Magnetohydrodynamic Effects on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium
Abstract
:1. Introduction
2. Formulation of the Problem
Flow Analysis
3. Solution Methodology
3.1. Similarity Formulation
3.2. Solution Technique
4. Results and Discussion
4.1. Influence of Involved Parameters on Velocity Profile Temperature Profile , and Mass Concentration
4.2. Influence of Parameters on Skin Friction Coefficient , Nusselt Number , and Sherwood Number
5. Conclusions
- rises as and rises, but the reverse scenario is noted against the elevating values of and .
- is elevated as and are raised, but the reverse scenario is noted owing to increase in and .
- is intensified as is augmented but falls down as and are elevated.
- It is concluded that the skin friction coefficient increases with increasing values of and , but the opposite trend is seen for increasing magnitudes of .
- The Nusselt number is elevated against elevating values of and the opposite action is viewed for increasing and .
- The Sherwood number fleshes out an increasing attitude for increasing and shows the decreasing trend for augmenting and .
- The present results for such a special case are compared with the previously published results and there is nice agreement between them, which validates the accuracy of the current results.
- In the future, this model can be extended to nanofluid and hybrid nanofluid with different fluid characteristics.
- This can also be extended to analyze the impact of reduced gravity on this model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Nomenclature | Local inertial coefficient |
Ambient temperature | Mass diffusion coefficient |
Wall concentration | Nussle number |
Ambient concentration | Mean temperature of fluid |
Wall temperature | Greeks |
Angle of inclination | Volumetric coefficient concentration expansion |
Velocity components in and directions | Dimensionless temperature |
Buoyancy ratio parameter | Volumetric coefficient thermal expansion |
Viscoelastic parameter | Dimensionless mass concentration |
Concentration in boundary layer | Thermal conductivity |
Schmidt number | Dynamic viscosity |
Coefficient of inertia | Third-grade fluid parameter |
Specific heaconstant pressure | Electrical conductivity |
Coordinates | Thermal diffusivity |
Sherwood number | Kinematic viscosity |
Cross viscous parameter | ρ Fluid density |
Skin friction | Material moduli |
Coordinates | Subscripts |
Richardson number | Ambient conditions |
Drag Coefficient | Wall conditions |
Reynolds number | |
T Fluid temperature in boundary layer | |
Prandtl number | |
Gravitational acceleration | |
Permeability parameter | |
Grashof number | |
Porous medium permeability |
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Pr | Magyari and Keller [31] | Present Study |
---|---|---|
1.0 | 0.9547 | 0.9551 |
3 | 1.8691 | 1.8121 |
5 | 2.5001 | 2.5577 |
10 | 3.6604 | 3.6868 |
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Abbas, A.; Jeelani, M.B.; Alharthi, N.H. Magnetohydrodynamic Effects on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium. Magnetochemistry 2022, 8, 61. https://doi.org/10.3390/magnetochemistry8060061
Abbas A, Jeelani MB, Alharthi NH. Magnetohydrodynamic Effects on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium. Magnetochemistry. 2022; 8(6):61. https://doi.org/10.3390/magnetochemistry8060061
Chicago/Turabian StyleAbbas, Amir, Mdi Begum Jeelani, and Nadiyah Hussain Alharthi. 2022. "Magnetohydrodynamic Effects on Third-Grade Fluid Flow and Heat Transfer with Darcy–Forchheimer Law over an Inclined Exponentially Stretching Sheet Embedded in a Porous Medium" Magnetochemistry 8, no. 6: 61. https://doi.org/10.3390/magnetochemistry8060061