Features of Radiative Mixed Convective Heat Transfer on the Slip Flow of Nanofluid Past a Stretching Bended Sheet with Activation Energy and Binary Reaction
Abstract
:1. Introduction
2. Description and Mathematical Modeling of the Problem
- Incompressible flow;
- Steady flow;
- Buoyancy flow (opposing and assisting flows);
- Permeable bended stretching sheet;
- Slip velocity;
- Nanofluid;
- Boundary-layer approximation;
- Boussinesq approximation.
3. Solution Methodology and Verification of the Code
4. Discussion of the Results
4.1. Interpretation of Velocity Profiles
4.2. Interpretation of Temperature Profiles
4.3. Interpretation of Concentration Profiles
4.4. Interpretation of Gradients in Terms of Bar Graphs
5. Final Remarks
- The velocity profile enhances for both ASF and OPF due to the higher impact of the radius curvature parameter; however, for the temperature and concentration profiles, a decreasing behavior is noticed.
- For increasing values of nanoparticle volume fraction, the temperature profile escalates, while velocity and concentration profiles decelerate for ASF and OPF.
- For ASF as well as OPF, the temperature profile significantly increases by incorporating the radiation parameter.
- With rising impact of the slip parameter, the shear stress output is smaller for the case of ASF as compared to the OPF.
- The heat transport rate improves by increasing the radiation parameter and radius of curvature parameter.
- The Arrhenius function factor, which appears in the activation energy parameter, causes the mass distribution to improve. However, as the reaction rate parameter improves, the mass distribution steadily decreases.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Radius of curvature (m) | |
Spatial or Curvilinear coordinates (m) | |
Velocity components (m/s) | |
Radiative heat flux | |
Wall stretching velocity (m/s) | |
Slip velocity (m/s) | |
Positive arbitrary constant (1/s) | |
Slip characteristic length (m) | |
Mass transpiration velocity (m/s) | |
Ambient temperature (K) | |
Ambient concentration | |
Temperature of the wall surface (K) | |
Temperature of the nanofluid (K) | |
Concentration of the nanofluid | |
Pressure (Pa or N/m2) | |
Specific heat at constant pressure (J/Kg. K) | |
Thermal conductivity (W/(m. K)) | |
Mass diffusion coefficient | |
Activation energy (W/m) | |
Chemical reaction rate | |
Mass suction/injection parameter | |
Mean absorption coefficient (1/m) | |
Dimensionless velocity | |
Prandtl number | |
Dimensionless concentration | |
Radius of curvature parameter | |
Schmidt number | |
Chemical reaction rate parameter | |
Activation energy parameter | |
Grashof number | |
Local Nusselt number | |
Skin friction coefficient | |
Local Reynolds number | |
Dimensionless temperature | |
Dimensionless pressure | |
Radiation parameter | |
Relative factor of the power-law index | |
Sherwood number | |
Heat flux | |
Greek symbols | |
Stefan-Boltzmann constant (W/(m2. K4)) | |
Kinematic viscosity (m2/s) | |
Thermal expansion coefficient (1/K) | |
Density (kg/m3) | |
Dynamic viscosity (N. s/m2) | |
Solid nanoparticle volume fraction | |
Pseudo-similarity variable | |
Velocity slip parameter | |
Temperature difference parameter | |
Mixed convection parameter | |
Mass flux | |
Shear stress | |
Acronyms | |
Cu | Copper |
Bvp4c | Boundary value problem of fourth-order |
CuO | Copper oxide |
MHD | Magneto-hydrodynamics |
MgO | Magnesium oxide |
Au | Gold |
ZnO | Zinc Oxide |
Al2O3 | Alumina |
H2O | Water |
ASF | Assisting flow |
2D | Two-dimensional |
OPF | Opposing flow |
MBLT | Momentum boundary layer thickness |
Subscripts | |
Regular based-fluid | |
Solid nanoparticles | |
Nanofluid | |
Wall boundary condition | |
Far-field condition | |
Superscript | |
‘ | Derivative with respect to |
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Properties | Alumina (Al2O3) | Water (H2O) |
---|---|---|
25.5 | 21 | |
40 | 0.613 | |
3970 | 997.1 | |
765 | 4179 | |
Pr | - | 6.2 |
Sanni et al. [33] | Zaheer et al. [34] | Present Results | |
---|---|---|---|
5 | 1.1507 | 1.1576 | 1.1507 |
10 | 1.0734 | 1.0735 | 1.0734 |
20 | 1.0355 | 1.0356 | 1.0356 |
30 | 1.0235 | 1.0235 | 1.0235 |
40 | 1.0176 | 1.0176 | 1.0175 |
50 | 1.0140 | 1.0141 | 1.0141 |
100 | 1.0070 | 1.0070 | 1.0070 |
200 | 1.0036 | 1.0036 | 1.0035 |
1000 | 1.0008 | 1.0008 | 1.0008 |
1.0000 | 1.0000 | 1.0000 |
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Khan, U.; Zaib, A.; Madhukesh, J.K.; Elattar, S.; Eldin, S.M.; Ishak, A.; Raizah, Z.; Waini, I. Features of Radiative Mixed Convective Heat Transfer on the Slip Flow of Nanofluid Past a Stretching Bended Sheet with Activation Energy and Binary Reaction. Energies 2022, 15, 7613. https://doi.org/10.3390/en15207613
Khan U, Zaib A, Madhukesh JK, Elattar S, Eldin SM, Ishak A, Raizah Z, Waini I. Features of Radiative Mixed Convective Heat Transfer on the Slip Flow of Nanofluid Past a Stretching Bended Sheet with Activation Energy and Binary Reaction. Energies. 2022; 15(20):7613. https://doi.org/10.3390/en15207613
Chicago/Turabian StyleKhan, Umair, Aurang Zaib, Javali K. Madhukesh, Samia Elattar, Sayed M. Eldin, Anuar Ishak, Zehba Raizah, and Iskandar Waini. 2022. "Features of Radiative Mixed Convective Heat Transfer on the Slip Flow of Nanofluid Past a Stretching Bended Sheet with Activation Energy and Binary Reaction" Energies 15, no. 20: 7613. https://doi.org/10.3390/en15207613