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Related Experiment Videos

The thermal explosion revisited

G I Barenblatt1, J B Bell, W Y Crutchfield

  • 1Department of Mathematics, University of California, Berkeley, CA 94720, USA.

Proceedings of the National Academy of Sciences of the United States of America
|November 13, 1998
PubMed
Summary
This summary is machine-generated.

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Partial wall insulation in cylindrical vessels reduces critical explosion radii. Periodic boundary conditions lead to scaling laws and distinct temperature profiles in the core and boundary layers.

Area of Science:

  • Thermodynamics
  • Chemical Engineering
  • Heat Transfer

Background:

  • The classical thermal explosion problem assumes uniform vessel wall conditions.
  • Real-world applications often involve non-uniform thermal properties of vessel walls.

Purpose of the Study:

  • To investigate the effect of partially thermally conducting walls on thermal explosion phenomena in cylindrical vessels.
  • To analyze the influence of periodic boundary conditions on critical parameters and temperature distribution.

Main Methods:

  • Numerical investigation of a modified thermal explosion model.
  • Analysis of a cylindrical vessel with a fraction (alpha) of its wall being conductive and the rest isolated.
  • Examination of periodic boundary structures with N segments.

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Main Results:

  • Partial wall isolation reduces the critical radius of the vessel.
  • For small alpha and large N, the critical radius follows a scaling law dependent on N.
  • A distinct temperature distribution emerges: axisymmetric in the core and sharply varying in the boundary layer near the wall.

Conclusions:

  • Partial thermal conductivity of vessel walls significantly alters thermal explosion dynamics.
  • Periodic boundary conditions introduce complex temperature profiles and predictable scaling laws for critical radii.
  • The study provides insights into heat transfer and explosion limits in systems with heterogeneous thermal boundaries.