scholarly journals Analytical solution for thermal transport in packed beds with volumetric heat source

2017 ◽  
Vol 316 ◽  
pp. 131-136 ◽  
Author(s):  
Mohammad-Sadegh Salehi ◽  
Maryam Askarishahi ◽  
Stefan Radl
2012 ◽  
Vol 90 (9) ◽  
pp. 911-918 ◽  
Author(s):  
B.S. Yilbas ◽  
A.Y. Al-Dweik

Analytical solution for laser short-pulse heating of a micro-sized metal wire is presented. In the analysis, volumetric and surface heat sources are incorporated for the same pulse intensity. The volumetric heat source resembles absorption by irradiated field according to Lambert’s Beer law while a surface heat source represents short pulse heating through high intensity thermal contact at the surface. The method of Lie point symmetries is combined with a Fourier cosine transformation to solve the temperature equation with appropriate boundary conditions. It is found that temperature profiles differ significantly for volumetric heat source and surface heat source considerations; in which case, volumetric heat source consideration results in considerably lower surface temperatures than that of the surface heat source consideration.


2021 ◽  
Author(s):  
Vito Busto ◽  
Donato Coviello ◽  
Andrea Lombardi ◽  
Mariarosaria De Vito ◽  
Donato Sorgente

Abstract In last decades, several numerical models of the keyhole laser welding process were developed in order to simulate the joining process. Most of them are sophisticated multiphase numerical models tempting to include all the several different physical phenomena involved. However, less computationally expensive thermo-mechanical models that are capable of satisfactorily simulating the process were developed as well. Among them, a moving volumetric equivalent heat source, whose dimensions are calibrated on experimental melt pool geometries, can estimate some aspects of the process using a Finite Element Method (FEM) modelling with no need to consider fluid flows. In this work, a double-conical volumetric heat source is used to arrange a combination of two half hourglass-like shapes with different dimensions each other. This particular arrangement aims to properly assess the laser joining of a Tailor Welded Blank (TWB) even in case of butt joint between sheets of different thicknesses. Experiments of TWBs made of 22MnB5 steel sheets were conducted in both equal and different thicknesses configurations in order to validate the proposed model. The results show that the model can estimate in a satisfactory way the shape and dimensions of the fused zone in case of TWB made of sheets with different thickness.


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