Analysis of a fire extinguishing model with a p-Laplacian operator and with non-linear advection and reaction

We provide a new model to describe the fire extinguisher dynamics in an aircraft engine nacelle. We connect the mathematical properties introduced by a non-linear operator with the physical mechanisms of a fire extinguishing process. Some discussions about diffusion and non-linear parabolic operators are carried out to justify the governing equation. In addition, the model introduces phenomena like forced convection and fast reaction to account for the discharge of pressurized fire suppressant agent that is released from the fire bottles. The driving equation is firstly discussed analytically to obtain existence and uniqueness results concerning weak solutions. Afterward, we explore profiles of solutions and a characterization of the propagating extinguisher front is introduced. In order to provide a validity note on the analytical conceptions used, a flight test has been executed. Based on this, we obtain particular values for the parameters involved in the model. The proposed assessments permit to obtain different time levels, for which the suppressant agent extinguishes a fire. Such times depend strongly on the involved physical processes connected with diffusion, forced convection and reaction.