Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management †
Abstract
:1. Introduction
- (i)
- incorporate the micropolar fluid as host fluid,
- (ii)
- analyze with and without quadratic convection on the dynamic of micropolar fluid, and
- (iii)
- consider the significant effects of magnetohydrodynamics subject to a rotating frame of reference.
Research Questions
- (1)
- To explore the significance of material, magnetic, and rotating parameters on the dynamic of microplar fluid: the case of linear and quadratic convection.
- (2)
- To observe the influence of Lorentz and Coriolis forces on micro-rotation profile: the case of linear and quadratic convection.
- (3)
- To observe the variations in skin friction coefficients and Nusselt number against growing values of rotating, magnetic, thermal buoyancy, and material parameters in the case of linear and quadratic convection.
2. Mathematical Formulation
3. Solution Procedure
4. Results and Discussion
- Case 1: with linear convection (, ).
- Case 2: with quadratic convection (, ).
5. Conclusions
- The primary () and secondary () velocities significantly decrease along with rising values of magnetic (M) parameter, rotating () parameter, and in case of linear convection. However, has a growing tendency for the material parameter (K), thermal buoyancy (), and quadratic convection case. The magnitude of has a decreasing behavior for nonlinear convection and material parameter.
- The incremented inputs of rotating, magnetic, and the case of without quadratic convection are augmented the micro-rotation distribution. However, for thermal buoyancy and nonlinear convection case, the micro-rotation profile () decreases.
- The fluid particles’ temperature increases with higher inputs of rotating and magnetic parameters in linear convection case but is reduced against growing strength of rotating () and material (K) parameters in quadratic convection case.
- Along the x direction, the skin friction coefficient decreases with the amplified value of magnetic, rotating, and material parameters in the linear convection case. Along the y direction, the skin friction coefficient is raised by enlargement in magnetic and material parameters without quadratic convection case. However, it decreases for thermal buoyancy and rotating parameters in the quadratic convection case.
- The magnitude of the Nusselt number is reduced with a higher contribution of rotating and magnetic parameters in the linear convection case. However, it increases against material and thermal buoyancy in the nonlinear convection case.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
T | non-dimensional temperature, K |
temperature away from the surface, K | |
Nusselt number | |
skin friction at x-direction | |
skin friction at y-direction | |
kinematic viscosity of nanofluid, ms | |
specific heat at constant pressure, JKgK | |
electrical conductivity of fluid, KgmA | |
Prandtl number | |
dynamic viscosity of fluid, Kgms | |
surface heat flux, Wm | |
thermal conductivity of the fluid, WmK | |
temperature at surface, K | |
Uniform magnetic field | |
angular velocity, s | |
Velocity components | |
velocity of stretching sheet, ms | |
Density of nanofluid, Kgm | |
Uniform magnetic field | |
K | Material parameter |
Cartesian co-ordinates | |
rotation parameter | |
dimensionless variable | |
M | magnetic parameter |
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Ali, B.; Ahammad, N.A.; Awan, A.U.; Guedri, K.; Tag-ElDin, E.M.; Majeed, S. Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management. Nanomaterials 2022, 12, 3100. https://doi.org/10.3390/nano12183100
Ali B, Ahammad NA, Awan AU, Guedri K, Tag-ElDin EM, Majeed S. Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management. Nanomaterials. 2022; 12(18):3100. https://doi.org/10.3390/nano12183100
Chicago/Turabian StyleAli, Bagh, N. Ameer Ahammad, Aziz Ullah Awan, Kamel Guedri, ElSayed M. Tag-ElDin, and Sonia Majeed. 2022. "Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management" Nanomaterials 12, no. 18: 3100. https://doi.org/10.3390/nano12183100
APA StyleAli, B., Ahammad, N. A., Awan, A. U., Guedri, K., Tag-ElDin, E. M., & Majeed, S. (2022). Dynamics of Rotating Micropolar Fluid over a Stretch Surface: The Case of Linear and Quadratic Convection Significance in Thermal Management. Nanomaterials, 12(18), 3100. https://doi.org/10.3390/nano12183100