Numerical Computation of Dufour and Soret Effects on Radiated Material on a Porous Stretching Surface with Temperature-Dependent Thermal Conductivity
Abstract
:1. Introduction
2. Governing Equations
3. Numerical Method for Solution
4. Results and Discussion
5. Conclusions
- The flow of nanoparticles on a hot surface is managed through the variation of magnetic field and porosity numbers. It is simulated that the motion of nanoparticles becomes slower versus growing values of the magnetic field and porosity numbers. The thickness of the MBL is investigated in view of this reduction;
- The intensity of magnetic field plays a vital role on heat energy and the TBL because thermal performance has improved under the action of a magnetic field. Moreover, the transportation of temperature becomes slowr versus an increment in the Prandtl number called ration of MBL to TBL;
- The maximum production of thermal energy has been observed with respect to the variation of the thermal radiation, thermophoresis, Brownian motion and Dufour numbers, whereas thickness of the TBL declines by changing the values of the Dufour number;
- The diffusion of fluid particles has been observed significantly against the variation of thermophoresis, Brownian motion, magnetic field, thermal relaxation time and concentration relaxation time numbers;
- The divergent velocity speeds up versus the Prandtl number, magnetic field, and the thermal radiation numbers, but reduces in speed in view of divergent flow against large values of the thermal radiation number.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Velocity field | |
Temperature | |
Fluid density | |
Small parameters | |
Dimensionless temperature | |
Porosity parameter | |
Lewis number | |
Mass transfer rate | |
Radiation parameter | |
Stream function | |
Temperature dependent diffusion coefficient | |
Wall concentration/ambient concentration | |
Space coordinates | |
Concentration | |
Chemical reaction parameter | |
Magnetic parameter | |
Dimensionless concentration | |
Dimensionless velocity | |
Chemical reaction parameter | |
Heat transfer rate | |
Temperature dependent thermal conductivity | |
Dimensionless independent variable | |
Wall temperature/ambient temperature | |
Wall stress |
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Pr | M | R | −θ′(0) [19] | −θ′(0) Present Results |
---|---|---|---|---|
1.0 | 0.0 | 0.0 | 0.9548 | 0.95484878 |
2.0 | 0.0 | 0.0 | 1.4714 | 1.4714548 |
3.0 | 0.0 | 0.0 | 1.8691 | 1.86906988 |
1.0 | 0.0 | 1.0 | 0.5315 | 0.53530132 |
1.0 | 1.0 | 0.0 | 0.8611 | 0.86150565 |
1.0 | 1.0 | 1.0 | 0.4505 | 0.46196426 |
Nb | Nt | Pr | Le | M | k1 | R | Γ | Df | Sr | n | δ1 | δ2 | −f″(0) | −θ′ (0) | −∅′(0) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 1.203130 | 1.692398 |
0.5 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 0.745205 | 1.730309 |
0.1 | 0.3 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 0.993797 | 1.705696 |
0.1 | 0.1 | 8.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 1.260018 | 1.691140 |
0.1 | 0.1 | 7.0 | 10.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 1.020337 | 2.459589 |
0.1 | 0.1 | 7.0 | 5.0 | 2.5 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 2.063846 | 1.080128 | 1.514741 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 2.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.93865 | 1.103093 | 1.545366 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 3.0 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 0.628864 | 3.137834 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 5.0 | 0.1 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 0.458712 | 1.664456 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.3 | 0.1 | 0.1 | 1.3 | 1.3 | 1.358958 | 0.688129 | 1.720053 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.3 | 0.1 | 1.3 | 1.3 | 1.358958 | 1.287439 | 1.347656 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.2 | 1.3 | 1.3 | 1.358958 | 1.045916 | 1.696398 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.5 | 1.3 | 1.358958 | 1.179728 | 1.694022 |
0.1 | 0.1 | 7.0 | 5.0 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 1.3 | 1.5 | 1.358958 | 1.216942 | 1.635957 |
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Naseem, T.; Nazir, U.; El-Zahar, E.R.; Algelany, A.M.; Sohail, M. Numerical Computation of Dufour and Soret Effects on Radiated Material on a Porous Stretching Surface with Temperature-Dependent Thermal Conductivity. Fluids 2021, 6, 196. https://doi.org/10.3390/fluids6060196
Naseem T, Nazir U, El-Zahar ER, Algelany AM, Sohail M. Numerical Computation of Dufour and Soret Effects on Radiated Material on a Porous Stretching Surface with Temperature-Dependent Thermal Conductivity. Fluids. 2021; 6(6):196. https://doi.org/10.3390/fluids6060196
Chicago/Turabian StyleNaseem, Tahir, Umar Nazir, Essam R. El-Zahar, Ahmed M. Algelany, and Muhammad Sohail. 2021. "Numerical Computation of Dufour and Soret Effects on Radiated Material on a Porous Stretching Surface with Temperature-Dependent Thermal Conductivity" Fluids 6, no. 6: 196. https://doi.org/10.3390/fluids6060196