Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region
Abstract
:1. Introduction
2. Flow Analysis for Region-I
3. Solution Process
3.1. Dimensionless Variables
3.2. Primitive Variable Formulation
3.3. Computational Technique
4. Flow Analysis for Plume Region-III
5. Solution Process
5.1. Dimensionless Variables
5.2. Primitive Variable Formulation
5.3. Computational Technique
6. Results and Discussion
6.1. Analysis of Heat and Fluid Flow Characteristics around the Sphere
6.2. Physical Behavior of Material Properties in the Plume Region-III
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Dimensionless velocity component in x direction | |
Dimensionless velocity component in direction | |
Dimensionless velocity component in direction in plume region | |
Dimensionless axes along and normal to the surface of a sphere | |
Dimensionless axes along and normal in the plume region | |
Primitive variable for velocity component in direction | |
Primitive variable for velocity component in direction | |
Primitive variable for velocity component in direction in plume region | |
Gravitational acceleration | |
Fluid temperature in boundary layer | |
Mass concentration in boundary layer | |
Specific heat at constant pressure | |
The radius of a sphere | |
Dimensioned radial distance from the symmetric axis to the surface of a sphere | |
Mass diffusion coefficient | |
Grashof number | |
Radiation parameter | |
Thermophoresis parameter | |
Brownian motion parameter | |
Radiative heat flux | |
Skin friction coefficient | |
Nusselt number | |
Sherwood number | |
Greek Symbols | |
Volumetric coefficient thermal expansion | |
Volumetric coefficient concentration expansion | |
Thermal diffusivity | |
Dimensionless temperature | |
Dimensionless mass concentration | |
Dynamic viscosity | |
Kinematic viscosity | |
Fluid density | |
Thermal conductivity | |
Stefan–Boltzmann constant | |
Mean absorption coefficient | |
Subscripts | |
Ambient conditions | |
Wall conditions |
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X | ||||||
---|---|---|---|---|---|---|
0.1 | 0.00981 | 0.01145 | 0.06308 | 0.06349 | 0.07619 | 0.07801 |
1.0 | 0.06199 | 0.04599 | 0.06578 | 0.08904 | 0.07682 | 0.10350 |
2.0 | 0.10721 | 0.04818 | 0.19978 | 0.09024 | 0.20579 | 0.10476 |
3.1 | 0.00534 | 0.00578 | 0.05831 | 0.05809 | 0.07276 | 0.07327 |
X | ||||||
---|---|---|---|---|---|---|
0.1 | 0.01271 | 0.01483 | 0.06050 | 0.05501 | 0.07456 | 0.07243 |
1.0 | 0.08087 | 0.08239 | 0.10321 | 0.09503 | 0.12380 | 0.12105 |
2.0 | 0.08619 | 0.08762 | 0.10548 | 0.09702 | 0.12654 | 0.12361 |
3.1 | 0.00611 | 0.00742 | 0.05663 | 0.04794 | 0.07183 | 0.06604 |
X | ||||||
---|---|---|---|---|---|---|
0.1 | 0.01812 | 0.01421 | 0.01271 | 0.06050 | 0.07342 | 0.07456 |
1.0 | 0.15241 | 0.08169 | 0.08087 | 0.10321 | 0.12246 | 0.12380 |
2.0 | 0.16466 | 0.08695 | 0.08619 | 0.10548 | 0.12508 | 0.12654 |
3.1 | 0.02562 | 0.00611 | 0.05072 | 0.05663 | 0.00679 | 0.07183 |
X | ||||||
---|---|---|---|---|---|---|
0.1 | 0.01271 | 0.01093 | 0.06050 | 0.00835 | 0.07456 | 0.02171 |
1.0 | 0.08087 | 0.25808 | 0.10321 | 2.87762 | 0.12380 | 0.18380 |
2.0 | 0.08619 | 0.26958 | 0.10548 | 0.09417 | 0.12654 | 0.19084 |
3.1 | 0.00611 | 0.01412 | 0.05663 | 0.06653 | 0.07183 | 0.05583 |
X | ||||||
---|---|---|---|---|---|---|
0.1 | 0.01271 | 0.03029 | 0.06050 | 0.03671 | 0.07456 | 0.07692 |
1.0 | 0.08087 | 0.12463 | 0.10321 | 0.06132 | 0.12380 | 0.11358 |
2.0 | 0.08619 | 0.13128 | 0.10548 | 0.06242 | 0.12654 | 0.11540 |
3.1 | 0.00611 | 0.01716 | 0.05663 | 0.02969 | 0.07183 | 0.07301 |
X | ||||||
---|---|---|---|---|---|---|
0.0 | 50.75594 | 46.76019 | 0.95139 | 0.23755 | 192.65468 | 179.60024 |
0.1 | 32.08902 | 34.08479 | 7.68669 | 7.03547 | 82.65567 | 75.70414 |
1.0 | 15.67088 | 13.73597 | 9.27360 | 11.81349 | 0.11835 | 0.12578 |
2.0 | 10.61131 | 8.79781 | 9.27483 | 11.81388 | 0.11340 | 0.11728 |
3.0 | 7.79274 | 5.95524 | 18.88779 | 17.98556 | 3.34746 | 4.44476 |
4.0 | 5.76776 | 3.84707 | 18.63854 | 18.20510 | 2.30285 | 4.74118 |
5.0 | 4.13138 | 2.18996 | 18.63854 | 17.75627 | 2.29610 | 6.89948 |
6.0 | 2.79540 | 1.27903 | 17.91728 | 16.67107 | 3.51993 | 9.09658 |
7.0 | 1.68713 | 0.95814 | 16.81319 | 15.59305 | 6.43594 | 12.18080 |
8.0 | 1.14654 | 0.78669 | 16.92500 | 14.97582 | 9.41521 | 13.28487 |
9.0 | 0.91312 | 0.68151 | 15.51050 | 14.72355 | 11.44516 | 13.84803 |
10.0 | 0.77717 | 0.60034 | 15.29638 | 14.52141 | 12.45936 | 14.1815 |
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Ashraf, M.; Khan, A.; Abbas, A.; Hussanan, A.; Ghachem, K.; Maatki, C.; Kolsi, L. Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region. Mathematics 2023, 11, 908. https://doi.org/10.3390/math11040908
Ashraf M, Khan A, Abbas A, Hussanan A, Ghachem K, Maatki C, Kolsi L. Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region. Mathematics. 2023; 11(4):908. https://doi.org/10.3390/math11040908
Chicago/Turabian StyleAshraf, Muhammad, Anwar Khan, Amir Abbas, Abid Hussanan, Kaouther Ghachem, Chemseddine Maatki, and Lioua Kolsi. 2023. "Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region" Mathematics 11, no. 4: 908. https://doi.org/10.3390/math11040908
APA StyleAshraf, M., Khan, A., Abbas, A., Hussanan, A., Ghachem, K., Maatki, C., & Kolsi, L. (2023). Finite Difference Method to Evaluate the Characteristics of Optically Dense Gray Nanofluid Heat Transfer around the Surface of a Sphere and in the Plume Region. Mathematics, 11(4), 908. https://doi.org/10.3390/math11040908