The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids
Abstract
:1. Introduction
2. Mathematical Formulation
3. Method of Solution
4. Table Discussion
5. Result and Discussion
6. Conclusions
- By increasing the unsteadiness parameter the velocity profile decreases and this effect is comparatively strong in the GO-EG nanofluid.
- The increasing value of the Prandtl number reduces the temperature profile. The effect is comparatively strong using the GO-EG nanofluid.
- Increasing the Eckert number increases the kinetic energy to enhance the temperature field.
- The increasing thickness of the thin film reduces the fluid motion.
Author Contributions
Funding
Conflicts of Interest
Nomenclatures
Acceleration due to gravity | |
Dynamic viscosity of the nanofluids axial directions | |
Density of the nanofluids | |
Eckert number | |
Heat generation/absorption parameter | |
Local temperature | |
Non-dimensional thickness of the liquid film | |
Nusselt number | |
Prandtl number | |
Specific heat | |
Stretching velocity | |
Similarity variable | |
Skin friction | |
Solid particle volume fraction | |
Thickness of the liquid film | |
Temperature at the free surface | |
Thermal conductivity of the nanoparticles | |
Velocity components |
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GO-W | GO-W | GO-EG | GO-EG | ||
---|---|---|---|---|---|
0.1 | 0.1 | 30.3264 | 30.3335 | 28.7696 | 30.4545 |
0.2 | - | 30.3140 | 30.3412 | 30.3040 | 30.3414 |
- | 0.2 | 30.2883 | 30.3261 | 30.2830 | 30.3264 |
- | 0.3 | 30.7430 | 28.7777 | 28.1609 | 28.7778 |
GO-W | GO-W | GO-EG | GO-EG | ||
---|---|---|---|---|---|
0.1 | 0.5 | −0.1437 | −0.4409 | −0.62116 | −0.4411 |
0.2 | - | −1.2456 | −1.2571 | −1.2458 | −1.2576 |
0.3 | - | −1.8697 | −1.8869 | −1.8700 | −1.8875 |
- | 0.6 | 0.6026 | −1.8337 | −0.6027 | −0.6098 |
- | 0.7 | 0.5870 | −1.8875 | −0.5871 | −0.5952 |
GO-W | GO-W | |
---|---|---|
6 | ||
12 | ||
18 | ||
24 | ||
30 |
GO-EG | GO-EG | |
---|---|---|
6 | ||
12 | ||
18 | ||
24 | ||
30 |
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Rehman, A.; Salleh, Z.; Gul, T.; Zaheer, Z. The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids. Mathematics 2019, 7, 653. https://doi.org/10.3390/math7070653
Rehman A, Salleh Z, Gul T, Zaheer Z. The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids. Mathematics. 2019; 7(7):653. https://doi.org/10.3390/math7070653
Chicago/Turabian StyleRehman, Ali, Zabidin Salleh, Taza Gul, and Zafar Zaheer. 2019. "The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids" Mathematics 7, no. 7: 653. https://doi.org/10.3390/math7070653
APA StyleRehman, A., Salleh, Z., Gul, T., & Zaheer, Z. (2019). The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids. Mathematics, 7(7), 653. https://doi.org/10.3390/math7070653