Hyperbolic heat conduction in the semi-infinite body with a time-dependent laser heat source

2001 ◽  
Vol 37 (4-5) ◽  
pp. 333-342 ◽  
Author(s):  
M. Lewandowska
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Infinite Body ◽  
Laser Heat ◽  
Laser Heat Source

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

Analytical Solution of the Hyperbolic Heat Conduction Equation for a Moving Finite Medium Under the Effect of Time Dependent Laser Heat Source

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
R. T. Al-khairy
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source ◽  
Reference Curves ◽  
Finite Medium ◽  
Phase Differences

This paper presents an analytical solution of the hyperbolic heat conduction equation for a moving finite medium under the effect of a time-dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g(x,t) = I(t) (1 – R)μe−μx while the finite body has an insulated boundary. The solution is obtained by the Laplace transforms method, and the discussion of solutions for two time characteristics of heat source capacities (instantaneous and exponential) is presented. The effect of the dimensionless medium velocity on the temperature profiles is examined in detail. It is found that there exists clear phase shifts in connection with the dimensionless velocity U in the spatial temperature distributions: the temperature curves with negative U values lag behind the reference curves with zero U, while the ones with positive U values precedes the reference curves. It is also found that the phase differences are the sole products of U, with increasing U predicting larger phase differences.

Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

2016 ◽  
Vol 33 (1) ◽  
pp. 65-75 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction

AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

Development of Multi-Axis Laser-Assisted Milling Device

2017 ◽  
Author(s):  
Dong-Hyeon Kim ◽  
Wan-Sik Woo ◽  
Won-Shik Chu ◽  
Sung-Hoon Ahn ◽  
Choon-Man Lee
Keyword(s):  
Heat Source ◽  
Tool Path ◽  
Cutting Tool ◽  
Field Studies ◽  
Flat Surfaces ◽  
Laser Heat ◽  
Complex Shapes ◽  
Laser Heat Source ◽  
Removal Processes ◽  
Machining Productivity

Laser-assisted machining (LAM) process is an effective method to facilitate material removal processes for difficult-to-cut materials. In LAM process, the mechanical strength of various materials is reduced by a laser heat source focused in front of the cutting tool during machining. Since the laser heat source is located ahead of the cutting tool, the workpiece is preheated by the heat source. This enables difficult-to-cut materials to be machined more easily with low cutting energy, increasing the machining productivity and accuracy. It is difficult to apply laser-assisted milling (LAMilling) to workpieces having complex shapes, because it is not easy to control laser preheating and the cutting tool path for three-dimensionally shaped workpieces. LAMilling has only been used in limited fields such as single-direction machining of flat surfaces. To apply this process in the industrial field, studies on workpieces having various shapes are needed. This study aims to develop a laser-assisted milling device having multiple axes and to investigate the machining characteristics of several difficult-to-cut materials.

Sign in / Sign up

Export Citation Format

Share Document