Analytical Solution for Transient Temperature Field Around a Cased and Cemented Wellbore

2005 ◽  
Author(s):  
Vanessa Pereira Separ King ◽  
Lucia Carvalho Coelho ◽  
Jaci Guigon ◽  
Gerson Cunha ◽  
Luiz Landau
Keyword(s):  
Temperature Field ◽  
Analytical Solution ◽  
Transient Temperature ◽  
Transient Temperature Field

scholarly journals A semi-analytical solution of three-dimensional transient temperature field for a uniform plate subjected to Gaussian-distribution laser heat source

2019 ◽  
pp. 268-268
Author(s):  
Xiaogui Wang ◽  
Yili Xiao ◽  
Ninghua Gao ◽  
Lihua Liang ◽  
Congda Lu ◽  
...  
Keyword(s):  
Temperature Field ◽  
Analytical Solution ◽  
Heat Source ◽  
Gaussian Distribution ◽  
Three Dimensional ◽  
Source Distribution ◽  
Transient Temperature ◽  
Laser Heat ◽  
Transient Temperature Field ◽  
Laser Heat Source

One three-dimensional transient temperature field model for a thin uniform plate caused by a moving laser heat source is described in present study. The heat source model with a power density in Gaussian-distribution form is considered when a finite-thin uniform plate is heated. By using the separate variable method (SVM) and the Newton Cotes method (NCM), a semi- analytical solution of three-dimensional heat conduction equation in the finite field is obtained. Numerical results show that the effect of laser heat source distribution, laser moving speed as well as aspect ratio of the thin uniform plate have great influence on the three-dimensional distribution of the temperature field.

scholarly journals Simulating Convective-Radiative Heat Sinks Effect by means of FEA-based Gaussian Heat Sources and Its Approximate Analytical Solutions for Semi-Infinite Body

2021 ◽  
Author(s):  
Ninh The Nguyen ◽  
John H Chujutalli
Keyword(s):  
Temperature Field ◽  
Heat Source ◽  
Analytical Solutions ◽  
Radiative Heat ◽  
Source Model ◽  
Heat Sinks ◽  
Transient Temperature ◽  
Measured Temperature ◽  
Heat Source Model ◽  
Transient Temperature Field

Abstract FEA-based Gaussian density heat source models were developed to study the effect of convective and radiative heat sinks on the transient temperature field predicted by the available approximate analytical solution of the purely conduction-based Goldak’s heat source. A new complex 3D Gaussian heat source model, incorporating all three modes of heat transfer, i.e., conduction, convection and radiation, has been developed as an extension of the Goldak heat source. Its approximate transient analytical solutions for this 3-D moving heat source were derived and numerically benchmarked with the available measured temperature & weld pool geometry data by Matlab programming with ~5 to 6 times faster than FEA-based simulation. The new complex 3D Gaussian heat source model and its approximate solution could significantly reduce the computing time in generating the transient temperature field and become an efficient alternative to extensive FEA-based simulations of heating sequences, where virtual optimisation of a melting heat source (i.e. used in welding, heating, cutting or other advanced manufacturing processes) is desirable for characterisation of material behaviour in microstructure evolution, melted pool, microhardness, residual stress and distortions.

Numerical Simulation of Three-Dimensional Molten Pool Temperature Field and Flow Field for Laser Melt Injection Based on Fluent

2012 ◽  
Vol 538-541 ◽  
pp. 1837-1842 ◽  
Author(s):  
Long Zhi Zhao ◽  
Zi Wang ◽  
Xin Yan Jiang ◽  
Jian Zhang ◽  
Ming Juan Zhao
Keyword(s):  
Temperature Field ◽  
Liquid Metal ◽  
Molten Pool ◽  
Metal Flow ◽  
Three Dimensional ◽  
Transient Temperature ◽  
Transient Temperature Field ◽  
Liquid Metal Flow ◽  
Fluent Software ◽  
Thermo Physical Properties

According to the characteristics of laser melt injection, a numerical model for a simplified 3D transient temperature field in molten pool was established using FLUENT software in this paper. In the model, many factors were considered such as liquid metal turbulence, latent heat of phase transformation and material thermo physical properties depending on temperature. The results show that the model can be developed well by FLUENT software. And the results also show that the driving force of the liquid metal flow mechanism.

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