Effects of Joule Heating, Viscous Dissipation, and Activation Energy on Nanofluid Flow Induced by MHD on a Vertical Surface
Abstract
:1. Introduction
2. Mathematical Formulation
3. Numerical Method
4. Results and Discussion
5. Conclusions
- As the magnetic parameter increases, the velocity profile over the vertical surface decreases.
- The temperature of the fluid rises as the magnetic parameters and Eckert number increases.
- The magnetic parameter, Eckert number, activation energy, Schmidt number, thermal radiation, and Prandtl number all rise as the solute concentration profile rises.
- When the Schmidt number, activation energy, radiation parameter, Prandtl number, and Eckert number increases, the fluid’s nanoparticle concentration decreases.
- Skin friction, local Sherwood number increase the Eckert number values as the Biot number increases.
- As Bi and Rd are increased, skin friction and the local Nusselt number increased.
- Skin friction and Nusselt number decrease upon increasing , Sc; nanoparticle Sherwood number increases as Sc increases.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Strength of magnetic field (kgsm) | |
C | Concentration |
Local Reynolds number | |
Schmidt number | |
Thermal radiation parameter | |
T | Temperature(K) |
Radiative heat flux | |
Brownian diffusion coefficient | |
Thermophoretic diffusion coefficient (ms) | |
Prandtl number of base fluid | |
E | Nondimensional activation energy |
n | Fitted rate constant |
Activation energy | |
Dimensionless velocity | |
Thermophoresis parameter | |
Local Grashof number | |
Buoyancy ratio parameter | |
g | Gravitational acceleration (ms) |
K | Boltzmann constant |
Regular buoyancy parameter | |
K’ | Mean absorption coefficient |
k | Thermal conductivity (mkgsK) |
Reaction rate | |
M | Magnetic field parameter |
Brownian diffusion parameter |
Greek Symbols
Mixed convection parameter | |
Dimensionless reaction rate | |
Dimensionless solute concentration | |
Temperature difference parameter | |
Dimensionless temperature | |
Kinematic viscosity (ms) | |
Effective heat capacity of the nanoparticle material | |
Heat capacity of the base fluid | |
Electrical conductivity | |
T | Ratio of the effective heat capacity of the fluid and the heat capacity of |
the nanoparticle material | |
Stefan–Boltzmann constant (WmK) | |
Thermal diffusivity of the base fluid (ms) | |
Density of the fluid (kgm) | |
Coefficient of thermal expansion (K) | |
Nanoparticle density | |
Dimensionless nanoparticle concentration |
Subscripts
w | Condition at a wall |
∞ | Condition at free stream |
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Pr | Nt | E | n | Mustafa et al. [36] | Devi et al. [20] | Present Study | ||
---|---|---|---|---|---|---|---|---|
2 | 0.5 | 1 | 1 | 0.5 | 0.5 | 0.706605 | 0.706831 | 0.706708 |
4 | 0.935952 | 0.936056 | 0.936052 | |||||
7 | 1.132787 | 1.132900 | 1.132892 | |||||
10 | 1.257476 | 1.257032 | 1.257374 | |||||
5 | 0.1 | 1 | 1 | 0.5 | 0.5 | 1.426267 | 1.426012 | 1.426112 |
0.5 | 1.013939 | 1.038594 | 1.038649 | |||||
0.7 | 0.846943 | 0.846593 | 0.846547 | |||||
1.0 | 0.649940 | 0.649752 | 0.649733 | |||||
10 | 0.5 | 1 | 2 | 0.5 | 0.0 | 1.032281 | 1.032085 | 1.032264 |
0.5 | 1.056704 | 1.056294 | 1.056327 | |||||
3.0 | 1.154539 | 1.154956 | 1.154851 | |||||
5.0 | 1.215937 | 1.216012 | 1.216242 |
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Jayanthi, S.; Niranjan, H. Effects of Joule Heating, Viscous Dissipation, and Activation Energy on Nanofluid Flow Induced by MHD on a Vertical Surface. Symmetry 2023, 15, 314. https://doi.org/10.3390/sym15020314
Jayanthi S, Niranjan H. Effects of Joule Heating, Viscous Dissipation, and Activation Energy on Nanofluid Flow Induced by MHD on a Vertical Surface. Symmetry. 2023; 15(2):314. https://doi.org/10.3390/sym15020314
Chicago/Turabian StyleJayanthi, Senthil, and Hari Niranjan. 2023. "Effects of Joule Heating, Viscous Dissipation, and Activation Energy on Nanofluid Flow Induced by MHD on a Vertical Surface" Symmetry 15, no. 2: 314. https://doi.org/10.3390/sym15020314
APA StyleJayanthi, S., & Niranjan, H. (2023). Effects of Joule Heating, Viscous Dissipation, and Activation Energy on Nanofluid Flow Induced by MHD on a Vertical Surface. Symmetry, 15(2), 314. https://doi.org/10.3390/sym15020314