MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet
Abstract
:1. Introduction
2. Mathematical Modeling
3. Spectral Relaxation Method
Algorithm 1: Spectral Relaxation Method |
Step 1: Introducing the transformation: . Step 2: Depict the original equation in terms of to decrease the order of the momentum equation for . Step 3: Assume that , , , are similar to the former iteration (indicated by , , , and ). Step 4: Construct an iteration scheme for , , , and . Step 5: Assume that only linear terms in , , , and are to be estimated at the present iteration scale (indicated by , , , ), and all other terms are presumed to be similar to the former iteration. |
4. Results and Discussion
5. Conclusions
- The comparison values of heat rate transfer were in good agreement with the former study, and hence led to the confidence of the present results to be reported further.
- The resultant velocity diminished with the increments in the magnetic parameter.
- Fluid temperature increased as the magnetic parameter, thermophoresis, and Brownian motion parameters increased.
- The concentration was reduced with the boost in the Lewis number and Brownian motion parameter.
- The concentration was increased with the increment in the Prandtl number, thermophoresis, and magnetic parameters.
- The density of the motile microorganism is a decreasing function of the Prandtl number, Lewis number, Peclet number, bioconvection Lewis number, and bioconvection parameter.
- The residual errors of , , , and were iteration dependent.
- For future research, it is suggested for the present study to consider all possible multiple solutions or dual solutions. This is driven by the fact that the multiple solutions cannot be seen experimentally and can only be obtained by using numerical simulation.
- It was also proposed for the stability of multiple solutions to be included as one of the main objective studies for future work. Stability analysis is important for identifying the reliability of the multiple solutions, which depend on the assumptions of the physical model.
Author Contributions
Funding
Conflicts of Interest
References
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Pr | Bidin and Nazar [30] | Magyari and Keller [31] | El-Aziz [32] | Loganthan and Vimala [33] | Present Study | |
---|---|---|---|---|---|---|
SRM | Bvp4c | |||||
1 | 0.9547 | 0.954782 | 0.954785 | 0.954955 | 0.9548 | 0.954782 |
1.5 | 1.2348 | 1.234755 | ||||
2 | 1.4714 | 1.4715 | 1.471460 | |||
2.5 | 1.6802 | 1.680229 | ||||
3 | 1.8691 | 1.869075 | 1.869074 | 1.869074 | 1.8691 | 1.869073 |
5 | 2.500135 | 2.500132 | 2.500184 | 2.5001 | 2.500131 | |
7 | 3.0133 | 3.013277 | ||||
10 | 3.660379 | 3.660372 | 3.660379 | 3.6604 | 3.660372 | |
20 | 5.3016 | 5.301625 |
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Ferdows, M.; Zaimi, K.; Rashad, A.M.; Nabwey, H.A. MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet. Symmetry 2020, 12, 692. https://doi.org/10.3390/sym12050692
Ferdows M, Zaimi K, Rashad AM, Nabwey HA. MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet. Symmetry. 2020; 12(5):692. https://doi.org/10.3390/sym12050692
Chicago/Turabian StyleFerdows, Mohammad, Khairy Zaimi, Ahmed M. Rashad, and Hossam A. Nabwey. 2020. "MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet" Symmetry 12, no. 5: 692. https://doi.org/10.3390/sym12050692