Analytical solution of dual-phase-lag heat conduction in a finite medium subjected to a moving heat source

Ma, Jingxuan; Sun, Yuxin; Yang, Jialing

doi:10.1016/j.ijthermalsci.2017.11.005

Cited by 44 publications

(21 citation statements)

References 41 publications

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“…Depending on the physical nature of the problem, a moving heat source can be roughly classified into three types, namely, the point, line, and plane heat source. All of them concentrate high power in a time-dependent localized region and can be well modeled by a Dirac delta Advances in Mathematical Physics function [1,2,8,12]. However, the singularity of delta function introduces additional difficulties especially for numerical simulation of practical engineering applications.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Now, we are in a position to describe the whole numerical algorithm that simulates the moving heat source problem with the moving mesh method. It is evident that the full discretization, including the system of the discretization (12) and the discretization of two 1D MMPDE6 for x n+1 i and y n+1 j , respectively, is coupled together via the monitor functions and the physical mesh. A simple decouple strategy is adopted in the present algorithm, that is, the mesh equation and the physical equation are solved alternately one by one.…”

Section: Discretization On the Moving Meshmentioning

confidence: 99%

“…In order to investigate the temperature field and the related thermal properties of the problem with moving heat sources, numerous methods, in either analytical or numerical approach, have been developed, since the 1930s, when the pioneering work of Rosenthal was proposed for the analytical solution of a simplified moving heat source problem [11]. Although analytical methods are still popular nowadays [12], they are usually only available for simple situations such as the quasistationary problem of a single heat source moving along a straight line with a constant speed. In comparison to analytical methods, numerical methods could only provide results approximately within an acceptable error tolerance, but they are more flexible to deal with the complicated yet practical situations such as the transient problem of multiple heat sources moving in a complex geometry of the material with time-dependent speeds [3].…”

Section: Introductionmentioning

confidence: 99%

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Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Liu

2020

Advances in Mathematical Physics

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This paper focuses on efficiently numerical investigation of two-dimensional heat conduction problems of material subjected to multiple moving Gaussian point heat sources. All heat sources are imposed on the inside of material and assumed to move along some specified straight lines or curves with time-dependent velocities. A simple but efficient moving mesh method, which continuously adjusts the two-dimensional mesh dimension by dimension upon the one-dimensional moving mesh partial differential equation with an appropriate monitor function of the temperature field, has been developed. The physical model problem is then solved on this adaptive moving mesh. Numerical experiments are presented to exhibit the capability of the proposed moving mesh algorithm to efficiently and accurately simulate the moving heat source problems. The transient heat conduction phenomena due to various parameters of the moving heat sources, including the number of heat sources and the types of motion, are well simulated and investigated.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Discretization On the Moving Meshmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Liu

2020

Advances in Mathematical Physics

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“…They derived the Green's function for the fourth-order vibration equation and derived the deflection of a heated beam. Ma et al [28,29] utilized the Green's function technique to present a general solution for the dual-phase-lag heat conduction equations of a two-dimensional square plate and a three-dimensional skin model.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

et al. 2018

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Abstract:In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green's function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail.

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“…Typical applications include contact surfaces such as free-boundary solidification [1], and many metallurgical processes such as laser cutting and welding [2][3][4][5]. Mathematically, this problem can be well modeled by the heat conduction equation with singular source terms, which utilize a time-dependent delta function to describe each highly localized and moving heat source (see [1,3,6,7] and references therein). It is well known nowadays that the solution of such a model equation is continuous and piecewise smooth with a jump for derivative of the solution when crossing each heat source [8].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Heat Conduction with Multiple Moving Heat Sources

2018

Symmetry

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This paper is concerned about the efficiently numerical simulation of heat conduction problems with multiple heat sources that are allowed to move with different speeds. Based on the dynamical domain decomposition upon the trajectories of moving sources, which are solved by a predictor–corrector algorithm, a non-overlapping domain-decomposed moving mesh method is developed. Such a method can not only generate the adaptive mesh efficiently by parallel computing, but also greatly simplify the discretization of the underlying equations without loss of accuracy. Numerical examples for various motions of sources are presented to illustrate the accuracy, the convergence rate and the efficiency of the proposed method. The dependence of the solution on the moving sources such as the types of motion and the distance between sources is numerically investigated. A blow-up phenomenon that occurs at multiple locations simultaneously can also be well observed for the case of symmetrically moving sources.

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Analytical solution of dual-phase-lag heat conduction in a finite medium subjected to a moving heat source

Cited by 44 publications

References 41 publications

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

Numerical Investigation of Heat Conduction with Multiple Moving Heat Sources

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