Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study
Abstract
:1. Introduction
2. Mathematical Modeling
3. Solution Procedure via CM
4. Results and Discussion
5. Conclusions
- The velocity is enhanced due to the higher impact of the parameter Ha (Hartmann number), while a different kind of behavior, actually a drop, is provided by the parameter f0.
- The parameter Nt caused an efficient enhancement in the temperature distribution, while the parameters Nt and f0 provided a drop in the temperature that actually affected the rate of heat transmission.
- Dual behavior of concentration is noted for parameter b, while it can be noted that mixed increasing behavior is available for the concentration against Le.
- The concentration and velocity profiles dropped due to the increasing values of parameter b, but the impact of parameter b is more significant on concentration. It showed a dual behavior for concentration after a particular stretch.
- It is observed that the proposed methodology is found to be really effective to deal with nonlinear mechanical or fluid dynamical problems.
- The presented method can be further used for a class of nonlinear problems arising in mechanics.
- The proposed scheme can be extended to investigate the solution of channel flow, fractional-order fluid flow, unsteady cavity models, etc.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Distance between two plates | |
and | Velocity components in - and -directions |
Free stream velocity | |
Temperature of the fluid | |
Concentration of the fluid | |
B | Magnetic field |
Pressure | |
Kinematic viscosity | |
Density | |
Brownian parameter | |
Thermophoresis diffusion parameter | |
Free stream temperature | |
Heat flux | |
Velocity at sensor surface | |
Ha | Hartmann number |
Squeezed parameter | |
Prandtl number | |
Thermophoretic parameter | |
Brownian motion parameter | |
Lewis number | |
Permeable velocity | |
Re | Local Reynolds number |
CM | Collocation method |
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0 | 0.5 | −0.5 | 3.97 | 0.3 | 0.5 | 2 | 1.41209 | 0.53992 | - |
1 | - | - | - | - | - | - | 1.60239 | 0.55369 | - |
2 | - | - | - | - | - | - | 1.77102 | 0.56518 | - |
0.5 | 0 | - | - | - | - | - | 1.71854 | 0.45771 | - |
- | 0.5 | - | - | - | - | - | 1.60239 | 0.55370 | - |
- | 1 | - | - | - | - | - | 1.48114 | 0.67073 | - |
- | 0.25 | −0.5 | - | - | - | - | 1.66109 | 0.50362 | - |
- | - | 0.5 | - | - | - | - | 1.09294 | −0.22818 | - |
- | - | −0.5 | 3 | - | - | - | - | 0.48136 | - |
- | - | - | 5 | - | - | - | - | 0.53414 | - |
- | - | - | 7 | - | - | - | - | 0.59050 | - |
- | - | - | 6.2 | 0.1 | - | - | - | 2.86340 | 0.2000 |
- | - | - | - | 0.2 | - | - | - | 0.35443 | 0.4000 |
- | - | - | - | 0.3 | - | - | - | 0.56881 | 0.6000 |
- | - | - | - | 0.3 | 0.1 | - | - | - | 3.0000 |
- | - | - | - | - | 0.2 | - | - | - | 1.5000 |
- | - | - | - | - | 0.3 | - | - | - | 1.0000 |
- | - | - | - | - | 0.5 | 0 | - | 3.09699 | - |
- | - | - | - | - | - | 2 | - | 0.56881 | - |
- | - | - | - | - | - | 5 | - | 0.65213 | - |
Veclocity | Temperature | Concentration | |
---|---|---|---|
0.00 | 0.00000000 | 1.80602974 | −0.11719518 |
0.30 | 0.40286279 | 1.46945390 | 0.00092259 |
0.60 | 0.66809369 | 0.99463258 | 0.06836315 |
0.90 | 0.82887854 | 0.47417323 | 0.08077955 |
1.20 | 0.91848603 | 0.13083488 | 0.04128107 |
1.50 | 0.96427592 | 0.01941746 | 0.00878368 |
1.80 | 0.98566979 | 0.00170315 | 0.00088685 |
2.10 | 0.99478720 | 0.00009441 | 0.00005156 |
2.40 | 0.99832789 | 0.00000335 | 0.00000187 |
2.70 | 0.99958484 | 0.00000007 | 0.00000004 |
3.00 | 1.00000000 | 0.00000000 | 0.00000000 |
[47] | [48] | [49] | [50] | [51] | [52] | Present | |
---|---|---|---|---|---|---|---|
0.0 | - | - | - | 1.0005 | 1.00000 | 1.00000 | 1.00000 |
0.2 | - | - | - | 1.0685 | 1.06874 | 1.06801 | 1.06871 |
0.4 | - | - | - | 1.1349 | 1.13521 | 1.13469 | 1.13522 |
0.6 | - | - | - | 1.1992 | 1.19930 | 1.19912 | 1.19924 |
0.8 | 1.261512 | 1.26104 | 1.261479 | - | 1.26099 | 1.26104 | 1.26092 |
1.2 | 1.378052 | 1.37772 | 1.377850 | - | 1.37755 | 1.37772 | 1.37761 |
2.0 | - | - | - | - | 1.58740 | 1.58737 | 1.58738 |
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Gao, F.; Yu, D.; Sheng, Q. Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study. Mathematics 2022, 10, 1556. https://doi.org/10.3390/math10091556
Gao F, Yu D, Sheng Q. Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study. Mathematics. 2022; 10(9):1556. https://doi.org/10.3390/math10091556
Chicago/Turabian StyleGao, Fengkai, Dongmin Yu, and Qiang Sheng. 2022. "Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study" Mathematics 10, no. 9: 1556. https://doi.org/10.3390/math10091556
APA StyleGao, F., Yu, D., & Sheng, Q. (2022). Analytical Treatment of Unsteady Fluid Flow of Nonhomogeneous Nanofluids among Two Infinite Parallel Surfaces: Collocation Method-Based Study. Mathematics, 10(9), 1556. https://doi.org/10.3390/math10091556