Radiative MHD Nanofluid Flow over a Moving Thin Needle with Entropy Generation in a Porous Medium with Dust Particles and Hall Current
Abstract
:1. Introduction
2. Mathematical Modeling
- Continuity equation:Fluid phase
- Momentum equation:Fluid phase
- Continuity equation:Particle phase
- Momentum equation:Particle phase
- Energy equation:Fluid phase
- Energy equation:Particle phase
3. Similarity Transformation
- Momentum equation:Fluid phase
- Momentum equation:Particle phase
- Energy equation:Fluid phase
- Energy equation:Particle phase
4. Nusselt Number and Skin Friction Coefficient
5. Entropy Generation
6. Numerical Scheme
7. Results and Discussion
8. Final Remarks
- ⮚
- Bejan number increased for larger values of Darcy–Forchheimer number.
- ⮚
- Velocity was on the decline once the size of the needle and Darcy–Forchheimer parameter’s values were enhanced.
- ⮚
- Higher estimates of Hall current parameter escalated the velocity profiles for both CNTs.
- ⮚
- An upsurge in entropy generation and the Bejan number was witnessed versus the radiation parameter.
- ⮚
- Sturdier magnetic field diminished the velocity of the fluid.
- ⮚
- Skin friction coefficient declined for growing estimates of dust particles’ mass concentration.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Coordinate measured in radial direction | |
Velocity components along and directions | |
Effective dynamic viscosity of nanofluid | |
Density of nanofluid | |
Kinematic viscosity of nanofluid | |
Darcy-permeability of the porous medium | |
Drag coefficient | |
Volume fraction of dust particles | |
Stokes resistance | |
Number density of dust particles | |
Electric conductivity | |
Applied magnetic field | |
Hall parameter | |
md | Mass concentration of the dust particles |
knf | Effective thermal conductivity of the nanofluid |
(ρCp)nf | Effective heat capacitance of the nanofluid |
N1 | Density of the particle phase |
τv | Relaxation time of dust particles |
τT | Thermal equilibrium time |
τw | Shear stress at the surface |
Entropy generation rate per unit volume | |
Velocity components of particle phase in x and r directions | |
Specific heat of the dust particles | |
Velocity of the moving needle | |
Velocity outside the boundary layer | |
Dimensional temperature of the nanofluid | |
Temperature of the dust particle | |
Constant surface temperature of the thin needle | |
Ambient temperature | |
Porosity parameter | |
Forchheimer parameter | |
Dust particles mass concentration | |
Fluid particle interaction parameter for velocity | |
Magnetic field parameter | |
Prandtl number | |
Nonlinear radiation parameter | |
Temperature ratio parameter | |
Eckert number | |
Fluid particle interaction parameter for temperature | |
Ratio of specific heat | |
Surface heat flux | |
Entropy generation number |
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Properties | Nano-Fluid |
---|---|
Density | |
Heat capacity | |
Viscosity | |
Thermal conductivity |
Thermo-Physical Properties | H2O | SWCNT | MWCNT |
---|---|---|---|
Cp (j/kg)K | 425 | 796 | |
ρ (kg/m3) | 997.1 | 2600 | 1600 |
k (W/mK) | 0.613 | 6600 | 3000 |
Prandtl number (Pr) |
Ishak et al. [47] | Chen and Smith [42] | M. Idrees Afridi et al. [43] | Present Results | |
---|---|---|---|---|
0.1 | 1.2888 | 1.28881 | 1.28881 | 1.28508 |
0.01 | 8.4924 | 8.49244 | 8.49233 | 8.4878 |
0.001 | 62.1637 | 62.16372 | 62.16370 | 62.1594 |
Skin Friction Coefficient | |||||||
---|---|---|---|---|---|---|---|
SWCNT | MWCNT | ||||||
0.001 | 0.00184647 | 0.00184157 | |||||
0.01 | 0.00583012 | 0.00581468 | |||||
0.2 | 0.02591430 | 0.02584880 | |||||
0.1 | 0.00583012 | 0.00581468 | |||||
2.0 | 0.00583276 | 0.00581722 | |||||
3.5 | 0.00583491 | 0.00581927 | |||||
0.10 | 0.00583012 | 0.00581468 | |||||
0.25 | 0.00644651 | 0.00640784 | |||||
0.4 | 0.00706302 | 0.00700110 | |||||
1.0 | 0.00583012 | 0.00581468 | |||||
2.0 | 0.00582586 | 0.00581043 | |||||
3.0 | 0.00582165 | 0.00580623 | |||||
0.2 | 0.00583012 | 0.00581468 | |||||
0.3 | 0.00711701 | 0.00710157 | |||||
0.4 | 0.00840431 | 0.00838888 | |||||
1.0 | 0.00583012 | 0.00581468 | |||||
1.4 | 0.00499559 | 0.00498015 | |||||
1.8 | 0.00447082 | 0.00445537 |
Nusselt Number | |||||||
---|---|---|---|---|---|---|---|
SWCNT | MWCNT | ||||||
0.10 | 1.10739 | 1.05489 | |||||
0.25 | 1.12048 | 1.06695 | |||||
0.40 | 1.13570 | 1.08087 | |||||
1.0 | 1.10739 | 1.05489 | |||||
2.0 | 1.28855 | 1.22836 | |||||
3.0 | 1.44647 | 1.37965 | |||||
0.3 | 1.12089 | 1.06788 | |||||
0.5 | 1.10739 | 1.05489 | |||||
0.9 | 1.09958 | 1.04738 | |||||
1.0 | 1.10739 | 1.05489 | |||||
1.4 | 1.09857 | 1.04640 | |||||
1.8 | 1.09329 | 1.04131 | |||||
6.0 | 1.10739 | 1.05489 | |||||
9.0 | 0.80951 | 0.77264 | |||||
15.0 | 0.59158 | 0.56589 | |||||
1.1 | 1.10739 | 1.05489 | |||||
1.4 | 0.80635 | 0.77013 | |||||
1.7 | 0.71356 | 0.68292 |
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Tlili, I.; Ramzan, M.; Kadry, S.; Kim, H.-W.; Nam, Y. Radiative MHD Nanofluid Flow over a Moving Thin Needle with Entropy Generation in a Porous Medium with Dust Particles and Hall Current. Entropy 2020, 22, 354. https://doi.org/10.3390/e22030354
Tlili I, Ramzan M, Kadry S, Kim H-W, Nam Y. Radiative MHD Nanofluid Flow over a Moving Thin Needle with Entropy Generation in a Porous Medium with Dust Particles and Hall Current. Entropy. 2020; 22(3):354. https://doi.org/10.3390/e22030354
Chicago/Turabian StyleTlili, Iskander, Muhammad Ramzan, Seifedine Kadry, Hyun-Woo Kim, and Yunyoung Nam. 2020. "Radiative MHD Nanofluid Flow over a Moving Thin Needle with Entropy Generation in a Porous Medium with Dust Particles and Hall Current" Entropy 22, no. 3: 354. https://doi.org/10.3390/e22030354