Mathematical modelling and numerical simulation of a glow-plug

In this work we derive a mathematical model that describes the working of a glow-plug of the type used in Diesel engines to preheat the air–diesel fuel mixture. The proposed model consists of a time dependent one-dimensional partial differential equation which incorporates the electro-thermal interaction between the electric current flowing in the plug and the temperature. It has been obtained by integrating the heat equation on each section of the plug, assuming axial symmetry and using thermal equilibrium relation in the radial direction. The problem is highly non-linear because of the radiation boundary conditions and the dependence on temperature of several parameters. In particular, heat is generated by an electric resistance whose characteristic strongly depends on temperature. We have adopted a quasi-Newton treatment of the non-linear term and a mixed finite element formulation for the linearized problem. Time advancing has been carried out using a semi-implicit Euler scheme. Several numerical simulations have been carried out in order to assess the validity of the model, whose predictions have been compared with available experimental data.