A Meshfree Method for Heat Explosion Problems with Natural Convection in Inclined Porous Media

Abstract

This paper investigates the interaction between natural convection and heat explosion in porous media. A meshless collocation method based on multiquadric radial basis functions has been applied to study the problem in an inclined two-dimensional porous media. The governing equations consist of coupling the Darcy equations in the Boussinesq approximation of low density variations to the heat equation with a nonlinear chemical source term. The numerical results obtained are in good agreement with some previous studies that consider the vertical direction. A complex behaviour of solutions is observed, including periodic and aperiodic oscillations. We have shown that a small inclination of the container stabilizes the reactive fluid and can prevent thermal explosion.

Keywords

• Heat explosion
• Natural convection
• Inclined porous media
• Frank-Kamenetskii parameter
• Multiquadric radial basis functions method