2004
DOI: 10.1023/b:ijot.0000034247.32646.d4
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Thermal Behavior of a Multi-layered Thin Slab Carrying Periodic Signals Under the Effect of the Dual-Phase-Lag Heat Conduction Model

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Cited by 40 publications
(21 citation statements)
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“…Analytical solutions for the hyperbolic heat conduction equation have been obtained for a few relatively simple problems [1,8]. Numerical methods for more complicated problems have been also developed, such as transient heat conduction in multilayer materials [9][10][11] and infinitely wide slab [12]. Miller & Haber [13] reviewed the modification of the Fourier conduction law and described its implementation of the Galerkin finite-element method within a discontinuous space-time that admits jumps in primary variables across element boundaries with an arbitrary orientation in space and time.…”
Section: Introductionmentioning
confidence: 99%
“…Analytical solutions for the hyperbolic heat conduction equation have been obtained for a few relatively simple problems [1,8]. Numerical methods for more complicated problems have been also developed, such as transient heat conduction in multilayer materials [9][10][11] and infinitely wide slab [12]. Miller & Haber [13] reviewed the modification of the Fourier conduction law and described its implementation of the Galerkin finite-element method within a discontinuous space-time that admits jumps in primary variables across element boundaries with an arbitrary orientation in space and time.…”
Section: Introductionmentioning
confidence: 99%
“…It is assumed that the material is transversely isotropic in the r-θ plane. Constitutive equations of the materials in cylindrical coordinate system are σ rr = c 11 ∂u ∂r…”
Section: Basic Governing Equationsmentioning
confidence: 99%
“…In addition, hyperbolic heat conduction with temperature-dependent thermal conductivity, specific heat and thermal diffusivity was also studied [10]. In addition, numerical methods for relatively complicated problems such as multilayered media were also developed [11][12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…To better describe the wave-like behaviour of heat conduction, instead of using Fourier law, the hyperbolic equation, which takes finite heat travelling speed into account, was presented as a constitutive equation that was coupled with the local energy balance [21,22]. Since then, considerable effort has been devoted to the solutions for the non-Fourier heat conduction equation for the cases of one-dimensional heat media [23][24][25][26][27][28], semi-infinite media [29] and layered composite media [30,31]. Further, temperature dependence of the thermal conductivity, specific heat and thermal diffusivity was also studied [32].…”
Section: Introductionmentioning
confidence: 99%