scholarly journals A generalized thermoelastic diffusion problem for an infinitely long solid cylinder

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Moncef Aouadi
Keyword(s):  
Generalized Thermoelasticity ◽  
Diffusion Problem ◽  
Cylinder Surface ◽  
Solid Cylinder ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic Diffusion ◽  
Stress Region ◽  
The Laplace Transform ◽  
Generalized Thermoelastic ◽  
Special Case

The theory of generalized thermoelastic diffusion, based on the theory of Lord and Shulman, is used to study the thermoelastic-diffusion interactions in an infinitely long solid cylinder subjected to a thermal shock on its surface which is in contact with a permeating substance. By means of the Laplace transform and numerical Laplace inversion the problem is solved. Numerical results predict finite speeds of propagation for thermoelastic and diffusive waves and the presence of a tensile stress region close to the cylinder surface. The problem of generalized thermoelasticity has been reduced as a special case of our problem.

A generalized thermoelastic diffusion problem with memory-dependent derivative

2018 ◽  
Vol 24 (5) ◽  
pp. 1438-1462 ◽  
Author(s):  
Yan Li ◽  
Tianhu He
Keyword(s):  
Time Delay ◽  
Chemical Potential ◽  
Diffusion Theory ◽  
Diffusion Problem ◽  
Kernel Functions ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic Diffusion ◽  
The Laplace Transform ◽  
Generalized Thermoelastic ◽  
With Memory

Based on the generalized thermoelastic diffusion theory with memory-dependent derivative in both the generalized heat conduction law and the generalized diffusion law, the transient response is investigated of a half-space subjected to a thermal shock and a chemical potential shock on its bounding surface. The coupled governing equations containing time-delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The non-dimensional temperature, chemical potential, displacement, stress, as well as concentration at different values of time, time-delay factors, and kernel functions are obtained and illustrated graphically. The results show that: all the considered variables have obvious changes with the passage of time; the thermal time-delay and kernel functions hardly influence the distributions of the non-dimensional chemical potential, modestly influence the distributions of the non-dimensional concentration, while appreciably influence the distributions of the non-dimensional temperature, displacement, and stress; the diffusion time-delay and kernel functions barely affect the distributions of the non-dimensional temperature, slightly affect the distributions of the non-dimensional concentration, while remarkably affect the distributions of the non-dimensional chemical potential, displacement and stress.

The Effects of Diffusion and Temperature-Dependent Properties on Generalized Thermoelastic Behaviors in Thermal Dynamics

2012 ◽  
Vol 625 ◽  
pp. 318-322 ◽  
Author(s):  
Yong Ping Liu ◽  
Shuan Hu Shi
Keyword(s):  
Finite Element ◽  
Diffusion Problem ◽  
Temperature Dependent ◽  
Thermal Dynamics ◽  
Thermoelastic Wave ◽  
Diffusion Wave ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic Diffusion ◽  
Generalized Thermoelastic ◽  
Temperature Dependent Properties

The generalized thermoelastic diffusion problem with temperature-dependent properties is investigated in the context of the theory of generalized thermoelastic diffusion. The problem is solved by means of finite element method and the derived finite element equations are solved directly in time domain. The effects of diffusion and temperature-dependent properties on generalized thermoelastic wave and mass diffusion wave are studied in detail. The results show that all the considered variables have a non-zero value only in a bounded region and vanish identically beyond this region, the temperature-dependent properties act to reduce all the considered variables and the diffusion barely influences the considered variables.

A Generalized Thermoelastic Diffusion Problem with Temperature-Dependent Properties

2014 ◽  
Vol 490-491 ◽  
pp. 670-675
Author(s):  
Tian Hu He ◽  
Yan Bo Niu ◽  
Shuan Hu Shi ◽  
Yong Bin Ma
Keyword(s):  
Diffusion Problem ◽  
Bounded Region ◽  
Temperature Dependent ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic Diffusion ◽  
Generalized Thermoelastic ◽  
Temperature Dependent Properties

The generalized thermoelastic diffusion problem with temperature-dependent properties is investigated in the context of the theory of generalized thermoelastic diffusion. The results show that all the considered variables have a non-zero value only in a bounded region and vanish identically beyond this region, and the temperature-dependent properties act to reduce all the considered variables.

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