Abstract
The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.
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Abbreviations
- λ:
-
Buoyancy effect due to the temperature difference
- λ*:
-
Buoyancy effect due to the concentration difference
- k*:
-
coefficient of the mean absorption
- β C :
-
coefficient of the concentration expansion
- ρ :
-
density of the fluid
- σ :
-
electrical conductivity
- M :
-
Hartmann number
- B :
-
magnetic field strength
- T m :
-
mean fluid temperature
- c s :
-
ratio of the thermal diffusion
- Re :
-
Reynolds number
- r :
-
stagnation point parameter
- Sr :
-
Soret number
- k :
-
thermal conductivity
- A :
-
unsteadiness parameter
- σ*:
-
Boltzmann constant
- k T :
-
concentration susceptibility
- Γ:
-
coefficient of the Williamson fluid
- β T :
-
coefficient of thermal expansion
- Du :
-
Dufour number
- g :
-
gravitational acceleration
- ν :
-
kinematic viscosity
- D B :
-
mass diffusivity coefficient
- Pr :
-
Prandtl number
- R :
-
ratio of λ* to λ
- c p :
-
specific heat
- S :
-
suction parameter
- Sc :
-
Schmidt number
- Rd :
-
thermal radiation
- Λ:
-
Williamson fluid parameter
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Acknowledgements
The authors are grateful to the reviewers and editor for suggesting suitable changes in the original manuscript. The first author is also grateful to the China Scholarship Council (CSC) for the financial assistance.
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Citation: HAMID, M., USMAN, M., HAQ, R. U., KHAN, Z. H., and WANG, W. Wavelet analysis of stagnation point flow of non-Newtonian nanofluid. Applied Mathematics and Mechanics (English Edition) 40(8), 1211–1226 (2019) https://doi.org/10.1007/s10483-019-2508-6
Project supported by the National Natural Science Foundation of China (Nos. 51709191, 51706149, and 51606130), the Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education of China (No.ARES-2018-10), and the State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University of China (No. Skhl1803)
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Hamid, M., Usman, M., Haq, R.U. et al. Wavelet analysis of stagnation point flow of non-Newtonian nanofluid. Appl. Math. Mech.-Engl. Ed. 40, 1211–1226 (2019). https://doi.org/10.1007/s10483-019-2508-6
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DOI: https://doi.org/10.1007/s10483-019-2508-6
Key words
- Williamson nanofluid
- heat and mass transfer
- stagnation point flow
- assisting and opposing flow
- Chebyshev wavelet method