Comparative studies on nonlinear hyperbolic and parabolic heat conduction for various boundary conditions: analytic and numerical solutions

A. Kar, Cholik Chan, J. Mazumder

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)14-20
Number of pages7
JournalJournal of Heat Transfer
Volume114
Issue number1
StatePublished - Feb 1992

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Heat conduction
conductive heat transfer
Boundary conditions
boundary conditions
Lasers
Thermal diffusivity
propagation velocity
thermophysical properties
thermal diffusivity
Processing
Wave propagation
lasers
wave propagation
Laser pulses
Materials properties
pulse duration
Thermodynamic properties
Heating
conduction
heating

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Physical and Theoretical Chemistry
  • Mechanical Engineering

Cite this

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abstract = "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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