Research Papers: Heat and Mass Transfer

Time-Fractional Hygrothermoelastic Problem for a Sphere Subjected to Heat and Moisture Flux

[+] Author and Article Information
Xue-Yang Zhang, Yi Peng

School of Civil Engineering,
Central South University,
Changsha 410075, China

Xian-Fang Li

School of Civil Engineering,
Central South University,
Changsha 410075, China
e-mail: xfli@csu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 2, 2017; final manuscript received August 22, 2018; published online October 8, 2018. Assoc. Editor: Evelyn Wang.

J. Heat Transfer 140(12), 122002 (Oct 08, 2018) (9 pages) Paper No: HT-17-1522; doi: 10.1115/1.4041419 History: Received September 02, 2017; Revised August 22, 2018

In this paper, a non-Fourier model of heat conduction and moisture diffusion coupling is proposed. We study a hygrothermal elastic problem within the framework of time-fractional calculus theory for a centrally symmetric sphere subjected to physical heat and moisture flux at its surface. Analytic expressions for transient response of temperature change, moisture distribution, displacement, and stress components in the sphere are obtained for heat/moisture flux pulse and constant heat/moisture flux at the sphere's surface, respectively, by using the integral transform method. Numerical results are calculated and the effects of fractional order on temperature field, moisture distribution, and hygrothermal stress components are illustrated graphically. Subdiffusive and super-diffusive transport coupling behavior as well as wave-like behavior are shown. When fractional-order derivative reduces to first-order derivative, the usual heat and moisture coupling is recovered, which obeys Fourier heat conduction and Fick's moisture diffusion.

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Grahic Jump Location
Fig. 1

Schematic of a solid sphere in heat and moisture environment

Grahic Jump Location
Fig. 2

The distribution of dimensionless temperature θ at κ = 0.25 for fundamental solution

Grahic Jump Location
Fig. 3

The distribution of dimensionless moisture ψ at κ = 0.25 for fundamental solution

Grahic Jump Location
Fig. 4

The distribution of dimensionless radial stress component σrr at κ = 0.25 for fundamental solution

Grahic Jump Location
Fig. 5

The distribution of dimensionless tangential stress component σφφ at κ = 0.25 for fundamental solution

Grahic Jump Location
Fig. 6

The distribution of dimensionless temperature θt¯α−1 at κ = 0.5 for constant heat flux

Grahic Jump Location
Fig. 7

The distribution of dimensionless moisture ψt¯α−1 at κ = 0.5 for constant heat flux

Grahic Jump Location
Fig. 8

The distribution of dimensionless radial stress component σrrt¯α−1 at κ = 0.5 for constant heat flux

Grahic Jump Location
Fig. 9

The distribution of dimensionless tangential stress component σφφt¯α−1 at κ = 0.25 for constant heat flux



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