Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative
Abstract
:1. Introduction
2. Problem Formulation
3. Ordinary Solution
3.1. Calculation of Temperature
3.2. Calculation of Concentration
3.3. Calculation of Velocity
4. Fractional Solution
4.1. Fractional Thermal Diffusion
4.2. Fractional Concentration
4.3. Fractional Velocity
5. Result and Discussion
6. Conclusions
- Increasing the values of , , Gr, and Gm increases the fluid’s velocity.
- Rises in the values of Pr, Sc, F, , and slow the fluid’s velocity down.
- Rises in the value of Pr decrease the fluid temperature.
- For a short time, the temperature field is a decreasing function of .
- Increasing the value of Sc decreases the concentration of the fluid.
- For a short time, the concentration field is a decreasing function of .
- The fractionalized outcomes for velocity, temperature, and concentration are generalized and are of a more decaying nature.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | Name | Unit |
U | Velocity of fluid | (m s) |
u | Velocity of fluid | (m s) |
T | Temperature of fluid | (K) |
C | Concentration of fluid | (Kg s) |
Concentration level at the plate | (Kg m) | |
Fluid concentration far from the plate | (Kg m) | |
Temperature of fluid at the plate | (K) | |
Fluid temperature far away from plate | (K) | |
Specific heat at constant pressure | (Jkg K) | |
D | Mass diffusivity | (m s) |
g | Acceleration due to gravity | (m s) |
K | Thermal conductivity of fluid | (W m K) |
Kinematic viscosity of fluid | (m s) | |
dynamic viscosity | (Kg m s) | |
Fluid density | (Kg m) | |
t | Time | (s) |
Volumetric coefficient of thermal expansion | (K) | |
Volumetric coefficient of mass expansion | (m Kg) | |
, | Fractional parameters | (-) |
M | Magnetic parameter | (-) |
s | Laplace transform variables | (-) |
Uniform applied magnetic field | (-) | |
Jeffrey’s fluid parameter | (-) | |
Relaxation and retardation time | (-) | |
Retardation time | (-) | |
Dimensional chemical reaction parameter | (-) | |
E | Heat generation | (-) |
H | Chemical reaction | (-) |
Appendix A
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Abbas, S.; Nazar, M.; Nisa, Z.U.; Amjad, M.; Din, S.M.E.; Alanzi, A.M. Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative. Symmetry 2022, 14, 2491. https://doi.org/10.3390/sym14122491
Abbas S, Nazar M, Nisa ZU, Amjad M, Din SME, Alanzi AM. Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative. Symmetry. 2022; 14(12):2491. https://doi.org/10.3390/sym14122491
Chicago/Turabian StyleAbbas, Shajar, Mudassar Nazar, Zaib Un Nisa, Muhammad Amjad, Sayed M. El Din, and Agaeb Mahal Alanzi. 2022. "Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative" Symmetry 14, no. 12: 2491. https://doi.org/10.3390/sym14122491
APA StyleAbbas, S., Nazar, M., Nisa, Z. U., Amjad, M., Din, S. M. E., & Alanzi, A. M. (2022). Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative. Symmetry, 14(12), 2491. https://doi.org/10.3390/sym14122491