An Inverse Problem Using Green’s Function and TFBGF Method to Identificate a Moving Heat Source in 3D Heat Conduction Problem

A numerical study of transient three-dimensional heat conduction problem with a moving source is presented. For numerical solution Douglas-Gunn alternating direction implicit method is applied and for the moving heat source flux distribution Gaussian function is used. An influence on numerical solution of input parameters figuring in flux boundary conditions is examined. This include parameters appearing in Gaussian function and heat transfer coefficient from free convection boundaries. Sensitivity of cooling time from 800 to 500?C with respect to input parameters is also tested.

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A Note on the General Formulation of Phase Change Problem as Heat Conduction Problem with a Moving Heat Source

Journal of Heat Transfer ◽

10.1115/1.3450813 ◽

1978 ◽

Vol 100 (2) ◽

pp. 370-371 ◽

Cited By ~ 6

Author(s):

M. Necati O¨zis¸ik

Keyword(s):

Heat Conduction ◽

Heat Source ◽

Phase Change ◽

Heat Conduction Problem ◽

Moving Heat Source ◽

Change Problem

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Green’s Function Solution of Dual-Phase-Lag Model

ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer, Volume 3 ◽

10.1115/mnhmt2009-18425 ◽

2009 ◽

Cited By ~ 3

Author(s):

Yung-Ming Lee ◽

Pei-Chi Lin ◽

Tsung-Wen Tsai

Keyword(s):

Heat Conduction ◽

Heat Source ◽

Green’S Function ◽

Green's Function ◽

Phase Lag ◽

Micro Scale ◽

Function Solution ◽

Lag Model ◽

Temperature Solution ◽

Good Agreement

In this study, the micro-scale heat conduction solution in a finite rigid slab computed with and without heat source is investigated. The analytical solution is derived by Laplace transform (LT) technique and Green’s function solution (GFS) method. The effect of heat source on the micro-scale heat conduction solution is also included in this paper. It is found that the temperature solution obtained by GFS method is smaller than that obtained by LT technique, and the GFS is in very good agreement with the solution obtained by the conventional Fourier’s law when τq = τT. Moreover, the temperature distributions computed by the LT technique are always overestimated in this study owing to the absence of the G2 effect. Hence, it is believed that the temperature solutions predicted by the GFS-LT method are more accurate than those evaluated by the LT technique. When time is increasing, the discrepancies of temperature solutions among various methods for τT > τq is increasing.

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Estimation of a Moving Heat Source due to a Micromilling Process Using the Modified TFBGF Technique

Mathematical Problems in Engineering ◽

10.1155/2018/9105940 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Sidney Ribeiro ◽

Ana Paula Fernandes ◽

Daniel Fernandes da Cunha ◽

Marcio Bacci da Silva ◽

Jerry Shan ◽

...

Keyword(s):

Heat Flux ◽

Heat Source ◽

Green’S Function ◽

Green's Function ◽

Optimization Technique ◽

Transient Heat Conduction ◽

Moving Heat Source ◽

Machining Processes ◽

Conduction Model ◽

Accessible Region

Moving heat sources are present in numerous engineering problems as welding and machining processes, heat treatment, or biological heating. In all these cases, the heat input identification represents an important factor in the optimization of the process. The aim of this study is to investigate the heat flux delivered to a workpiece during a micromilling process. The temperature measurements were obtained using a thermocouple at an accessible region of the workpiece surface while micromilling a small channel. The analytical solution is calculated from a 3D transient heat conduction model with a moving heat source, called direct problem. The estimation of the moving heat source uses the Transfer Function Based on Green’s Function Method. This method is based on Green’s function and the equivalence between thermal and dynamic systems. The technique is simple without iterative processes and extremely fast. From the temperature on accessible regions it is possible to estimate the heat flux by an inverse procedure of the Fast Fourier Transform. A test of micromilling of 6365 aluminium alloy was made and the heat delivered to the workpiece was estimated. The estimation of the heat without use of optimization technique is the great advantage of the technique proposed.

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