Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach
Abstract
:1. Introduction
- What are the factors that cause variations in the flow pattern of nanofluid?
- Does bioconvection help in controlling the fluid temperature and cooling of the surface?
- Does nanofluidic properties influence the shear force and rate of heat diffusion from the surface?
- How are NEPCM nanoparticles different from other nanoparticles?
2. Mathematical Formulation
- Porous material was considered to be a non-Darcy medium with Forchheimer;
- Fluid was laminar, viscous, incompressible, and electrically conductive;
- The induced magnetic field was neglected;
- The fluid was assumed to be Newtonian, and the flow was laminar two-dimensional, where the cylinder was assumed to be infinitely long;
- The porous medium was assumed to be homogeneous and isotropic, with a constant permeability;
- The influence of pressure gradient was neglected.
3. Thermophysical Properties of the Nanofluid
4. Numerical Solution
5. Discussion
Pe | φ | Lb | ε | |||||
---|---|---|---|---|---|---|---|---|
1.0 | 0.05 | 0.4 | 0.3 | 45 | 1.7752 | 0.5694 | 0.2611 | 0.857 |
1.5 | 1.7711 | 0.5721 | 0.2571 | 0.9692 | ||||
2.0 | 1.767 | 0.5747 | 0.2534 | 1.0818 | ||||
0.0 | 1.5529 | 0.4865 | 0.2742 | 0.8684 | ||||
0.03 | 1.6861 | 0.5364 | 0.2657 | 0.8608 | ||||
0.05 | 1.7752 | 0.5694 | 0.2611 | 0.857 | ||||
0.5 | 1.7792 | 0.5654 | 0.2668 | 1.1493 | ||||
0.8 | 1.7964 | 0.5526 | 0.2853 | 1.6213 | ||||
1.2 | 1.8153 | 0.5418 | 0.3009 | 2.4097 | ||||
0.0 | 1.6263 | 1.1589 | −1.2229 | −1.1057 | ||||
0.2 | 1.7232 | 0.7016 | −0.1123 | 0.3843 | ||||
0.4 | 1.8192 | 0.4781 | 0.5624 | 1.4808 | ||||
0.0 | 1.7145 | 0.5836 | 0.2407 | 0.9488 | ||||
60 | 1.8118 | 0.5632 | 0.2699 | 0.9857 | ||||
90 | 1.9130 | 0.5385 | 0.3055 | 1.0336 |
Ste | Nv | Nc | Ns | |||||
---|---|---|---|---|---|---|---|---|
0.05 | 0.3 | 6.0 | 3.0 | 2.0 | 1.7539 | 1.233 | 0.3156 | 1.0607 |
0.5 | 1.7535 | 1.2315 | 0.3162 | 1.0624 | ||||
0.9 | 1.7532 | 1.2229 | 0.3183 | 1.0667 | ||||
0.4 | 1.7538 | 1.2316 | 0.316 | 1.0616 | ||||
0.5 | 1.7537 | 1.2306 | 0.3163 | 1.0622 | ||||
0.6 | 1.7536 | 1.23 | 0.3165 | 1.0626 | ||||
0.3 | 1.5736 | 1.214 | 0.3191 | 1.0569 | ||||
3.0 | 1.7539 | 1.2331 | 0.3156 | 1.0608 | ||||
6.0 | 1.9531 | 1.2495 | 0.3128 | 1.0652 | ||||
0.3 | 1.7639 | 1.0521 | 0.2859 | 1.0036 | ||||
3.0 | 1.7589 | 1.1412 | 0.3008 | 1.0319 | ||||
6.0 | 1.7539 | 1.2331 | 0.3156 | 1.0608 | ||||
0.3 | 1.7537 | 1.2338 | 0.3155 | 1.0605 | ||||
3.0 | 1.7540 | 1.2326 | 0.3157 | 1.061 | ||||
6.0 | 1.7543 | 1.2312 | 0.3161 | 1.0615 |
- Highlights of the physical significance of the findings
6. Conclusions
- The fusion temperature plays a significant role in optimizing the heat transfer efficiency; in this investigation, the optimal range of the fusion temperature was . In this range, the rate of heat transfer from the surface of the cylinder was maximum, and beyond this range, the rate of heat transfer declined.
- Increasing the Peclet number () and the inclination angle () significantly enhanced the Nusselt number, indicating improved heat transfer rates. Specifically, led to a heat transfer enhancement of up to 12%, demonstrating its role in optimizing thermal regulation.
- The wall shear stress decreased with higher , highlighting its impact on reducing frictional resistance, which can contribute to the design of energy-efficient systems.
- The interplay of , , and nanoparticle volume fraction () intensified the density gradient of microorganisms by nearly 15%, amplifying bioconvection and facilitating enhanced mixing in the fluid system.
