27 September 2024 / Revised: 29 September 2024 / Accepted: 8 October 2024 / Published: 17 October 2024
Figures: In Section 5, we aligned Figures 14–18 by consistently adding all the modelling parameters inside the labels [1]. We also revised the captions for Figures 14–18 to clearly state what they represent [1]. The correct Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 appears below.
Text Correction: In Section 2, the following text was added: “Similar to previous studies [2]”, “b is a parameter that is b > 0 for heated and b < 0 for cooled plate”. The correct text appears below.
Similar to previous studies [2], here, u ,   v ,   u p , and v p are the velocity components of a fluid and dusty fluid phase along the x- and y-directions, respectively; the dusty and fluid phase temperatures are Tp and T; μ is the dynamic viscosity; ρ is the effective density; κ is the thermal conductivity; b is a parameter that is b > 0 for heated and b < 0 for cooled plate; σ is the electrical conductivity; C p and C m are the specific heat coefficients; τ T is the heat equilibrium time; L 1 is the Stokes drag/resistance term; ν is the kinematic viscosity of nanoparticles N; k 1 is the flow permeability; and τ v = m L 1 is a relaxation time parameter, where m denotes the mass of dusty particles [2].
In Section 2, we corrected the typographical error in the definition of the Prandtl number. The correct one is Pr = μ C p κ f .
In Section 5, we revised the text to avoid ambiguity regarding the results of Figure 14, Figure 15, Figure 16 [1]. The correct text appears below.
Figure 14, Figure 15, Figure 16 show the temperatures for the fluid and dusty phases for different values of S = −2, 0 and 2, respectively. Increasing S value increases the thermal boundary layer thickness of the fluid phase. The dusty phase exhibits an increase in the thermal boundary layer when S increases from −2 to 0, while decreases for S = 2.
Equations: In Equations (35)–(39), there are typographical errors. We revised the subscript thnf to tnf. In Equation (38), we also revised the κnf to κf. The correct equations appears below:
μ t n f = 1 1 ϕ A g 2.5 1 ϕ C u 2.5 1 ϕ T i O 2 2.5 .
ρ t n f ρ f = 1 ϕ A g 1 ϕ C u 1 ϕ T i O 2 + ϕ T i O 2 ρ T i O 2 ρ f + ϕ C u ρ C u ρ f + ϕ A g ρ A g ρ f .
ρ C p t n f ρ C p f = 1 ϕ A g 1 ϕ C u × 1 ϕ T i O 2 + ϕ T i O 2 ρ C p T i O 2 ρ C p f + ϕ C u ρ C p C u ρ C p f + ϕ A g ρ C p A g ρ C p f .
κ t n f κ h n f = κ A g + 2 κ h n f 2 ϕ A g κ h n f κ A g κ A g + 2 κ h n f + ϕ A g κ h n f κ A g , κ h n f κ n f = κ C u + 2 κ n f 2 ϕ C u κ n f κ C u κ C u + 2 κ n f + ϕ C u κ n f κ C u , κ n f κ f = κ T i O 2 + 2 κ f 2 ϕ T i O 2 κ f κ T i O 2 κ T i O 2 + 2 κ f + ϕ T i O 2 κ f κ T i O 2 .
σ t n f σ h n f = 1 + 3 σ A g σ h n f 1 ϕ A g σ A g σ h n f + 2 σ A g σ h n f 1 ϕ A g , σ h n f σ n f = 1 + 3 σ C u σ n f 1 ϕ C u σ C u σ n f + 2 σ C u σ n f 1 ϕ C u , σ n f σ f = 1 + 3 σ T i O 2 σ f 1 ϕ T i O 2 σ T i O 2 σ f + 2 σ T i O 2 σ f 1 ϕ T i O 2 .
Nomenclature: We added the units that were missing in several parameters and corrected the typographical errors in some of the parameters [1]. The correct Nomenclature appears below.
The authors state that the scientific conclusions are unaffected. These corrections were approved by the Academic Editor. The original publication has also been updated.

