Critical parameters for thermal conduction equations

Abstract Thermal stability of two models, whose thermal conductivity is a function of temperature, is investigated. Studies are made for the cylindrical geometry for both exponetial and power forms for the temperature dependence of conductivity. The maximum value of a certain parameter, δ cr , defines criticality and this is the condition for explosion. The purpose of this paper is to ascertain the way in which explosion is affected by boundary conditions and how changes in the values of a certain constant, β, affect the critical parameter δ cr .