A Unified Approach to Hyperbolic Heat Conduction of the Semi-infinite Functionally Graded Body with a Time-Dependent Laser Heat Source

2019 ◽  
Vol 43 (4) ◽  
pp. 729-737 ◽  
Author(s):  
Durmuş Yarımpabuç
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Functionally Graded ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Unified Approach ◽  
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.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

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.

Laser Lock-In Thermography for Fatigue Crack Detection

2013 ◽  
Vol 558 ◽  
pp. 76-83 ◽  
Author(s):  
Yun Kyu An ◽  
Ji Min Kim ◽  
Hoon Sohn
Keyword(s):  
Fatigue Crack ◽  
Heat Source ◽  
High Power ◽  
Crack Detection ◽  
Laser Source ◽  
Cw Laser ◽  
Laser Heat ◽  
Laser Heat Source ◽  
Fatigue Crack Detection ◽  
Lock In

This study proposes a new nondestructive evaluation methodology named laser lock-in thermography (LLT) for fatigue crack detection. LLT utilizes a high power continuous wave (CW) laser as a heat generation source for lock-in thermography instead of commonly used flash and halogen lamps. The advantages of the proposed LLT method are that (1) the laser heat source can be positioned at an extended distance from a target structure thank to the directionality and low energy loss of the laser source, (2) thermal image degradation due to surrounding temperature disturbances can be minimized because of high temperature gradient generated by the laser source and (3) a large target surface can be inspected using a scanning laser heat source. The developed LLT system is composed of a modulated high power CW laser, galvanometer and infrared camera. Then, a holder exponent-based data processing algorithm is proposed for intuitive damage evaluation. The developed LLT is employed to detect a micro fatigue crack in a metal plate. The test result confirms that 5 μm (or smaller) fatigue crack in a dog-bone shape aluminum plate with a dimension of 400 x 140 x 3 mm3 can be detected.

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