Have a personal or library account? Click to login
Application of a generalized heat equation to ultra-fast processes in viscoanelastic isotropic medium Cover

Application of a generalized heat equation to ultra-fast processes in viscoanelastic isotropic medium

Open Access
|Dec 2025

Figures & Tables

Fig. 1

Thickness of metal sheet: l = 1.0E–6 meters.
Thickness of metal sheet: l = 1.0E–6 meters.

Fig. 2

Geometry of dimensionless problem.
Geometry of dimensionless problem.

Fig. 3

Left panel: Fourier’s parabolic heat equation. Right panel: MCV’s hyperbolic heat equation. β = 1 × 10−4.
Left panel: Fourier’s parabolic heat equation. Right panel: MCV’s hyperbolic heat equation. β = 1 × 10−4.

Fig. 4

Left panel: Diffusion z1 = z2 ≠ = 0. Right panel: Generalised heat equation. β = 1 × 10−4.
Left panel: Diffusion z1 = z2 ≠ = 0. Right panel: Generalised heat equation. β = 1 × 10−4.

Fig. 5

Left panel: Trend of the dimensionless of heat absorption respect to time dimensionless, due at stimulation of laser. Right panel: Trend rate temperature normalized respect to maximum rate temperature dimensionless.
Left panel: Trend of the dimensionless of heat absorption respect to time dimensionless, due at stimulation of laser. Right panel: Trend rate temperature normalized respect to maximum rate temperature dimensionless.

Fig. 6

Left panel: Trend of the dimensionless temperature of gold metal film when the dimensionless depth changes for various values of the dimensionless time. Right panel: Trend of the dimensionless temperature of gold metal film when the dimensionless time changes for various values of the dimensionless depth.
Left panel: Trend of the dimensionless temperature of gold metal film when the dimensionless depth changes for various values of the dimensionless time. Right panel: Trend of the dimensionless temperature of gold metal film when the dimensionless time changes for various values of the dimensionless depth.

Physical significance: λ(ξ, ξ), λ(q,q), λ(0), a(ξ, ξ)_

CoefficientDescriptionMeasurement unit

λ (ξ, ξ ), λ (q,q), λ (0)Thermal conductivityW =(meters Kelvin)
a(ξ, ξ )Thermal conductivity rateW =(meters Kelvin seconds)

Parameter estimation values for some metals_

Metalα′ (10−4 × m2/s)t1 (picoseconds)t2 (picoseconds)

Ag1.66200.743889.286
Cu1.12830.434870.883
Au1.24950.743889.286
Pb0.23010.167012.097
Language: English
Page range: 389 - 404
Submitted on: Jul 28, 2024
|
Accepted on: Sep 8, 2024
|
Published on: Dec 18, 2025
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Armando Ciancio, Bruno Felice Filippo Flora, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.