Thermal explosions in spherical vessels at large Rayleigh numbers Articles uri icon

publication date

  • December 2017

start page

  • 1042

end page

  • 1053


  • 115, Part B

International Standard Serial Number (ISSN)

  • 0017-9310

Electronic International Standard Serial Number (EISSN)

  • 1879-2189


  • This paper investigates effects of buoyancy-driven motion on the 'slowly reacting” mode of combustion, and its thermal-explosion limits, of an initially cold gaseous mixture enclosed in a spherical vessel with a constant wall temperature. As in Frank-Kamenetskii"s seminal analysis, the strong temperature dependence of the effective overall reaction is modeled with a single irreversible reaction with an Arrhenius rate having a large activation energy. Besides the classical Damköhler number Da, measuring the ratio of the heat-release rate by chemical reaction evaluated at the wall temperature to the rate of heat removal by heat conduction to the wall, the solution is seen to depend on the Rayleigh number Ra, measuring the effect of buoyancy-induced motion on the heat-transport rate (...)


  • thermal explosions; laminar reacting flows; natural convection; boundary-layer theory