Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation
Abstract
:1. Introduction
2. Problem Formulation
3. Finite Element Method
4. Results and Discussions
5. Conclusions
- The decline in the velocity profile was brought about by increasing the electrical parameters.
- As Eckert’s number increased, so did the temperature profile.
- Growing the thermophoresis parameter decreased the concentration profile.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
horizontal components of velocity | |
Cartesian co-ordinate | |
kinematic viscosity | |
density of fluid | |
concentration of fluid | |
Brownian diffusion coefficient | |
specific heat capacity | |
strength of electric field | |
reaction rate | |
reaction rate parameter | |
time constant (s) | |
magnetic parameter | |
Prandtl number | |
Brownian motion variable | |
electrical conductivity of the fluid | |
temperature of fluid | |
temperature of fluid at the wall | |
ambient temperature of the fluid | |
concentration on the wall | |
ambient concentration | |
strength of imposed transverse magnetic field | |
thermal diffusivity | |
dynamic viscosity | |
effective heat capacity of fluid | |
Eckert number | |
thermophoresis variable | |
Schmidt number |
Appendix A
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Number of Elements/Grid Points | ||||||
---|---|---|---|---|---|---|
F.E.M | bvp4c | F.E.M | bvp4c | F.E.M | bvp4c | |
0.7148 | ||||||
0.7148 | ||||||
Khan & Pop [45] | Srinivasulu & Goud [46] | Present | |
---|---|---|---|
0.01 | ||||
γ | ||
---|---|---|
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Arif, M.S.; Shatanawi, W.; Nawaz, Y. Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation. Energies 2023, 16, 2778. https://doi.org/10.3390/en16062778
Arif MS, Shatanawi W, Nawaz Y. Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation. Energies. 2023; 16(6):2778. https://doi.org/10.3390/en16062778
Chicago/Turabian StyleArif, Muhammad Shoaib, Wasfi Shatanawi, and Yasir Nawaz. 2023. "Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation" Energies 16, no. 6: 2778. https://doi.org/10.3390/en16062778