Microstructure and Inertial Characteristics of MHD Suspended SWCNTs and MWCNTs Based Maxwell Nanofluid Flow with Bio-Convection and Entropy Generation Past a Permeable Vertical Cone
Abstract
:1. Introduction
2. Mathematical Analysis
3. Entropy Generation Modeling
4. Engineering Quantities
4.1. Skin Friction Coefficients CFx
4.2. Heat Transfer Rate
4.3. Mass Transfer Rate
4.4. Local Density of Motile Microorganisms
5. Solution Technique
6. Validation of the Results
7. Discussion
7.1. Temperature
7.2. Micro Rotation Profile
7.3. Concentration
7.4. Local Density of Motile Microorganisms
7.5. Entropy Optimization
7.6. Engineering Quantities
7.7. Surface Drag Force
7.8. Heat Transfer Rate
7.9. Mass Transfer Rate
7.10. Local Density of Motile Microorganisms Nnx
8. Conclusions
- The motion of the nanoparticle increases for enlarging values of solid volume fraction (Φ).
- For a larger value of magnetic parameter (M) the Lorentz forces enhance which raises the forces of resistance of the Maxwell micropolar motion which in turn reduces velocity f′(η).
- The augmented Nr reduced the fluid motion.
- The momentum boundary layer reduces with enhances value of k1.
- Micro rotation velocity S(η) augmented with a higher value of K, γ*, and α.
- Augmentation in the θ(η) with enhancement radiation parameter Rd is observed.
- The higher value of Ec amplified the kinetic energy of CNTs Maxwell micropolar nanofluid molecules, which thus enhanced the heat transmission rate.
- The augmented rate of Gr reduces the concentration of Maxwell micropolar nanofluid.
- As the estimate of the number of Peclets increases, the number of motion densities also increases.
- With the rise in estimations of Pe, h(η) are increases.
- For both CNTs, f′(η) intensifies against rising values of suction. For rising values of Nr, θ(η) is reducing.
- For these CNTs, g(η) is reduced on the increasing of n.
- For the growth estimates of Nr, Shx is reduced and raises against numerical values of Cr.
- For solid volume fraction Cf is increased.
- Magnetic force M reduces Nux.
- A comparison between the present and previous outcomes for justification is given in Table 1.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
Prandtl number | |
Porous parameter | |
Magnetic parameter | |
Schmidt number | |
Solutal stratification | |
Vortex velocity or material parameter | |
Heat suction/Injection parameter | |
Bio-convection Lewis number | |
Radiation parameter | |
Bio-convection Rayleigh number | |
Buoyancy ratio parameter | |
Bio-convection Rayleigh number | |
Chemical reaction parameter | |
Boit number | |
Bio-convection Peclet number | |
Bio-convection constant | |
Temperature difference parameter | |
Brinkman number | |
concentration difference parameter, and | |
diffusive constant parameter | |
Reynold number |
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Sc | Ramzan et al. [21] | Present Results | ||
---|---|---|---|---|
−g′ (0) SWCNT | −g′ (0) MWCNT | −g′ (0) SWCNT | −g′ (0) MWCNT | |
0.1 | 0.31891 | 0.31882 | 0.3189450 | 0.3188567 |
0.5 | 0.50221 | 0.50155 | 0.5022674 | 0.5015768 |
0.9 | 0.74207 | 0.74087 | 0.7420467 | 0.7408564 |
Material | Water | SWCNT | MWCNT |
---|---|---|---|
Cp (j/kgK) | 4179 | 425 | 796 |
ρ (kg/m3) | 997.1 | 2600 | 1600 |
k (W/mK) | 0.613 | 6600 | 3000 |
Φ | k1 | V0 | Rb | C | ||
