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Applied Mathematics and Mechanics

, Volume 38, Issue 1, pp 125–136 | Cite as

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

  • Jing ZhuEmail author
  • Shengnan Wang
  • Liancun Zheng
  • Xinxin Zhang
Article

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.

Keywords

nanofluid second-order slip nanoparticle migration homotopy analysis method (HAM) semi-analytical relation 

Nomenclature

B0

magnetic field strength

Cp

specific heat (m2 · s−2 · K−1)

qw

surface heat flux

Np

non-dimensional pressure drop

Nu

Nusselt number

Ha

Hartmann number

ϕ

nanoparticle volume fraction

NBT

ratio of the Brownian to thermophoretic diffusivities

Chtc

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

Chinese Library Classification

O241.81 

2010 Mathematics Subject Classification

34A25 76D10 80A20 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Jing Zhu
    • 1
    Email author
  • Shengnan Wang
    • 1
  • Liancun Zheng
    • 1
  • Xinxin Zhang
    • 2
  1. 1.Department of Applied MathematicsUniversity of Science and Technology BeijingBeijingChina
  2. 2.Department of Mechanical EngineeringUniversity of Science and Technology BeijingBeijingChina

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