Three-Dimensional Theory of Temperature Distribution for Solid Materials with Step Optical Excitation

Applied laser ◽  
2011 ◽  
Vol 31 (5) ◽  
pp. 433-438
Author(s):  
张晓琳 Zhang Xiaolin ◽  
陈赵江 Chen Zhaojiang ◽  
苏晓强 Su Xiaoqiang ◽  
赵鹏程 Zhao Pengcheng ◽  
方健文 Fang Jianwen ◽  
...  
Author(s):  
David J. Steigmann

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.


2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.


Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.


2021 ◽  
pp. 105290
Author(s):  
Everton Fernandes Silva ◽  
Hatice Çalık ◽  
Wim Vancroonenburg ◽  
Aline Aparecida Souza Leao ◽  
Tony Wauters

2007 ◽  
Vol 129 (6) ◽  
pp. 1028-1034 ◽  
Author(s):  
Liang Wang ◽  
Sergio Felicelli

A three-dimensional finite element model was developed to predict the temperature distribution and phase transformation in deposited stainless steel 410 (SS410) during the Laser Engineered Net Shaping (LENS™) rapid fabrication process. The development of the model was carried out using the SYSWELD software package. The model calculates the evolution of temperature in the part during the fabrication of a SS410 plate. The metallurgical transformations are taken into account using the temperature-dependent material properties and the continuous cooling transformation diagram. The ferritic and martensitic transformation as well as austenitization and tempering of martensite are considered. The influence of processing parameters such as laser power and traverse speed on the phase transformation and the consequent hardness are analyzed. The potential presence of porosity due to lack of fusion is also discussed. The results show that the temperature distribution, the microstructure, and hardness in the final part depend significantly on the processing parameters.


2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.


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