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Research Papers: Heat and Mass Transfer

Analytical Solution for 2D Non-Fickian Transient Mass Transfer With Arbitrary Initial and Periodic Boundary Conditions

[+] Author and Article Information
Yaohong Suo

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China;
School of Science,
Xi'an University of Science and Technology,
Xi'an 710054, China
e-mail: Yaohongsuo@126.com

Shengping Shen

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: sshen@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received August 23, 2012; final manuscript received January 29, 2013; published online July 18, 2013. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 135(8), 082001 (Jul 18, 2013) (9 pages) Paper No: HT-12-1453; doi: 10.1115/1.4024352 History: Received August 23, 2012; Revised January 29, 2013

Two-dimensional non-Fickian diffusion equation is solved analytically under arbitrary initial condition and two kinds of periodic boundary conditions. The concentration field distributions are analytically obtained with a form of double Fourier series, and the damped diffusion wave transport is discussed. At the same time, the numerical simulation is carried out for the problem with homogeneous boundary condition and arbitrary initial condition, which shows that the concentration field gradually changes from the initial distribution to the steady distribution and it changes faster for the smaller Vernotte number. The numerical results agree well with the experimental results.

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Figures

Grahic Jump Location
Fig. 1

Sketch of 2D non-Fickian diffusion

Grahic Jump Location
Fig. 2

The evolution of concentration field for Ve2 = 1. (a) T = 0, (b) T = 0.1, (c) T = 0.2, and (d) T = 10.

Grahic Jump Location
Fig. 3

The evolution of concentration field for Ve2 = 5. (a) T = 0, (b) T = 0.1, (c) T = 0.2, and (d) T = 13.

Grahic Jump Location
Fig. 4

The comparison between Fickian and non-Fickian diffusion

Grahic Jump Location
Fig. 5

The comparison between non-Fickian diffusion and experimental result in Ref. [12]

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