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.
Highlights
Porous materials make their appearance in a wide variety of settings, natural and artificial and in diverse technological applications
The fractional order parameterα has a significant effect on the temperature distribution, where increasing onα causes increasing on T and the rate of change of T with respect to x increases when α increases which is compatible with the definition of the thermal conductivity
And 3, the fractional order parameterα has a significant effect on the displacement u and w distributions, where increasing onα causes increasing on the absolute values of u and w, and the rate of change of them with respect to x increase when α increases which is compatible with the definition of the thermal conductivity
Summary
Porous materials make their appearance in a wide variety of settings, natural and artificial and in diverse technological applications. A new formula of heat conduction has been considered in the context of the fractional integral operator definition by Youssef (2010) This new consideration generated the fractional order generalized thermoelasticity which was cited by Youssef who approved the uniqueness of its solutions. Youssef solved one dimensional problem in the context of the fractional order generalized thermoelasticity and discussed the effects of the fractional order parameter on all the studied fields and with Al-Leheabi i(2010). A two-dimensional problem of a porous material will be considered within the context of the fractional order generalized thermoelasticity theory with one relaxation time. The effect of the fractional order of the temperature, displacement components, the stress and components, changes in volume fraction field distribution will be depicted graphically
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