Effectiveness factor for general porous catalytic particle in Langmuir–Hinshelwood kinetics for isothermal and non-isothermal reactions

The heat and mass balance equations for diffusion and chemical reactions in a catalyst pellet are resolved for reactions adhering to a standard class of Langmuir–Hinshelwood and general-order kinetics. An explicit new algebraic expression for the effectiveness factor concerning the kinetic, adsorption, and transport characteristics in isothermal/non-isothermal conditions is reported using HFM and AGM methods. This equation may be used directly in fixed-bed reactor computations to account for the effects of adsorption and intraparticle dynamics. The advantage of HFM and AGM starts from their powerful approach for handling nonlinearities and complex boundary conditions, making them preferred for steady-state analysis in physical reaction systems. The results validate that both methods are superior, mainly when accuracy and computational efficiency are critical.