Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws

A mathematical model for thermal explosion in a combustible dusty gas containing fuel droplets with general Arrhenius reaction-rate laws, convective and radiative heat losses, and interphase heat exchange between gas and inert solid particles is investigated. The objective of the study is to examine the effects of interphase heat exchange between the gas and solid particles on i ignition of reacting gas, ii accumulation of heat by the solid particles during combustion process iii evaporation of the liquid fuel droplets, and iv consumption of reacting gas concentration. The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. Therefore, we present numerical solutions as well as different qualitative effects of varying interphase heat exchange parameter. Graphs and Table feature prominently to explain the results obtained.