2011
DOI: 10.1007/s11242-011-9840-8
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A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

Abstract: In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic materi… Show more

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Cited by 54 publications
(14 citation statements)
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“…1, 2 , 3, 4, 5, 6. In these figures, the solid line represents the solution obtained in the frame of the dynamic coupled theory (t ¼ 0) (Biot 1955), and the dotted lines represent the solution obtained in the frame of the generalized thermoelasticity with thermal relaxation time t ¼ 1:0; s o ¼ ð 0:02Þ (Sherief and Hussein 2012), while the dashed lines represent the solution obtained in the frame of generalized thermoelasticity with fractional heat transfer 0 \ t \ 1; ð s o ¼ 0:02Þ (Ezzat 2012).…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
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“…1, 2 , 3, 4, 5, 6. In these figures, the solid line represents the solution obtained in the frame of the dynamic coupled theory (t ¼ 0) (Biot 1955), and the dotted lines represent the solution obtained in the frame of the generalized thermoelasticity with thermal relaxation time t ¼ 1:0; s o ¼ ð 0:02Þ (Sherief and Hussein 2012), while the dashed lines represent the solution obtained in the frame of generalized thermoelasticity with fractional heat transfer 0 \ t \ 1; ð s o ¼ 0:02Þ (Ezzat 2012).…”
Section: Numerical Results and Discussionmentioning
confidence: 99%
“…To eliminate these anomalies, Cattaneo (1948) and Vernotte (1958) proposed a damped version of Fourier's law by introducing a heat flux relaxation term, by taking Taylor's series to expand q is ðx i ; t þ s s Þ, q if ðx i ; t þ s f Þ and retaining terms up to the first order in s s and s f . The first well-known generalization of such a type (Sherief and Hussein 2012) …”
Section: Derivation Of Fractional Heat Conduction Equation In Poro-thmentioning
confidence: 99%
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“…Kumar and Devi (2008) investigated a porous, generalized thermoelastic medium subjected to thermomechanical boundary conditions permeated with various heat sources. 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.…”
Section: Latin American Journal Of Solids and Structures 14 (2017) 93mentioning
confidence: 99%