Semi-Analytical Solution for a Single-Phase Conduction Problem of a Finite-Slab With a Growing or Receding Boundary

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Abstract

Thermal conduction considerations of a solid media with moving boundaries are of great interest in many research areas. Unfortunately, it is very difficult to find analytical or semi-analytical solutions for the single-phase heat equation in real-time with a growing or receding boundary. While non-numerical solutions for infinite and semi-infinite domains are available, these cannot accurately model many common situations. In order to overcome this shortcoming, an approximate semi-analytical solution for the heat equation for a single phase, homogeneous, and finite-slab with a growing or receding boundary under unit loading was derived using the Laplace transform method and Zakian series representation of the inverse Laplace transform. Predictions were compared to finite element solutions with good agreement obtained for low to moderate growth or recession rates with improvements shown to be possible by using a heuristic approach. Applications of this work could include direct or inverse prediction of temperatures during machining, wear, corrosion, and/or additive manufacturing via cold spray.

Original languageEnglish (US)
Article number061001
JournalASME Journal of Heat and Mass Transfer
Volume146
Issue number6
DOIs
StatePublished - Jun 1 2024

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Mechanics of Materials
  • General Materials Science

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