Mathematical Modeling of Self‐Heating and Self‐Ignition Behavior of Lignocellulosic Biomass Fuel in a Rectangular Stockpile: A Spectral Approach

ABSTRACT The adoption of lignocellulosic biomass fuels as substitutes for fossil fuels has been known to lower greenhouse gas emissions and enhance the quality of life. However, their tendency for self‐heating, which could result in explosions, presents a significant challenge. To overcome this challenge, a mathematical model for the flow of biomass fuel in a rectangular stockpile is considered in this study. It is assumed that lignocellulosic material behaves like a Bingham fluid with a large yield stress, and the chemical reaction in the biomass fuel particles follows Arrhenius's kinetic theory. The governing equations of the problem are strongly nonlinear. Hence, a numerical method (Chebyshev spectral collocation method) is adopted to provide a solution to the governing equations. Our results indicate that the delay of self‐ignition can be achieved by enhancing the thermal Biot number and activation energy while reducing the Rayleigh number and mass Biot number. This study encourages the wider use of biomass fuels by addressing safety issues, advocating for sustainable energy practices, and improving environmental conservation.