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Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

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Abstract

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al2O3, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

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Abbreviations

u :

velocity components along the x-axis

v :

velocity components along the y-axis

a, b, c :

constants

l :

reference length of the sheet

T :

temperature inside the boundary layer

η :

similarity variable

θ :

dimensionless temperature

φ :

dimensionless concentration

μ :

dynamic viscosity

ν :

kinematic viscosity of the fluid

B 0 :

constant magnetic flux density

M :

magnetic parameter

R :

radiation parameter

C w :

uniform concentration of the fluid

Le :

Lewis number

N T :

thermophoresis parameter

Pr :

Prandtl number

Ec :

Eckert number

C :

fluid concentration

D :

coefficient of the mass diffusivity

σ :

electrical conductivity

ρ :

fluid density

K n :

Knudsen number

λ :

molecular mean free path

C p :

effective heat capacity

f w :

suction/injection parameter

k nf :

thermal conductivity of the nanofluid

ρ nf :

density of the nanofluid

T w :

uniform temperature of the fluid

N B :

Brownian motion parameter

K 1,K 2 :

velocity slip parameters

L 1,L 2 :

temperature jump parameters

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Authors and Affiliations

  1. School of Mathematica and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Jing Zhu, Liu Zheng & Liancun Zheng

  2. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Xinxin Zhang

Authors
  1. Jing Zhu
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  2. Liu Zheng
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  3. Liancun Zheng
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  4. Xinxin Zhang
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Corresponding author

Correspondence to Jing Zhu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 51276014 and 51476191) and the Fundamental Research Funds for the Central Universities (No. FRF-BR-12-004)

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Zhu, J., Zheng, L., Zheng, L. et al. Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction. Appl. Math. Mech.-Engl. Ed. 36, 1131–1146 (2015). https://doi.org/10.1007/s10483-015-1977-6

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  • DOI: https://doi.org/10.1007/s10483-015-1977-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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