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Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

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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.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    M. Hamid & Wei Wang

  2. BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, China

    M. Usman

  3. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China

    M. Usman

  4. Department of Electrical Engineering, Bahria University, Islamabad, 44000, Pakistan

    R. U. Haq

  5. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu, 610065, China

    Z. H. Khan

  6. Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Tsinghua University, Beijing, 100084, China

    Z. H. Khan

Authors
  1. M. Hamid
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  2. M. Usman
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  4. Z. H. Khan
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  5. Wei Wang
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Corresponding author

Correspondence to Z. H. Khan.

Additional information

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

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