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A non-field analytical method for heat transfer problems through a moving boundary.

Vladimir Kulish1, Vladimír Horák2

  • 1Department of Thermodynamics and Fluid Mechanics, Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic. vladimir.kulish@fs.cvut.cz.

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|September 24, 2021
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Summary

This study extends the Kulish method for analyzing heat transfer in moving boundary problems, offering new solutions for various scientific applications like combustion and explosions. The research details front propagation laws in Stefan-type problems at large times.

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Area of Science:

  • Thermodynamics
  • Applied Mathematics
  • Chemical Engineering

Background:

  • Heat transfer problems with moving boundaries are crucial in diverse scientific fields, including chemical reactions, ignition, explosions, and combustion.
  • Existing analytical methods may have limitations in addressing the complexities of arbitrarily moving boundaries.
  • The non-field analytical method, specifically the Kulish method, offers a unique approach to these problems.

Purpose of the Study:

  • To extend the non-field analytical method (Kulish method) for solving heat transfer problems in domains with moving boundaries.
  • To derive a general form of the non-field solution for arbitrarily moving boundaries.
  • To investigate the front propagation law in Stefan-type problems at large times.

Main Methods:

  • Extension of the non-field analytical method (Kulish method).
  • Derivation of general and particular solutions for arbitrarily moving boundaries.
  • Analysis of boundary speed variations (linear, parabolic, exponential, polynomial).
  • Determination of asymptotic solutions for front propagation in Stefan-type problems.

Main Results:

  • A general form of the non-field solution has been obtained for arbitrarily moving boundaries.
  • Specific solutions were derived for boundary speeds changing linearly, parabolically, exponentially, and polynomially.
  • The derived solutions were compared with existing known solutions where applicable.
  • Asymptotic solutions for front propagation laws in Stefan-type problems at large times were determined for several important cases.

Conclusions:

  • The extended Kulish method provides a robust analytical framework for heat transfer problems with moving boundaries.
  • The study offers valuable insights into the behavior of front propagation in Stefan-type problems over extended time scales.
  • The developed methodology has broad applicability in various scientific and engineering disciplines involving dynamic thermal processes.