Heat diffusion vs. wave propagation in solids subjected to exponentially-decaying heat source: Analytical solution

Lam, Tung T.; Fong, Ed

doi:10.1016/j.ijthermalsci.2011.05.006

Cited by 36 publications

(14 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3. The predictions calculated from (70) agree excellently well with those obtained using the solution structure theorem (Lam and Fong, 2011b). Thus far, the terms associated with initial conditions and energy generation of the solution (40) as well as the Green's function shown in Table 3 is verified.…”

Section: Examplesupporting

confidence: 72%

See 1 more Smart Citation

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

2018

JTST

View full text Add to dashboard Cite

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.

show abstract

Section: Examplesupporting

confidence: 72%

“…The solution to (66) has previously been obtained by Fong (2011a and2011b) using the solution structure…”

Section: Numerical Examplesmentioning

confidence: 99%

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

2018

JTST

View full text Add to dashboard Cite

show abstract

“…To evaluate the accuracy of the obtained solution, the results were compared to the results of Lam and Fong [40], which is a linear analytical study (Fig. 2).…”

Section: Resultsmentioning

confidence: 99%

“…2b show the temperature profile for Fo = 0.1 and Fo = 0.5, respectively. Other parameters were initialized based on the values in Lam and Fong [40] (g 0 = 100,μ = 5,β = 1,δ = 5). Under these conditions, the bulk distance and the perturbation functions coefficients are as follows: [40] (V e = 1, γ = 0)…”

Section: Resultsmentioning

confidence: 99%

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

Noroozi¹,

Saedodin²,

Ganji³

2016

Archive of Mechanical Engineering

View full text Add to dashboard Cite

The effect of laser, as a heat source, on a one-dimensional finite body was studied in this paper. The Cattaneo-Vernotte non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The obtained equations were solved using the approximate-analytical Adomian Decomposition Method (ADM). It was concluded that the non-linear analysis is important in non-Fourier heat conduction problems. Significant differences were observed between the Fourier and non-Fourier solutions which stresses the importance of non-Fourier solutions in the similar problems.

show abstract

“…With the aid of these methods, numerous problems are investigated in the context of HHC law, such as thermal wave phenomena in a thin finite film subjected to nonhomogeneous boundary conditions [14], two-layers slab under periodic boundary temperature with perfect and imperfect thermal contact [12], fast precooling process of a cylindrically shaped food product [20], the effect of a timedependent laser heat source on a moving finite medium [21], HHC problems in an infinitely long layered solid cylinder with radiation surface [22], hyperbolic conduction and radiation heat transfer problem in a planar participating medium [17], thermal waves in a rigid heat conductor [23], a semi-infinite layer in contact with a finite one excited by a modulated heat source [24]. The HHC is also adopted to analyze laser heating or thermal processing of materials employing the internal heat source [21,[25][26][27][28]. Some inverse HHC problems are investigated within hyperbolic heat conductive law [29][30][31][32][33][34].…”

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

View full text Add to dashboard Cite

Heat diffusion vs. wave propagation in solids subjected to exponentially-decaying heat source: Analytical solution

Cited by 36 publications

References 16 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

Nonlinear Solution to a Non-Fourier Heat Conduction Problem in a Slab Heated by Laser Source

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

Contact Info

Product

Resources

About