Nomenclature

A 1 , A 2 , A 3 , A 4 , A 5 Constants
aStretching coefficient ( s 1 )
B 0 Magnetic parameter (Tesla)
C m , C p Specific heat coefficient ( JK 1 kg 1 )
dStretching/shrinking parameter
D a 1 Inverse Darcy number
E c Eckert number
f ( η ) Velocity function fluid phase
F ( η ) Velocity function dusty phase
k 1 Permeability of porous medium ( m 2 )
l Mass number
L 1 Stokes drag term (kg/s)
m Mass of the dusty particles ( kg )
Mdimensionless magnetic parameter
Ni Heat source/sink parameter
Nr Thermal radiation parameter
N Quantity of nanoparticles ( m 3 )
P r Prandtl number
pPressure ( Nm 2 )
q r Radiative heat flux ( Wm 2 )
Q 0 Heat source/sink ( Wm 3 K 1 )
SDimensionless mass suction/injection parameter
S > 0 Mass suction parameter
S = 0 No permeability
T p Dusty-phase temperature ( K )
T w Surface temperature ( K )
TFluid temperature ( K )
T Ambient temperature ( K )
u , v x, y-axis velocity of fluid phase ( ms 1 )
u p , v p x, y-axis velocity of dusty phase ( ms 1 )
u w Wall velocity ( ms 1 )
v w Wall mass transfer velocity ( ms 1 )
xCoordinate along the plate ( m )
yCoordinate normal to the plate ( m )
Greek symbols
α Stretching speed of dust particles ( ms 1 )
β T Fluid–particle interaction parameters
β Solution parameters
λ 1 , λ 2 , λ 3 Solution roots
ξ 1 , ξ 2 , ξ 3 , ξ 4 Constants
η Similarity variable
γ Heat coefficient
Λ Brinkman number
κ Thermal conductivity ( Wm 1 K 1 )
κ * Absorption coefficient ( m 1 )
μ e f f Effective dynamic viscosity ( kg ( ms ) 1 )
μ , μ p Dynamic viscosity of the fluid and dusty phase ( kg ( ms ) 1 )
ν , ν p Kinematic viscosity of fluid and dusty phase ( m 2 s 1 )
ρ Fluid density ( kgm 3 )
ρ p Particle phase density ( kgm 3 )
ψ Stream function
σ , σ p Electrical conductivity ( S i e m e n s / m = A 2 s 3 m 3 kg 1 )
σ * Stephen–Boltzmann constant ( Wm 2 K 4 )
τ T Heat equilibrium time ( s )
τ v Relaxation time parameter ( s )
φ Fluid nanoparticle volume fraction ratio
θ ( η ) Dimensionless temperature of fluid phase
Φ ( η ) Dimensionless temperature of dusty phase
Abbreviations
HNFHybrid nanofluid
ODEOrdinary differential equation
PDEPartial differential equation
MHDMagnetohydrodynamics
BCsBoundary conditions
TNFTernary nanofluid

Reference

  1. Sachhin, S.M.; Mahabaleshwar, U.S.; Laroze, D.; Drikakis, D. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94. [Google Scholar] [CrossRef]
Figure 14. Temperature profiles for the dusty and fluid phases versus similarity variable for S = −2.
Figure 14. Temperature profiles for the dusty and fluid phases versus similarity variable for S = −2.
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Figure 15. Temperature profiles for the dusty and fluid phases versus similarity variable for S = 0.
Figure 15. Temperature profiles for the dusty and fluid phases versus similarity variable for S = 0.
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Figure 16. Temperature profiles for the dusty and fluid phases versus similarity variable for S = 2.
Figure 16. Temperature profiles for the dusty and fluid phases versus similarity variable for S = 2.
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Figure 17. Temperature profile versus similarity variable for a shrinking boundary.
Figure 17. Temperature profile versus similarity variable for a shrinking boundary.
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Figure 18. Velocity profile versus similarity variable variation in D a 1 .
Figure 18. Velocity profile versus similarity variable variation in D a 1 .
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MDPI and ACS Style

Sachhin, S.M.; Mahabaleshwar, U.S.; Laroze, D.; Drikakis, D. Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94. Fluids 2024, 9, 241. https://doi.org/10.3390/fluids9100241

AMA Style

Sachhin SM, Mahabaleshwar US, Laroze D, Drikakis D. Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94. Fluids. 2024; 9(10):241. https://doi.org/10.3390/fluids9100241

Chicago/Turabian Style

Sachhin, Sudha Mahanthesh, Ulavathi Shettar Mahabaleshwar, David Laroze, and Dimitris Drikakis. 2024. "Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94" Fluids 9, no. 10: 241. https://doi.org/10.3390/fluids9100241

APA Style

Sachhin, S. M., Mahabaleshwar, U. S., Laroze, D., & Drikakis, D. (2024). Correction: Sachhin et al. Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection. Fluids 2024, 9, 94. Fluids, 9(10), 241. https://doi.org/10.3390/fluids9100241

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