Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability
Abstract
:1. Introduction
2. Formulation of the Problem
3. Numerical Procedure and Convergence
4. Stability Analysis
5. Error Explanation
6. Analysis and Discussion
7. Key Notes
- It is observed that for both situations of wall extension or contraction with injection, the temperature is the increasing function of the thermophoresis and Brownian motion factors.
- It is analyzed that the temperature is raised when the heat source is increased in both cases of wall expansion or contraction but declines in the case of a heat sink.
- In the case of a heat source, the temperature rises as the Hartmann and Prandtl numbers are enhanced, but in the case of a heat sink, the temperature falls.
- In the presence of heat sinks and injections when the thermophoresis factor is increased, the concentration of nanoparticles is increased in both wall expansion and contraction.
- In both situations of wall expansion or contraction, along with injection, the concentration of nanoparticles is a decreasing function of , while the concentration of nanoparticles is an increasing function in the case of a heat source.
- It is also observed that is increased for and decreased for.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
radius of the pipe | ||
the injection/suction coefficient | ||
applied magnetic field | ||
dimensional nanoparticle concentration | ||
reference nanoparticle concentration at the center | ||
specific heat at constant pressure | ||
nanoparticle concentration at the wall | ||
first-order chemical reaction rate | ||
Lewis number | ||
Hartmann number | ||
thermophoresis parameter | ||
Brownian motion parameter | ||
Prandtl number | ||
heat source/sink parameter | ||
dimensional cylindrical coordinates | ||
dimensional temperature | ||
reference temperature at the center | ||
mean temperature | ||
mean fluid temperature | ||
temperature near the wall | ||
velocity components along ^r and ^z directions respectively | ||
injection/suction velocity | ||
density of the base fluid | ||
electrical conductivity | ||
thermal diffusivity | ||
dimensionless temperature | ||
heat capacity of the nanoparticle | ||
dimensionless concentration |
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Srinivas et al. [49] | 25th–Order Approximation | ||
---|---|---|---|
3 | 0.92763 | −1.1398871 | −1.147523 |
2 | 0.99429 | −1.166290 | −1.166291 |
0 | 0.87134 | −1.179535 | −1.179537 |
−3 | 0.87134 | −1.182623 | −1.182623 |
−2 | 0.87134 | −1.187371 | −1.187371 |
Srinivas et al. [49] | 25th–Order Approximation | ||
---|---|---|---|
3 | 0.97289 | −1.173991 | −1.176380 |
2 | 0.97134 | −1.176393 | −1.178475 |
0 | 0.87134 | −1.177947 | −1.179692 |
−3 | 0.87134 | −1.178881 | −1.178881 |
−2 | 0.87134 | −1.179290 | −1.179290 |
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Zeeshan; Ahammad, N.A.; Shah, N.A.; Chung, J.D.; Attaullah. Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability. Mathematics 2023, 11, 1844. https://doi.org/10.3390/math11081844
Zeeshan, Ahammad NA, Shah NA, Chung JD, Attaullah. Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability. Mathematics. 2023; 11(8):1844. https://doi.org/10.3390/math11081844
Chicago/Turabian StyleZeeshan, N. Ameer Ahammad, Nehad Ali Shah, Jae Dong Chung, and Attaullah. 2023. "Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability" Mathematics 11, no. 8: 1844. https://doi.org/10.3390/math11081844
APA StyleZeeshan, Ahammad, N. A., Shah, N. A., Chung, J. D., & Attaullah. (2023). Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability. Mathematics, 11(8), 1844. https://doi.org/10.3390/math11081844