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Research Papers: Micro/Nanoscale Heat Transfer

Effects of Brownian Diffusion and Thermophoresis on the Laminar Forced Convection of a Nanofluid in a Channel

[+] Author and Article Information
Eugenia Rossi di Schio

e-mail: eugenia.rossidischio@unibo.it

Michele Celli

e-mail: michele.celli3@unibo.it

Antonio Barletta

e-mail: antonio.barletta@unibo.it

DIENCA,
Alma Mater Studiorum,
Università di Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 29, 2012; final manuscript received September 2, 2013; published online November 7, 2013. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 136(2), 022401 (Nov 07, 2013) (10 pages) Paper No: HT-12-1473; doi: 10.1115/1.4025376 History: Received August 29, 2012; Revised September 02, 2013

A steady laminar forced convection in a parallel–plane channel using nanofluids is studied. The flow is assumed to be fully developed, and described through the Hagen–Poiseuille profile. A boundary temperature varying with the longitudinal coordinate in the thermal entrance region is prescribed. Two sample cases are investigated in detail: a linearly changing wall temperature, and a sinusoidally changing wall temperature. A study of the thermal behavior of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. The numerical solution is obtained by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). With reference to both the wall temperature distributions prescribed along the thermal entrance region, the governing equations have been solved separately both for the fully developed region and for the thermal entrance region. The analysis shows that if a linearly varying boundary temperature is assumed, for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. On the other hand, in case of a longitudinally periodic boundary temperature, nonhomogeneities in the nanoparticle concentration distribution arise, which are wrongly neglected whenever the homogeneous model is employed.

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References

Figures

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Fig. 1

Sketch of the geometry and of the boundary conditions

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Fig. 2

Function η(x) for Pe = 10−2 and for Pe = 10−4

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Fig. 3

Function ξ(x) for Pe = 10−2 and for three different values assumed by the parameter γ

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Fig. 4

Function ξ(x) for Pe = 10−4 and for three different values assumed by the parameter γ

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Fig. 5

Dimensionless temperature distribution in a half channel for Pe = 10−2, evaluated at three different axial positions

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Fig. 6

Dimensionless temperature distribution in a half channel for Pe = 10−4, evaluated at three different axial positions

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Fig. 7

Nanoparticle concentration distribution in a half channel for Pe = 10−2 and γ = 1.01, evaluated at three different axial positions

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Fig. 8

Nanoparticle concentration distribution in a half channel for Pe = 10 − 2 and γ = 1.001, evaluated at three different axial positions

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Fig. 9

Nanoparticle concentration distribution in a half channel for Pe = 10−2 and γ = 1.0001, evaluated at three different axial positions

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Fig. 15

Nanoparticle concentration distribution versus x at y = 0.9, for Ω = π and different values of the parameter Γ

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Fig. 16

Dimensionless temperature distribution versus y at x = 1, for Ω = π and different values of the parameter Γ

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Fig. 17

Nanoparticle concentration distribution versus y at x = 1, for Ω = π and different values of the parameter Γ

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Fig. 10

Dimensionless temperature versus x at y = 0.9, for Ω = π and Γ = 0.1: test of the mesh independence

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Fig. 11

Nanoparticle concentration versus x at y = 0.9, for Ω = π and Γ = 0.1: test of the mesh independence

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Fig. 12

Dimensionless temperature versus x at y = 0.9, for Ω = π and Γ = 0.1: test of the domain independence

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Fig. 13

Nanoparticle concentration versus x at y = 0.9, for Ω = π and Γ = 0.1: test of the domain independence

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Fig. 14

Dimensionless temperature distribution versus x at y = 0.9, for Ω = π and different values of the parameter Γ

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