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

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Xue-Yang Zhang ◽  
Yi Peng ◽  
Xian-Fang Li
Keyword(s):  
Heat Conduction ◽  
Fractional Order ◽  
Integral Transform ◽  
Moisture Diffusion ◽  
Moisture Flux ◽  
Moisture Distribution ◽  
Order Derivative ◽  
Transform Method ◽  
Stress Components ◽  
Heat And Moisture

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.

Analytical solution for heat and moisture diffusion in layered materials

2010 ◽  
Vol 47 (6) ◽  
pp. 595-608 ◽  
Author(s):  
Jeongwoo Lee ◽  
Ji-Tae Kim ◽  
Il-Moon Chung ◽  
Nam Won Kim
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Moisture Diffusion ◽  
Layered Materials ◽  
Diffusion Problem ◽  
Moisture Distribution ◽  
Coupled Flow ◽  
Coupled Diffusion ◽  
Heat And Moisture

The study of heat and moisture flows in multiple layers of different materials that make up the unsaturated zone is of great importance when characterizing the behaviour of these materials. In the present paper, analytical solutions of the one-dimensional heat and moisture coupled diffusion problem for layered materials under two different sets of boundary conditions are proposed. The coupled flow of heat and moisture are assumed to follow the theory of Philip and De Vries, and the solutions are derived analytically using integral transform methods. A comparison between the analytical and numerical solutions for one example problem shows satisfactory results. Furthermore, a procedure is presented for estimating heat and moisture distribution profiles in any layered materials using the derived analytical solutions. It is expected that the proposed analytical solutions will be used effectively for preliminary analyses of coupled heat and moisture movements in unsaturated porous media.

Transient response of the hygro-thermo-elastic field in hollow cylinders under heat-moisture shock via hyperbolic non-Fourier heat conduction and non-Fick diffusion

2020 ◽  
pp. 095440622095447
Author(s):  
Y Peng ◽  
C-M Cheng ◽  
X-T Chen ◽  
X-Y Zhang ◽  
X-F Li
Keyword(s):  
Relaxation Time ◽  
Heat Conduction ◽  
Transient Response ◽  
Elastic Field ◽  
Moisture Flux ◽  
Elastic Displacement ◽  
Phase Lag ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Heat And Moisture

The classical Fourier heat conduction theory as well as the widely used Fick’s diffusion law predicts an infinite wave velocity. This is physically unrealistic. By generalizing the classical Fourier’s and Fick’s laws, this paper presents a hyperbolic diffusion law to apply heat and moisture coupling. The transient response of the hygro-thermo-elastic field in infinitely long hollow cylinders subjected to sudden heat and moisture shock on the inner and outer surfaces is studied. With the aid of the Laplace transform and the decoupling technique, the closed-form solutions of temperature, moisture, elastic displacement and stresses are determined respectively. The analytical results show that the thermal and moisture relaxation time effect between temperature and moisture is significant for composites. Compared with the classic counterpart, the finite hygrothermal wave speed of the pipe is achieved and decreases with the relaxation time rising. The temperature, moisture, elastic displacement and stresses are calculated. Numerical results are displayed graphically to show the influence of the phase lag of heat/moisture flux on the response of the hygro-thermo-elastic fields. Non-Fourier and non-Fick effects are remarkable between the classic model and hyperbolic hygrothermal coupling model. Some drawbacks induced by the classical Fourier’s and Fick’s laws are averted.

scholarly journals On the Agaciro Equation via the Scope of Green Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Abdon Atangana ◽  
Innocent Rusagara
Keyword(s):  
Exact Solution ◽  
Green Function ◽  
Fractional Order ◽  
Mellin Transform ◽  
Integral Transform ◽  
Special Functions ◽  
Order Derivative ◽  
Third Order ◽  
Fractional Order Derivative ◽  
The Green Function

We have undertaken an investigation of a kind of third-order equation called Agaciro equation within the folder of both integer and fractional order derivative. In the way of deriving the general exact solution of this equation, we employed the philosophy of the Green function together with some integral transform operators and special functions including but not limited to the Laplace, Fourier, and Mellin transform. We presented some examples of exact solution of this class of third-order equations for integer and fractional order derivative. It is important to point out that the value of Agaciro equation can be extended to describe assorted phenomenon in sciences.

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