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Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity

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Abstract

The heat transfer of a magnetohydrodynamics nanofluid inside an annu-lus considering the second-order slip condition and nanoparticle migration is theoret-ically investigated. A second-order slip condition, which appropriately represents the non-equilibrium region near the interface, is prescribed rather than the no-slip condi-tion and the linear Navier slip condition. To impose different temperature gradients, the outer wall is subjected to q2, the inner wall is subjected to q1, and q1 > q2. A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofluid, which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow. The homotopy analysis method (HAM) is employed to solve the equations, and the h-curves are plotted to verify the accuracy and efficiency of the solutions. Moreover, the effects of the physical factors on the flow and heat transfer are discussed in detail, and the semi-analytical relation between NuB and NBT is obtained.

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Abbreviations

B 0 :

magnetic field strength

C p :

specific heat (m2 · s−2 · K−1)

q w :

surface heat flux

N p :

non-dimensional pressure drop

N u :

Nusselt number

H a :

Hartmann number

ϕ :

nanoparticle volume fraction

N BT :

ratio of the Brownian to thermophoretic diffusivities

C htc :

dimensionless heat transfer coefficient

λ1, λ2 :

slip parameters of the velocity

ρ :

density (g·m−3)

R :

radius (m)

p :

pressure (Pa)

U :

axial velocity (m·s−1)

η :

transverse direction

σ :

electrical conductivity

μ :

dynamic viscosity (kg·m−1·s−1)

k :

thermal conductivity (W·m−1·K−1)

h :

heat transfer coefficient (W·m−2·K−1)

γ:

ratio of the temperature difference between the wall and the fluid to the absolute temperature

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China

    Jing Zhu, Shengnan Wang & Liancun Zheng

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

    Xinxin Zhang

Authors
  1. Jing Zhu
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  2. Shengnan Wang
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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. 51476191 and 51406008)

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Zhu, J., Wang, S., Zheng, L. et al. Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity. Appl. Math. Mech.-Engl. Ed. 38, 125–136 (2017). https://doi.org/10.1007/s10483-017-2155-6

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  • DOI: https://doi.org/10.1007/s10483-017-2155-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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