Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

Abstract

In the work, a two-dimensional problem of a porous material is considered within the context of the fractional order generalized thermoelasticity theory with one relaxation time. The medium is assumed initially quiescent for a thermoelastic half space whose surface is traction free and has a constant heat flux. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. The effect of the fractional order of the temperature, displacement components, the stress components, changes in volume fraction field and temperature distribution have been depicted graphically.

Analytical and Numerical Solution of 2D Problem for Transversely Isotropic Generalized Thermoelastic Medium with Green-Naghdi Model II

“…ε1 . Equations (23)-(25) can be written in a vectormatrix differential equation as follows: [40][41][42][43]…”

Normal Mode Analysis to a Poroelastic Half-Space Problem under Generalized Thermoelasticity

“…Sherief and Hussein (2012) developed a set of governing equations that effectually create a mathematical model of generalized thermoelasticity in poroelastic materials, then, they used this model to solve a thermal shock problem regarding the use of half-space. Abbas and Youssef (2015) solved a two-dimensional problem of a porous material in the context of the fractional order generalized thermoelasticity theory with one relaxation time. Wei et al (2016) studied the reflection and refraction phenomenon that occurs in an oblique incidence longitudinal wave at a plane interface between an isotropic, homogeneous, thermoelastic medium and a porous thermoelastic medium.…”

Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity

“…Song et al [29] studied the vibration of microcantilevers during a photothermal process by coupling the theories of fractional order heat conduction and elastic waves. Abbas and Youssef [30] investigated a twodimensional problem of a porous half-space with a tractionfree surface and a constant heat flux with fractional order generalized thermoelasticity theory. Recently, a completely new fractional order generalized thermoelasticity theory was introduced by Sherief et al [31].…”