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Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium

Saeed Ur Rahman (COMSATS University Islamabad, Wah Cantt, Pakistan)
José Luis Díaz Palencia (UDIMA Universidad a Distancia de Madrid, Madrid, Spain)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 30 May 2023

Issue publication date: 5 June 2023

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Abstract

Purpose

This article aims to study a model of flame propagation in a nonhomogeneous medium with a p-Laplacian operator. The intention with such operator is to model the effects of slow and fast diffusion, that can appear in a nonhomogeneous media, depending on the pressure driven conditions. In addition, the authors introduce a general form in the reaction term, that introduces the flame chemical kinetics.

Design/methodology/approach

To introduce the governing equations, the authors depart from previously reported models in flame propagation, but the authors consider a new modeling approach based on a p-Laplacian operator.

Findings

The authors provide evidences of regularity and uniqueness of solutions. Afterward, the authors introduce profiles of stationary solutions based on the definition of a Hamiltonian for the newly discussed model. Eventually, the authors obtain exponential profiles solutions with the help of a scaling, that transforms the model into a nonlinear Hamilton–Jacobi equation.

Originality/value

The new model has not been previously reported in the literature. The authors consider that the mathematical properties of a p-laplacian (in particular the property known as finite propagation) is of inherent interest to model pressure drive flames with slow or fast diffusion. Indeed, the authors’ approach has the value of providing an operator that can fit better to model flame propagation. In addition, the authors introduce a general form of chemical kinetics, to make the authors’ model further general.

Keywords

Citation

Rahman, S.U. and Díaz Palencia, J.L. (2023), "Analysis and profiles of solution for a highly nonlinear model of pressure driven flame propagation in nonhomogeneous medium", Multidiscipline Modeling in Materials and Structures, Vol. 19 No. 4, pp. 545-564. https://doi.org/10.1108/MMMS-11-2022-0247

Publisher

:

Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

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