Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet
Abstract
:1. Introduction
2. Mathematical Model
- (1)
- : Linear stretching.
- (2)
- : non-Linear stretching.
Engineering Coefficients
3. Numerical Procedure
4. Results and Discussion
5. Conclusions
- Improvement in the Casson parameter will decline the axial velocity in directions due to higher viscous force.
- The thermal distribution is improved with enhancement in the Casson parameter due to an increment in boundary layer thickness.
- Improved values of the Schmidt number will decline the concentration due to an increase in mass diffusivity.
- An increase in the values of the thermophoretic parameter affects the concentration profiles due to an increment in the temperature gradient.
- The rate of mass transfer will decrease with an upsurge in the values of the thermophoretic parameter.
- The rate of thermal distribution will improve with an increment in the Casson parameter due to an enhancement in the thickness of the boundary layer.
- The axial velocity and thermal distribution will be more in the case of , but a reverse trend is perceived in the case of concentration profile.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Aluminium oxide. | |
Sodium Alginate. | |
Stretching rate. | |
Concentration. | |
Concentration at wall. | |
Ambient concentration. | |
Specific heat. | |
Skin friction. | |
Diffusivity. | |
Thermal conductivity. | |
Thermophoretic constant. | |
Dimensionless velocity components. | |
Power law index. | |
Nusselt number. | |
Prandtl number. | |
Local Reynolds number. | |
Sherwood number. | |
Schmidt number. | |
Temperature. | |
Reference temperature. | |
Wall temperature. | |
Ambient temperature. | |
Thermophoretic velocity. | |
Greek Symbols | |
Casson parameter. | |
Dynamic viscosity. | |
Density. | |
Kinematic viscosity. | |
Similarity variable. | |
Dimensionless temperature and concentration. | |
Solid volume fraction. | |
Thermophoretic parameter. | |
Subscripts: | |
Fluid. | |
Nanofluid. | |
Solid particle. | |
Abbreviations | |
PDE | Partial differential equation. |
ODE | Ordinary differential equation. |
RKF-45 | Runge Kutta Felhberg 4th 5th order. |
TPD | Thermophoretic particle deposition. |
MHD | Magneto hydrodynamic. |
3D | Three dimensional. |
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Property | ||
---|---|---|
6.45 | - | |
989 | 3970 | |
4175 | 765 | |
0.613 | 40 |
Khan et al. [23] | Raju et al. [22] | Present Result | |
---|---|---|---|
1 | −1.414214 | −1.4142141 | −1.415192 |
3 | −2.297186 | −2.2971860 | −2.297297 |
Khan et al. [23] | Raju et al. [22] | Present Result | |
---|---|---|---|
1 | −1.414214 | −1.4142140 | −1.415192 |
3 | −2.297186 | −2.2971860 | −2.297297 |
1 | 0.428707 | 0.428707 | 23.723047 | 2.883644 | ||||
2 | 0.576782 | 0.576782 | 23.720796 | 3.072287 | ||||
3 | 0.01 | 0.1 | 0.8 | 0.1 | 0.694439 | 0.694439 | 23.718549 | 3.231165 |
0.01 | 0.694439 | 0.694439 | 23.718549 | 3.231092 | ||||
0.02 | 0.695638 | 0.695638 | 34.085641 | 4.164654 | ||||
0.03 | 0.696469 | 0.696469 | 42.056350 | 4.941831 | ||||
0.1 | 0.694439 | 0.694439 | 23.718549 | 3.231092 | ||||
0.2 | 0.940005 | 0.940005 | 23.712475 | 3.182007 | ||||
0.3 | 1.106068 | 1.106068 | 23.707350 | 3.148383 | ||||
0.8 | 0.694439 | 0.694439 | 23.718549 | 3.231092 | ||||
1.0 | 0.694439 | 0.694439 | 23.718549 | 3.873363 | ||||
1.2 | 0.694439 | 0.694439 | 23.718549 | 4.496217 | ||||
0.1 | 0.694439 | 0.694439 | 23.718549 | 3.231092 | ||||
0.2 | 0.694439 | 0.694439 | 23.718549 | 5.174942 | ||||
0.3 | 0.694439 | 0.694439 | 23.718549 | 7.125058 |
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Shankaralingappa, B.M.; Madhukesh, J.K.; Sarris, I.E.; Gireesha, B.J.; Prasannakumara, B.C. Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet. Micromachines 2021, 12, 1474. https://doi.org/10.3390/mi12121474
Shankaralingappa BM, Madhukesh JK, Sarris IE, Gireesha BJ, Prasannakumara BC. Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet. Micromachines. 2021; 12(12):1474. https://doi.org/10.3390/mi12121474
Chicago/Turabian StyleShankaralingappa, Bheemasandra M., Javali K. Madhukesh, Ioannis E. Sarris, Bijjanal J. Gireesha, and Ballajja C. Prasannakumara. 2021. "Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet" Micromachines 12, no. 12: 1474. https://doi.org/10.3390/mi12121474