Nonlinear Hyperbolic Equations and Linear Heat Conduction with Memory

2010 ◽  
pp. 63-70 ◽  
Author(s):  
Sandra Carillo
Keyword(s):  
Heat Conduction ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equations ◽  
Linear Heat ◽  
Heat Conduction With Memory ◽  
With Memory

A Note on Heat Conduction With Memory

1973 ◽  
Vol 40 (4) ◽  
pp. 1124-1125
Author(s):  
F. R. Norwood
Keyword(s):  
Heat Conduction ◽  
Heat Conduction With Memory ◽  
With Memory

Comparative Studies on Nonlinear Hyperbolic and Parabolic Heat Conduction for Various Boundary Conditions: Analytic and Numerical Solutions

1992 ◽  
Vol 114 (1) ◽  
pp. 14-20 ◽  
Author(s):  
A. Kar ◽  
C. L. Chan ◽  
J. Mazumder
Keyword(s):  
Heat Conduction ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Short Pulse ◽  
Materials Processing ◽  
Hyperbolic Heat Conduction ◽  
Nonlinear Hyperbolic Equations ◽  
Various Boundary Conditions ◽  
Kirchhoff Transformation ◽  
Finite Domains

With the advent of lasers with very short pulse durations and their use in materials processing, the effect of thermal wave propagation velocity becomes important. Also, localized heating in laser-aided materials processing causes significant variations in the material properties. To account for these two effects, hyperbolic heat conduction is studied in this paper by considering all the thermophysical properties, except the thermal diffusivity, to be temperature dependent. The resulting nonlinear hyperbolic equations are linearized by using Kirchhoff transformation. Both analytical and numerical solutions are obtained for finite domains. Results are presented and compared with parabolic conduction results.

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