An unconditionally stable three level finite difference scheme for solving parabolic two‐step micro heat transport equations in a three‐dimensional double‐layered thin film

Dai, Weizhong; Li, Quang; Nassar, Raja; Shen, Liran

doi:10.1002/nme.887

Cited by 20 publications

(6 citation statements)

References 21 publications

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“…The heat source for both layers is given as

Q (x, t) = 0.94 J \frac{1 - R}{t_{p} δ} \exp [- \frac{x}{δ} - 2.77 {(\frac{t - 2 t_{ρ}}{t_{ρ}^{2}})}^{2}],

where J = 13.7 (J/m

^{2}), δ = 15.3

true(

), t_{p} = 100

(fs) and

R = 0.93.

Here, 1 (ps)

= 10^{- 12}

(s), 1

true(

) = 10^{- 15}

true(

),

and

1

true(

) = 10^{- 9}

true(

) .

The initial temperature was chosen to be 300 (K).…”

Section: Numerical Examplesmentioning

confidence: 99%

A second‐order finite difference scheme for solving the dual‐phase‐lagging equation in a double‐layered nanoscale thin film

Sun

Dai

2016

Numerical Methods Partial

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This article considers the dual-phase-lagging (DPL) heat conduction equation in a double-layered nanoscale thin film with the temperature-jump boundary condition (i.e., Robin's boundary condition) and proposes a new thermal lagging effect interfacial condition between layers. A second-order accurate finite difference scheme for solving the heat conduction problem is then presented. In particular, at all inner grid points the scheme has the second-order temporal and spatial truncation errors, while at the boundary points and at the interfacial point the scheme has the second-order temporal truncation error and the first-order spatial truncation error. The obtained scheme is proved to be unconditionally stable and convergent, where the convergence order in L ∞ -norm is two in both space and time. A numerical example which has an exact solution is given to verify the accuracy of the scheme. The obtained scheme is finally applied to the thermal analysis for a gold layer on a chromium padding layer at nanoscale, which is irradiated by an ultrashort-pulsed laser.

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“…The heat source for both layers is given as

Q (x, t) = 0.94 J \frac{1 - R}{t_{p} δ} \exp [- \frac{x}{δ} - 2.77 {(\frac{t - 2 t_{ρ}}{t_{ρ}^{2}})}^{2}],

where J = 13.7 (J/m

^{2}), δ = 15.3

true(

), t_{p} = 100

(fs) and

R = 0.93.

Here, 1 (ps)

= 10^{- 12}

(s), 1

true(

) = 10^{- 15}

true(

),

and

1

true(

) = 10^{- 9}

true(

) .

The initial temperature was chosen to be 300 (K).…”

Section: Numerical Examplesmentioning

confidence: 99%

A second‐order finite difference scheme for solving the dual‐phase‐lagging equation in a double‐layered nanoscale thin film

Sun

Dai

2016

Numerical Methods Partial

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“…Here, A e , C l , k 0 and G are all positive constants. The above coupled equations (1) and (2), often referred to as parabolic two-step microscale heat transport equations, have been widely applied in analysis of microscale heat transfer [6][7][8][9][10][11][12][13][14][15]. However, when the laser pulse duration is much shorter than the electron-lattice thermal relaxation time that is the characteristic time for the activation of ballistic behavior in the electron gas, the parabolic two-step model may lose accuracy [8,10].…”

Section: Introductionmentioning

confidence: 99%

A finite difference scheme for solving a nonlinear hyperbolic two-step model in a double-layered thin film exposed to ultrashort-pulsed lasers with nonlinear interfacial conditions

Dai

Niu

2008

Nonlinear Analysis: Hybrid Systems

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“…To date, a number of models that focus on heat transfer in the context of ultrashort pulsed lasers have been developed [11][12][13][14][15][16][17][18][19][20][21][22][23]. However, only a few mathematical models for studying thermal deformation induced by ultrashort pulsed lasers have been developed [1,[24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A Finite-Difference Method for Studying Thermal Deformation in a 3-D Microsphere Exposed to Ultrashort Pulsed Lasers

Dai

Wang

2007

Numerical Heat Transfer, Part A: Applications

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Studying the thermal deformation induced by ultrashort pulsed lasers is important for preventing thermal damage. This article presents a numerical method for studying thermal deformation in a 3-D microsphere exposed to ultrashort pulsed lasers. The method is obtained based on the parabolic two-step model and implicit finite-difference scheme on a staggered grid. In particular, a fourth-order compact scheme is developed for evaluating those stress derivatives in the dynamic equations of motion. The method allows us to avoid nonphysical oscillations in the solution. Its performance is demonstrated by a numerical example.

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An unconditionally stable three level finite difference scheme for solving parabolic two‐step micro heat transport equations in a three‐dimensional double‐layered thin film

Cited by 20 publications

References 21 publications

A second‐order finite difference scheme for solving the dual‐phase‐lagging equation in a double‐layered nanoscale thin film

A second‐order finite difference scheme for solving the dual‐phase‐lagging equation in a double‐layered nanoscale thin film

A finite difference scheme for solving a nonlinear hyperbolic two-step model in a double-layered thin film exposed to ultrashort-pulsed lasers with nonlinear interfacial conditions

A Finite-Difference Method for Studying Thermal Deformation in a 3-D Microsphere Exposed to Ultrashort Pulsed Lasers

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