Abstract
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.
Highlights
Heat conduction phenomena of material involving moving heat sources, which have attracted increasing attention by scientists and engineers in the past few decades, have been studied in a wide range of fields, such as welding, cutting, drilling, laser hardening/forming, plasma spraying, heat treating of metals, manufacturing of electronic components, and even firing a gun barrel, solid propellant burning, and dental treatment, see e.g., [1,2,3,4,5] and references therein
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]
Most of numerical studies, regardless using meshless methods [13, 14] or meshbased methods such as the finite element method [6, 10], were concerned about problems involving only a heat source moving along a straight line with a constant speed, or multiple heat sources moving along parallel straight lines with the same constant speed
Summary
Heat conduction phenomena of material involving moving heat sources, which have attracted increasing attention by scientists and engineers in the past few decades, have been studied in a wide range of fields, such as welding, cutting, drilling, laser hardening/forming, plasma spraying, heat treating of metals, manufacturing of electronic components, and even firing a gun barrel, solid propellant burning, and dental treatment, see e.g., [1,2,3,4,5] and references therein. The most important physical quantity of interest for such practical applications is the temperature field of the medium, which is usually modeled by the heat conduction equation with time-dependent localized source terms for moving heat sources. 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]. Based on the above observations, this paper is concerned about the efficiently numerical study of two-dimensional (2D) heat conduction problems involving multiple moving heat sources by the moving mesh method.
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