The effects of heat exchange and fluid production on the ignition of a porous solid
The authors consider a combustion model when a solid fuel decomposes in an exothermic reaction in fluid and solid products. The authors here allow different temperatures in the fluid and in the solid parts. They write the balance equations which describe the evolution of the temperature, that of the volume fraction of the solid fuel and that of the density of the fluid part. Darcy's law is assumed in the fluid part. The problem is posed in a (\( n+1\)) dimensional parabolic cylinder. Dirichlet boundary conditions are imposed on the lateral boundary of the parabolic cylinder. Initial conditions are imposed at \(t=0\). The authors first introduce adimensional parameters. Then they assume, among other hypotheses, that the system is close to the ambient initial stage, which means that the unknowns or initial data take small perturbations around their initial values. The final problem is a coupled system of nonlinear parabolic equations involving five parameters. The authors prove a local in time existence and uniqueness result for this problem with a possible blow up behaviour in finite time. The authors then describe steady-state solutions in some particular case. The paper ends with a comparison between the solution of this model and that of comparable other models.
scientific article; zbMATH DE number 5276136
scientific article