Green's function for infinite thin plate with elliptic hole under bending heat source and interaction between elliptic hole and crack under uniform bending heat flux

2016 ◽  
Vol 39 (2) ◽  
pp. 170-182 ◽  
Author(s):  
Norio Hasebe ◽  
Jian Jun Han
Keyword(s):  
Heat Flux ◽  
Heat Source ◽  
Green’S Function ◽  
Thin Plate ◽  
Green's Function ◽  
Elliptic Hole

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

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
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.

Green's function for a coated elliptic hole problem in plane elasticity

2010 ◽  
Vol 1 (4) ◽  
pp. 281 ◽  
Author(s):  
Ching Kong Chao ◽  
Chin Kun Chen ◽  
Fu Mo Chen ◽  
Alexander M. Korsunsky
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elliptic Hole ◽  
Plane Elasticity

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
David Gonzalez Cuadrado ◽  
Francisco Lozano ◽  
Valeria Andreoli ◽  
Guillermo Paniagua
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Green’S Function ◽  
Convective Heat ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Filter Method ◽  
Convective Heat Flux ◽  
Inverse Heat Transfer

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on discrete Green's functions . The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions; in this case, the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the digital filter method is applied in order to take advantage of the response of the temperature to heat flux pulses. The discrete Green's function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In this procedure, the terms of the Green's function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green's functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green's function method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material, and the physical properties of the rotor casing.

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