Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces
Abstract
:1. Introduction
2. Mathematical Formulation
3. Solution Procedure
3.1. Practical and Engineering Interests
3.1.1. Skin Friction Coefficients
3.1.2. Nusselt Numbers
3.1.3. Sherwood Number
3.1.4. Numerical Solution and Modeling for Thermophysical Properties of (HNfd)
4. Solution of the Problem
5. Result and Discussion
6. Numerical Stability
7. Conclusions
- The skin friction coefficient increases at both porous walls with the increase in the permeable Reynolds number, and a similar trend is observed for the nanoparticles volume fraction.
- The Nusselt number shows significant results under the effect of the hybrid nanofluid flow.
- The Prandtl number has a significant role in the heat transfer system for every type of hybrid nanofluid flow.
- When the dimensionless activation energy parameter has higher values, the rate of the mass transfer rises.
- The measurements of the dimensionless exothermic/endothermic parameter and the dimensionless reaction rate parameter are increased; the flow of heat transfer improves progressively.
- As the values of the Schmidt number rise, the mass transfer flow improves on the lower porous surfaces.
- For the injection cases, the hybrid nanoparticles have a significant effect on the temperature as well as the radial velocity.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
u, v | Velocity components |
Sc | Schmidt number |
T | Temperature |
Hybrid nanofluids specific heat | |
Expansion ratio | |
E | Dimensionless activation energy Parameter |
Activation energy | |
Lower plate concentration | |
Upper plate temperature | |
Magnetic field strength | |
Nanoparticles volume fraction | |
Water density (base fluid) | |
Density for nanoparticles 1st and 2nd | |
Thermal conductivity | |
, | Thermal conductivity for nanoparticles 1st and 2nd |
M | Magnetic field |
Boltzmann constant | |
Exothermic/endothermic coefficient | |
Prandtl number | |
n | Dimensionless parameter |
Reynolds number | |
N | Size |
Dimensionless exothermic/endothermic Parameter | |
Dimensionless reaction rate | |
T1 | Lower plate temperature |
C2 | Upper plate concentration |
Temperature difference parameter | |
x, y | Space coordinate |
Hybrid nanofluids density | |
Hybrid nanofluid’s thermal conductivity | |
Water dynamic velocity | |
Base fluid | |
Thermal diffusivity hybrid Nanofluid | |
N | Similarity variable |
D | Diffusion coefficient |
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Properties | Hybrid Nanofluid |
---|---|
Density () | = + − (1 − − ) |
Viscosity () | |
Heat Capacity | ()() |
Thermal Conductivity () | = Where = |
Title | ||||||
---|---|---|---|---|---|---|
kg | 997.1 | 4250 | 8933 | 3970 | 6320 | 10,500 |
(J k). | 4180 | 686.2 | 385 | 765 | 531.5 | 235 |
0.6013 | 8.9538 | 401 | 40 | 76.5 | 429 |
1 | 1 | 0.01 | 0.01 | 1 | 3.1951 | 3.1951 |
1.2 | 3.3435 | 3.3435 | ||||
1.4 | 3.4983 | 3.4983 | ||||
1 | 2.0561 | 2.0561 | ||||
3 | 2.0954 | 2.0954 | ||||
5 | 2.1342 | 2.1342 | ||||
0.01 | ||||||
0.03 | ||||||
0.05 | ||||||
0.03 | ||||||
0.06 | ||||||
0.09 | ||||||
0.1 | ||||||
0.5 | ||||||
0.9 |
1 | 1 | 0.01 | 0.01 | 1 | 0.5 | 1 | 0.1 | 0.1 | ||
1.2 | ||||||||||
1.4 | ||||||||||
1 | ||||||||||
3 | ||||||||||
5 | ||||||||||
0.01 | ||||||||||
0.03 | ||||||||||
0.05 | ||||||||||
0.03 | ||||||||||
0.06 | ||||||||||
0.09 | ||||||||||
0.1 | 1 | |||||||||
0.5 | ||||||||||
0.9 | ||||||||||
0.2 | ||||||||||
0.5 | ||||||||||
0.8 | ||||||||||
0.35 | ||||||||||
0.70 | ||||||||||
0.95 | ||||||||||
0.15 | ||||||||||
0.20 | ||||||||||
0.25 | 1 | |||||||||
0.20 | ||||||||||
0.50 | ||||||||||
0.80 |
5.0 | 6.2 | ||
5.5 | |||
6.2 | |||
1.3 | |||
1.5 | |||
1.7 |
0.01 = 1% | 0.05680 | 0.05725 | 0.05703 | 0.05680 | 0.05532 | |||
0.03 = 3% | 0.07621 | 0.07712 | 0.07651 | 0.07585 | 0.07158 | |||
0.05 = 5% | 0.09524 | 0.09616 | 0.09520 | 0.09415 | 0.08734 | |||
0.07 = 7% | 0.11368 | 0.11440 | 0.11310 | 0.11172 | 0.01025 | |||
0.09 = 9% | 0.13152 | 0.13187 | 0.13023 | 0.12858 | 0.11733 |
AHMAD et al. [57] | Present Results | ||
---|---|---|---|
1.1 | 2 | 1.17039 | 1.17040 |
1.2 | 1.27024 | 1.27025 | |
1.4 | 1.36100 | 1.36101 | |
1.6 | 1.41025 | 1.41026 | |
1.1 | 2 | 1.17039 | 1.17040 |
1.5 | 1.10472 | 1.10474 | |
1 | 1.01015 | 1.01017 | |
0.5 | 0.82109 | 0.82110 |
f(−1) | f′(−1) | f″(−1) | |
---|---|---|---|
−1 | −1 | 0 | |
−0.9 | |||
−0.8 | |||
−0.7 | |||
−0.6 | |||
−0.5 | |||
−0.4 | |||
−0.3 | |||
−0.2 | |||
−0.1 | |||
0 | |||
0.1 | |||
0.2 | |||
0.3 | |||
0.4 | |||
0.5 | |||
0.6 | |||
0.7 | |||
0.8 | |||
0.9 | |||
1 | 1 | 0 |
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Raza, Q.; Qureshi, M.Z.A.; Khan, B.A.; Kadhim Hussein, A.; Ali, B.; Shah, N.A.; Chung, J.D. Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces. Mathematics 2022, 10, 3013. https://doi.org/10.3390/math10163013
Raza Q, Qureshi MZA, Khan BA, Kadhim Hussein A, Ali B, Shah NA, Chung JD. Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces. Mathematics. 2022; 10(16):3013. https://doi.org/10.3390/math10163013
Chicago/Turabian StyleRaza, Qadeer, M. Zubair Akbar Qureshi, Behzad Ali Khan, Ahmed Kadhim Hussein, Bagh Ali, Nehad Ali Shah, and Jae Dong Chung. 2022. "Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces" Mathematics 10, no. 16: 3013. https://doi.org/10.3390/math10163013
APA StyleRaza, Q., Qureshi, M. Z. A., Khan, B. A., Kadhim Hussein, A., Ali, B., Shah, N. A., & Chung, J. D. (2022). Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces. Mathematics, 10(16), 3013. https://doi.org/10.3390/math10163013