- The non-Darcy porous medium increased resistance to flow but contributed to stabilizing the thermal boundary layer, improving heat transfer efficiency around the cylinder.
- In a horizontal configuration, the microorganism concentration gradients and the associated bioconvective flow patterns were more evenly distributed around the surface, leading to enhanced diffusion. Such behavior can be beneficial in applications like microbial fuel cells and bioreactors, where maximizing microorganism activity and distribution can enhance efficiency and performance.
- A lower indicates the dominance of latent heat effects, which enhances heat absorption or release during the phase-change process. This leads to a more pronounced thermal gradient near the surface, thereby increasing the Nusselt number, which measures the rate of convective heat transfer.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbols | Symbols | ||
Fluid velocity components along and axis | Buoyancy parameter | ||
Coordinates | Peclet number | ||
Magnetic field strength | Prandtl number | ||
Nanoparticle concentration | Schmidt number | ||
Drag coefficient | Sherwood number | ||
Ambient concentration | Ste | Stefan number | |
Concentration at the surface | Temperature | ||
Concentration at the surface | t | weight ratio of the core–shell | |
Skin friction | Ambient temperature | ||
Coefficient of Brownian diffusion | Wall temperature | ||
Diffusivity of microorganism | Maximum cell swimming speed | ||
Coefficient of thermophoretic diffusion | Fluid density | ||
Non-dimensional stream function | Mass density of nanoparticles | ||
Dimensionless velocity | Curvature parameter | ||
Forchheimer number | Dynamic viscosity | ||
Non-dimensional fusion function | Kinematic viscosity | ||
Acceleration due to gravity | Dimensionless temperature | ||
J | Variable electric current | Dimensionless concentration | |
Permeability | Dimensionless density of motile microorganisms | ||
Permeability constant | Similarity variable | ||
Bioconvection Lewis number | Expansion coefficient | ||
Magnetic parameter | Electrical conductivity | ||
Density of the motile microorganism | Chemo-taxis constant | ||
Ambient motile microorganism | Inclination angle | ||
Density of the motile microorganism at the surface | Heat capacity ratio | ||
Brownian motion number | Mass concentration | ||
Thermophoresis number | Density ratio | ||
Brownian parameter | Abbreviations | ||
Nusselt number | Nanofluid | ||
Density number of motile microorganisms | Base fluid | ||
Thermophoresis parameter | Nano-encapsulated phase-change material |
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Substance | ||||
---|---|---|---|---|
Water | 995.6 | 4180 | 0.615 | 796 |
Nonadecane (core) | 721 | 2037 | 0.190 | --- |
Polyurethane (shell) | 786 | 1317 | 0.025 | --- |
M | Present, NSM −f″(0) | Present, Runge–Kutta −f″(0) | [32] −f″(0) | [33] −f″(0) |
---|---|---|---|---|
0 | 0.9984 | 0.9988 | 1.00000 | 1.00000 |
0.2 | 1.0146 | 1.0139 | 1.01981 | 1.01980 |
0.5 | 1.0901 | 1.0868 | 1.11803 | 1.11803 |
0.8 | 1.2709 | 1.2847 | 1.28062 | 1.28062 |
1.0 | 1.4101 | 1.4036 | 1.41421 | 1.41421 |
Δη = 0.001 | Δη = 0.0001 | |||||||
---|---|---|---|---|---|---|---|---|
η | f″(η) | θ(η) | ϕ(η) | χ(η) | f″(η) | θ(η) | ϕ(η) | χ(η) |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0.1726 | 0.4870 | 0.9209 | 0.5116 | 0.1727 | 0.4871 | 0.9210 | 0.5117 |
2 | −0.0378 | 0.4870 | 0.9209 | 0.2230 | −0.0378 | 0.2251 | 0.7313 | 0.2230 |
3 | −0.0724 | 0.2251 | 0.7312 | 0.0745 | −0.0724 | 0.1117 | 0.4618 | 0.0746 |
4 | −0.0492 | 0.1116 | 0.4617 | 0.01881 | −0.04992 | 0.0462 | 0.2140 | 0.0181 |
5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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Das, B.; Ahmed, S.; Zueco, J. Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach. Mathematics 2024, 12, 4012. https://doi.org/10.3390/math12244012
Das B, Ahmed S, Zueco J. Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach. Mathematics. 2024; 12(24):4012. https://doi.org/10.3390/math12244012
Chicago/Turabian StyleDas, Bikash, Sahin Ahmed, and Joaquín Zueco. 2024. "Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach" Mathematics 12, no. 24: 4012. https://doi.org/10.3390/math12244012
APA StyleDas, B., Ahmed, S., & Zueco, J. (2024). Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach. Mathematics, 12(24), 4012. https://doi.org/10.3390/math12244012