Pulse heating of a medium by assemblies of hollow cylindrical conductors inductively heated in the magnetic field of a solenoid

Results of mathematical modelling of induction heating of a heat-conducting medium by assemblies of hollow thin-walled cylindrical conductors heated by Foucault currents in an alternating magnetic field are presented. The magnetic field is generated during the discharge of a capacitor bank through a solenoid with coaxial conductors inside the wall thickness of which is much less than the internal radius. The sets of inductively coupled conductors form the assemblies. The process was modeled using the exact analytical solutions of the problems of conjugate heat transfer between conductors and medium and the generation of electrical currents in conductors during capacitor bank discharge through the solenoid. The solutions were obtained on the assumptions of uniform cross-sectional current and temperature distribution in the solenoid and conductors; constant heat capacities of solenoid, conductors, and medium; and linear temperature dependence of the resistivity of solenoid and conductors. The heat transfer between conductors and adjacent fuel layers occurs according to Newton's law.
The mathematical model is reduced to several coupled conjugate heat transfer problems solved simultaneously with the Joule heating problem of conductors. The efficiency of electrothermal conversion of the energy in the device, the characteristic parameters of the solenoid and conductors, and the heating time of adjacent reactive medium layers to ignition temperature were estimated by parametric analysis.