Integral transform solution for hyperbolic heat conduction in a finite slab

Monteiro, Evaldiney Ribeiro; Macêdo, Emanuel Negrão; Quaresma, João Nazareno Nonato; Cotta, Renato M.

doi:10.1016/j.icheatmasstransfer.2009.01.002

Cited by 25 publications

(9 citation statements)

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“…as boundary conditions for HHC (Gheitaghy and Talaee, 2013;Lam, 2014, Lam, 2010;Lam and Fong, 2012;Monteiro et al, 2009). Although the nonhomogeneous boundary condition can be solved by performing a functional transformation or using integral transform method, the meaning of the prescribed function…”

Section: General Hyperbolic Heat Conduction Modelmentioning

confidence: 99%

Analytical solutions to hyperbolic heat conductive models using Green's function method

2018

JTST

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In this work, the existing theoretical heat conductive models such as: Cattaneo-Vernotte model, simplified thermomass model, and single-phase-lag two-step model are summarized, and then a general model of hyperbolic heat conduction (HHC) is presented with boundary conditions prescribed as: (1) temperature at the boundary; (2) heat flux (not the temperature gradient) at the boundary. The convective boundary condition is not considered because it is impossible to produce a fluid motion at such time scale, e.g. picoseconds. In the context of HHC, the reciprocity relation of Green's function is systematically proven, based on which Green's function solution equation of the general model is completely derived. Meanwhile, Green's functions are deduced under several different sets of boundary conditions. Thus, solution to HHC based on Green's function is obtained, and it consists of three parts, i.e. boundary conditions, initial conditions and heat generations. The priority of the present solution is that the time-dependent boundary condition and heat generation may be dealt with, and that it is easy to extend the solution to multi-dimensional case. The accuracy of the solution is verified through numerical examples, and Laplace transform method is adopted to avoid the dispersions around the front of temperature wave for jump-type boundary conditions, thus the solution is further perfected.

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Section: General Hyperbolic Heat Conduction Modelmentioning

confidence: 99%

Analytical solutions to hyperbolic heat conductive models using Green's function method

2018

JTST

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“…The Neumann boundary condition (or gradient-type boundary condition) is always applied in Fourier heat conduction to denote heat flux at the boundary, and some works in the context of HHC also incautiously adopt same form as heat flux boundary conditions [12,14,[49][50][51]. Although these nonhomogeneous boundary condition can be solved by performing a functional transformation or using integral transform method, the kind of boundary condition is, however, not appropriate, which will also be discussed systematically.…”

Section: Introductionmentioning

confidence: 99%

The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale

Xue

et al. 2016

Physics Letters A

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“…The HHCE incorporates a wave nature for heat propagation and a finite speed through the introduction of a thermal relaxation time [10,11]. The HHCE has since been applied to homogeneous engineering bulk materials [12][13][14], thin films [15][16][17], and multilayer materials [18,19]. Several authors have questioned the validity of using the HHCE because it produces sharp wavefronts [12] and violates the second law of thermodynamics through negative absolute temperatures [20] and negative entropy generation [21] results.…”

Section: Introductionmentioning

confidence: 99%

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

Shenoy

Bayazıtoğlu

2015

Numerical Heat Transfer, Part B: Fundamentals

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The effect of non-Fourier boundary condition on the 3-omega method for measuring the thermal conductivity of microscale thin films using the hyperbolic heat conduction equation and the Fourier equation is examined. Non-Fourier boundary condition with the Fourier equation leads to 80% error in the temperature oscillations and increases the error to 85% in the case of non-Fourier boundary condition with the hyperbolic heat conduction equation. The solution of the non-Fourier boundary condition with the hyperbolic heat conduction equation gives the most accurate thermal conductivity expression. The analysis also provides a method for determining the relaxation time of thin films.

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Integral transform solution for hyperbolic heat conduction in a finite slab

Cited by 25 publications

References 25 publications

Analytical solutions to hyperbolic heat conductive models using Green's function method

Analytical solutions to hyperbolic heat conductive models using Green's function method

The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

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