Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect
Abstract
:1. Introduction
2. Mathematical Framework
2.1. Basic Equation
2.2. Thermophysical Properties
2.3. Similarity Solution
3. Stability of the Solutions
3.1. Unsteady-State Problem
3.2. New Similarity Transformation
3.3. Introducing Linear Eigenvalue Equations
3.4. Relaxation of Boundary Condition
4. Numerical Solutions and Discussions
5. Conclusions
- The presence of double solutions is noticeable for a stretching and shrinking sheet when suction parameter is imposed.
- A stability analysis was carried out and the first solution proved to be stable, whereas the other solution was not.
- An increase in the Cu nanoparticle volume fraction in the dusty nanofluid has a tendency to improve the local Nusselt number for all range of , and to increase the local skin friction for shrinking sheet; however, the opposite is true for a stretching sheet.
- The simultaneous increase of velocity and thermal slip parameters decrease the local Nusselt number for fluid phase.
- The similarity solutions can be widened with an increase in Cu nanoparticle volume fraction and slip parameters (velocity and thermal ), thereby delaying boundary layer separation.
- The momentum thickness in fluid phase decreases and dust phase increases as velocity fluid interaction parameter increases.
- An upsurge of fluid interaction for temperature parameter decreases the thermal boundary layer thickness of the fluid phase, while it does the opposite in the dust phase.
- The mass concentration of dust particle decreases the momentum thickness but increases the thermal thickness in both phases.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Properties | Nanofluid | Hybrid Nanofluid |
---|---|---|
Density | ||
Heat capacity | ||
Dynamic viscosity | ||
Thermal conductivity | where |
Physical Properties | Cu | Water | Al2O3 |
---|---|---|---|
(Wm-1K-1) | 400 | 0.613 | 40 |
(J kg-1K-1) | 385 | 4179 | 765 |
(kg m-3) | 8933 | 997.1 | 3970 |
Hayat et al. [65] (Homotopy Analysis Method) | Ibrahim and Shankar [53] (Shooting) | Present Result (Bvp4c) | |
---|---|---|---|
0 | −1.000000 | −1.0000 | −1.000000 |
0.1 | −0.872082 | −0.8721 | −0.872083 |
0.2 | −0.776377 | −0.7764 | −0.776377 |
0.5 | −0.591195 | −0.5912 | −0.591196 |
2.0 | −0.283981 | −0.2840 | −0.283981 |
5.0 | −0.144841 | −0.1448 | −0.144842 |
Gireesha et al. [57] | Naramgari and Sulochana [30] | Present Result | |
---|---|---|---|
0.72 | 1.0885 | 1.088561 | 1.088527 |
1 | 1.3333 | 1.333333 | 1.333333 |
10 | 4.7968 | 4.796817 | 4.796873 |
1st Solution | 2nd Solution | ||
---|---|---|---|
0 | −1.6121 | 0.0026 | −0.0027 |
−1.612 | 0.0131 | −0.0130 | |
−1.61 | 0.0590 | −0.0580 | |
0.01 | −1.6677 | 0.0115 | −0.0114 |
−1.667 | 0.0363 | −0.0359 | |
−1.66 | 0.1158 | −0.1120 | |
0.02 | −1.7207 | 0.0085 | −0.0085 |
−1.72 | 0.0359 | −0.0355 | |
−1.7 | 0.1924 | −0.1825 |
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Anuar, N.S.; Bachok, N.; Pop, I. Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect. Mathematics 2021, 9, 643. https://doi.org/10.3390/math9060643
Anuar NS, Bachok N, Pop I. Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect. Mathematics. 2021; 9(6):643. https://doi.org/10.3390/math9060643
Chicago/Turabian StyleAnuar, Nur Syazana, Norfifah Bachok, and Ioan Pop. 2021. "Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect" Mathematics 9, no. 6: 643. https://doi.org/10.3390/math9060643
APA StyleAnuar, N. S., Bachok, N., & Pop, I. (2021). Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect. Mathematics, 9(6), 643. https://doi.org/10.3390/math9060643