---|---|---|---|---|---|---|
SWCNTs | MWCNTs | |||||
0.01 | 0.5 | 1.0 | 0.1 | 0.1 | 1.8355 | 1.7511 |
0.03 | – | – | – | – | 2.2996 | 1.8007 |
0.05 | – | – | – | – | 2.4875 | 1.8673 |
– | 0.5 | – | – | – | 1.1596 | 1.1465 |
– | 0.7 | – | – | – | 1.4990 | 1.4987 |
– | 0.9 | – | – | – | 1.8355 | 1.8165 |
– | – | 0.5 | – | – | 2.8463 | 2.7389 |
– | – | 0.6 | – | – | 2.5630 | 2.5314 |
– | – | 0.7 | – | – | 2.3591 | 2.3284 |
– | – | – | 0.2 | – | 2.9477 | 2.2959 |
– | – | – | 0.3 | – | 1.9302 | 1.9281 |
– | – | – | 0.4 | – | 1.9201 | 1.8890 |
– | – | – | – | 0.1 | 2.1976 | 2.0633 |
– | – | – | – | 0.2 | 2.0917 | 2.0528 |
– | – | – | – | 0.3 | 2.0750 | 2.0450 |
Φ | Rd | B1 | M | Ec | ||
---|---|---|---|---|---|---|
SWCNTs | MWCNTs | |||||
0.01 | 0.1 | 1.0 | 0.1 | 0.5 | 0.0122 | 0.0138 |
0.03 | – | – | – | – | 0.0200 | 0.0142 |
0.05 | – | – | – | – | 0.0222 | 0.0153 |
– | 0.2 | – | – | – | 0.0205 | 0.0323 |
– | 0.3 | – | – | – | 0.0232 | 0.0181 |
– | 0.4 | – | – | – | 0.0290 | 0.0160 |
– | – | 0.5 | – | – | 0.0134 | 0.0133 |
– | – | 0.7 | – | – | 0.0137 | 0.0138 |
– | – | 1.0 | – | – | 0.0139 | 0.0177 |
– | – | – | 0.1 | – | 0.0122 | 0.0119 |
– | – | – | 0.2 | – | 0.0139 | 0.0138 |
– | – | – | 0.3 | – | 0.0142 | 0.0141 |
– | – | – | – | 0.1 | 0.0116 | 0.0115 |
– | – | – | – | 0.5 | 0.0139 | 0.0138 |
– | – | – | – | 1.0 | 0.0159 | 0.0158 |
Sc | Gr | n | Nr | ||
---|---|---|---|---|---|
SWCNTs | MWCNTs | ||||
0.1 | 0.1 | 0.1 | 0.5 | 0.3430 | 0.3428 |
0.5 | – | – | – | 0.6290 | 0.6102 |
0.9 | – | – | – | 0.9227 | 0.8932 |
– | 0.1 | – | – | 0.6290 | 0.6102 |
– | 0.2 | – | – | 0.6977 | 0.6972 |
– | 0.3 | – | – | 0.7513 | 0.7508 |
– | – | 0.0 | – | 0.6290 | 0.6274 |
– | – | 0.1 | – | 0.6147 | 0.6102 |
– | – | 0.2 | – | 0.5782 | 0.6066 |
– | – | – | 0.6 | 0.6072 | 0.6187 |
– | – | – | 0.7 | 0.6005 | 0.6589 |
– | – | – | 0.8 | 0.5954 | 0.6033 |
Lb | Pe | Rb | δ | ||
---|---|---|---|---|---|
SWCNTs | MWCNTs | ||||
0.5 | 0.5 | 0.1 | 0.1 | 0.7525 | 0.7515 |
0.6 | – | – | – | 0.8386 | 0.8375 |
0.7 | – | – | – | 0.9640 | 0.8806 |
– | 0.1 | – | – | 0.5504 | 0.5175 |
– | 0.2 | – | – | 0.5602 | 0.5760 |
– | 0.3 | – | – | 0.6074 | 0.6779 |
– | – | 0.0 | – | 0.7493 | 0.7483 |
– | – | 0.1 | – | 0.7441 | 0.7789 |
– | – | 0.2 | – | 0.7493 | 0.7847 |
– | – | – | 0.6 | 0.7792 | 0.7515 |
– | – | – | 0.7 | 0.7996 | 0.8050 |
– | – | – | 0.8 | 0.8494 | 0.8231 |
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Shah, Z.; Alzahrani, E.; Jawad, M.; Khan, U. Microstructure and Inertial Characteristics of MHD Suspended SWCNTs and MWCNTs Based Maxwell Nanofluid Flow with Bio-Convection and Entropy Generation Past a Permeable Vertical Cone. Coatings 2020, 10, 998. https://doi.org/10.3390/coatings10100998
Shah Z, Alzahrani E, Jawad M, Khan U. Microstructure and Inertial Characteristics of MHD Suspended SWCNTs and MWCNTs Based Maxwell Nanofluid Flow with Bio-Convection and Entropy Generation Past a Permeable Vertical Cone. Coatings. 2020; 10(10):998. https://doi.org/10.3390/coatings10100998
Chicago/Turabian StyleShah, Zahir, Ebraheem Alzahrani, Muhammad Jawad, and Umair Khan. 2020. "Microstructure and Inertial Characteristics of MHD Suspended SWCNTs and MWCNTs Based Maxwell Nanofluid Flow with Bio-Convection and Entropy Generation Past a Permeable Vertical Cone" Coatings 10, no. 10: 998. https://doi.org/10.3390/coatings10100998