Fracture path emanating from a rapidly moving heat source—the effect of thermal shock waves under high rate response

1992 ◽  
Vol 41 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Da Yu Tzou
Keyword(s):  
Shock Waves ◽  
Heat Source ◽  
Thermal Shock ◽  
High Rate ◽  
Moving Heat Source ◽  
Fracture Path

The Vibration of Nano-Beam Subjected to Thermal Shock and Moving Heat Source with Constant Speed

2020 ◽  
Vol 61 ◽  
pp. 136-150 ◽  
Author(s):  
Najat A. Alghamdi
Keyword(s):  
Heat Source ◽  
Thermal Shock ◽  
Numerical Solutions ◽  
Time Variable ◽  
Constant Speed ◽  
Moving Heat Source ◽  
Governing Equations ◽  
Lateral Deflection ◽  
Temperature Increment ◽  
Fourier Heat Conduction

This paper deals with a mathematical model of thermoelastic rectangular nano-beam, which is thermally loaded by thermal shock and subjected to moving heat source with constant speed. The nano-beam has been clamped-clamped and its length along the x-axis. The governing equations have been written by using the Euler–Bernoulli equation of nano-beams and the non-Fourier heat conduction with one-relaxation time. Laplace transform has been applied with respect to the time variable, and the solutions have been derived in its domain. The numerical solutions for the Silicon material have been done by using Tzou method. The results have been shown in figures for the temperature increment and the lateral deflection with various values of heat source speed to stand on its effects. Moreover, the effects of the ratio between the length and the width of the beam have been discussed. The speed of the heat source and the dimensions of the beam have significant effects on the temperature increment and the lateral deflection of the beam.

On the Thermal Shock Wave Induced by a Moving Heat Source

1989 ◽  
Vol 111 (2) ◽  
pp. 232-238 ◽  
Author(s):  
D. Y. Tzou
Keyword(s):  
Shock Wave ◽  
Temperature Field ◽  
Heat Source ◽  
Thermal Shock ◽  
Thermal Field ◽  
Heat Propagation ◽  
Moving Heat Source ◽  
Finite Speed ◽  
Wave Angle ◽  
Wave Induced

Analytical solutions for the temperature field around a moving heat source in a solid with finite speed of heat propagation are obtained via the method of Green’s functions. When the speed of the moving heat source is equal to or faster than that of the thermal wave propagated in the solid, the thermal shock wave is shown to exist in the thermal field. The shock wave angle is obtained as sin−1 (1/M) for M ≥1. Orientation of crack initiation in the vicinity of the heat source is also estimated by considering the temperature gradient T,θ along the circumference of a continuum circle centered at the heat source. Such an orientation is established as a function of the thermal Mach number in the subsonic, transonic, and supersonic regimes, respectively.

scholarly journals Analysis of hyperbolic Pennes bioheat equation in perfused homogeneous biological tissue subject to the instantaneous moving heat source

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Ali Kabiri ◽  
Mohammad Reza Talaee
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Method Comparison ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Profiles ◽  
Moving Heat Source ◽  
Bioheat Equation ◽  
Perfusion Rate

AbstractThe one-dimensional hyperbolic Pennes bioheat equation under instantaneous moving heat source is solved analytically based on the Eigenvalue method. Comparison with results of in vivo experiments performed earlier by other authors shows the excellent prediction of the presented closed-form solution. We present three examples for calculating the Arrhenius equation to predict the tissue thermal damage analysis with our solution, i.e., characteristics of skin, liver, and kidney are modeled by using their thermophysical properties. Furthermore, the effects of moving velocity and perfusion rate on temperature profiles and thermal tissue damage are investigated. Results illustrate that the perfusion rate plays the cooling role in the heating source moving path. Also, increasing the moving velocity leads to a decrease in absorbed heat and temperature profiles. The closed-form analytical solution could be applied to verify the numerical heating model and optimize surgery planning parameters.

Temperature field in a hollow finite-length cylinder with an arbitrarily moving heat source

1972 ◽  
Vol 22 (3) ◽  
pp. 381-385 ◽  
Author(s):  
L. A. Brichkin ◽  
Yu. V. Darinskii ◽  
L. M. Pustyl'nikov
Keyword(s):  
Temperature Field ◽  
Heat Source ◽  
Finite Length ◽  
Moving Heat Source
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