Investigating bifurcations and thermal behavior in chaotic fractional-order exothermic reactions with reactant consumption

Abstract

<title>Abstract</title> This study presents a complete investigation of the chaotic fractional-order exothermic decomposition in a flow channel, concentrating on the interaction between reactant consumption and thermal dynamics. By employing a time-fractional derivative method, we originate and solve the system of differential equations along with boundary conditions, leading to a vigorous numerical procedure that apprehends the complex behavior of the system. The simulations deliver complete profiles of velocity, temperature, and concentration, depicting both stable and unstable solutions. The Nusselt number and Sherwood number are assessed, highlighting their implication in understanding thermal and flow characteristics. The algorithm highlights stable and unstable solutions by implementing the fractional order derivatives, using a numerical scheme to identify stable/unstable regions of the solution across various governing parameters. We investigate bifurcation phenomena and analyze the effects of the Biot number and reactant consumption rate on the bifurcation plane. Additionally, we discover temperature and concentration profiles, as well as Nusselt and Sherwood numbers. The perceptions attained from this research not only improve the forecast and control of thermal behaviors in industrial processes but also contribute to enhanced safety and efficiency in chemical manufacturing. These discoveries underline the potential for advanced control strategies to discourse challenges modelled by exothermic reactions, guaranteeing optimal operational conditions. It is believed that this research might be useful in enhancing temperature control in catalytic reactors, enhancing effectiveness and safety in chemical production processes. One noteworthy application of this research is in the optimization of temperature control in catalytic reactors used in the making of fine chemicals and pharmaceuticals, wherein the precise temperature management is crucial for yield and product quality.