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Technical Brief

Fisher–Kolmogorov–Petrovsky– Piscounov Reaction and n-Diffusion Cattaneo Telegraph Equation

[+] Author and Article Information
Ulrich Olivier Dangui-Mbani, Jize Sui

School of Energy and Environmental Engineering,
University of Science and Technology Beijing,
Beijing 100083, China;
School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China

Liancun Zheng

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: liancunzheng@ustb.edu.cn

Bandar Bin-Mohsin

Department of Mathematics,
College of Science,
King Saud University,
Riyadh 14451, Saudi Arabia

Goong Chen

Department of Mathematics and
Institute for Quantum Science and Engineering,
Texas A&M University,
College Station, TX 77843;
Science Program,
Texas A & M University at Qatar,
Education City Student Center,
Doha, Qatar

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 17, 2016; final manuscript received February 9, 2017; published online March 21, 2017. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 139(7), 074502 (Mar 21, 2017) (5 pages) Paper No: HT-16-1516; doi: 10.1115/1.4036005 History: Received August 17, 2016; Revised February 09, 2017

This paper presents research for a class of recombination reaction and diffusion problems in which the Cattaneo relaxation, n-diffusion flux, and p-Fisher–Kolmogorov–Petrovsky–Piscounov (KPP) reaction are considered. Approximate analytical solutions are obtained by Adomian decomposition method (ADM) and shown graphically. Some interesting results for spatial variable and temporal variable evolution are obtained. For specified spatial variable, the temperature profiles decrease with respect to the increase of relaxation parameter and power-law index n but decrease with respect to Fisher–KPP reaction parameter p. For specified temporal variable, the temperature profiles are seem oscillating with values of the relaxation parameter and power-law index n.

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References

Figures

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Fig. 1

Comparison between ADM and exact temperature profiles when n=1,p=0,ζ=τ0=0.02 at t=0.1

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Fig. 2

The effects of relaxation parameter ζ on the temperature profile at x=0.1 when n=0.5,p=3

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Fig. 3

The effects of power-law exponent n on the temperature profile at x=0.1 when ζ=0.1,p=2

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Fig. 4

The effects of Fisher–KPP reaction parameter p on temperature at x=0.1 when n=0.5,ζ=0.2

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Fig. 5

The effects of relaxation parameter ζ on temperature at t=0.1 when n=2,p=0.2

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Fig. 6

The effects of Fisher–KPP reaction parameter p on temperature at t=0.1 when n=2,ζ=0.2

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Fig. 7

The effects of n on temperature at t=0.1 when p=0.8,ζ=0.2

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