Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder
Abstract
:1. Introduction
2. Mathematical Formulation
3. Numerical Method
4. Model Validity
5. Results and Discussions
6. Conclusions
- The mixed convection parameter enhances the velocity profile.
- The Prandtl number reduces the temperature distribution across the flow.
- The velocity profile abruptly decreases in the presence of a velocity slip.
- The temperature profile diminishes due to the thermal slip effect.
- The skin friction was observed to increase for larger values of velocity slip and mixed convection parameter.
- The Nusselt number increased due to an increase of magnetic, velocity–temperature slip, and radiation parameters.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Ambient temperature (°C) | |
C | Curvature parameter (m−1) |
Cylinder temperature (°C) | |
θ | Dimensionless temperature (-) |
Density of fluid (kg m−3) | |
σ | Electrical conductivity (S m−1) |
υ | Kinematic viscosity (m2 s−1) |
B | Magnetic field (Tesla) |
M | Magnetic parameter (W m−2) |
λ | Mixed convective parameter (W m−2 K−1) |
MHD | Magnetohydrodynamic (-) |
BLF | Boundary layer flow (-) |
Nu | Nusselt number (-) |
Pr | Prandtl number (-) |
Radiative heat flux (kg s−3) | |
K | Radiation parameter (-) |
Re | Reynolds number (-) |
ν | r-direction velocity (m s−1) |
Specific heat (J kg−1 K−1) | |
η | Self-reliant similarity variable (-) |
ψ | Stream function (-) |
Surface shear stress (pascal) | |
Surface heat flux (W m−2) | |
Skin friction coefficient (-) | |
β | Thermal expansion coefficient (-) |
γ | Thermal slip parameter (-) |
L, S | Velocity and temperature slip length (m) |
δ | Velocity slip factor (m) |
u | z-direction velocity (m s−1) |
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M | Analytical Solution | Numerical Solution | Error |
---|---|---|---|
0 | −1.00000 | −1.00001 | −0.00001 |
0.5 | −1.11803 | −1.11803 | −0.00000 |
1.0 | −1.41421 | −1.41421 | −0.00000 |
1.5 | −1.80277 | −1.80278 | −0.00001 |
n | C | M | δ | λ | Pr | γ | K | −f″(0) | −θ′(0) |
---|---|---|---|---|---|---|---|---|---|
1 | 1.12685 | 0.33489 | |||||||
2 | 1.20155 | 0.38309 | |||||||
3 | 1.26145 | 0.41789 | |||||||
2 | 1 | 1.20155 | 0.38309 | ||||||
2 | 1.33150 | 0.43739 | |||||||
3 | 1.44063 | 0.47790 | |||||||
1 | 1 | 1.20155 | 0.38309 | ||||||
2 | 1.48689 | 0.35397 | |||||||
3 | 1.73211 | 0.33479 | |||||||
1 | 0.1 | 1.66038 | 0.40184 | ||||||
0.5 | 0.94980 | 0.37065 | |||||||
1 | 0.63069 | 0.35164 | |||||||
0.3 | −2 | 1.71442 | 0.34021 | ||||||
0 | 1.20155 | 0.38309 | |||||||
2 | 0.83701 | 0.43027 | |||||||
0 | 0.1 | 1.20155 | 0.31291 | ||||||
0.5 | 0.83701 | 0.38309 | |||||||
1 | 1.20155 | 0.44830 | |||||||
0.5 | 1 | 1.20155 | 0.38309 | ||||||
2 | 1.20155 | 0.27698 | |||||||
3 | 1.20155 | 0.21691 | |||||||
1 | 1 | 1.20155 | 0.38309 | ||||||
2 | 1.20155 | 0.32934 | |||||||
3 | 1.20155 | 0.30183 |
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Tamoor, M.; Kamran, M.; Rehman, S.; Farooq, A.; Khan, R.; Lee, J.R.; Shin, D.Y. Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder. Processes 2021, 9, 1077. https://doi.org/10.3390/pr9061077
Tamoor M, Kamran M, Rehman S, Farooq A, Khan R, Lee JR, Shin DY. Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder. Processes. 2021; 9(6):1077. https://doi.org/10.3390/pr9061077
Chicago/Turabian StyleTamoor, Muhammad, Muhammad Kamran, Sadique Rehman, Aamir Farooq, Rewayat Khan, Jung Rye Lee, and Dong Yun Shin. 2021. "Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder" Processes 9, no. 6: 1077. https://doi.org/10.3390/pr9061077
APA StyleTamoor, M., Kamran, M., Rehman, S., Farooq, A., Khan, R., Lee, J. R., & Shin, D. Y. (2021). Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder. Processes, 9(6), 1077. https://doi.org/10.3390/pr9061077