Transient gravity‐driven flow of a third‐grade fluid (TGF) on an inclined plane with non‐isothermal effects, exothermic reactions, and porous medium influence

Abstract Comprehending the dynamics of reactive viscoelastic third‐grade fluids (VTGF) in gravity‐driven flows along inclined planes is crucial for numerous engineering and industrial applications. This research focuses to explore the transient behavior of such a fluid under non‐isothermal conditions, with an emphasis on the impact of exothermic reactions. The inclined plane region, filled with a porous material of constant permeability, is modeled using a modified version of Darcy's law to account for resistance to flow. The viscosity‐temperature dependence follows the Nahme‐type principle, while convective cooling at the free surface is simulated using Newton's cooling law. The exothermic chemical reaction of the material is described using Arrhenius kinetics. The resulting mathematical model for energy balanced and momentum comprises a set of non‐homogeneous and nonlinear partial differential equations (PDEs), which are transformed into dimensionless form and solved using semi‐implicit numerical techniques based on finite difference methods (FDM) implemented in Matlab. The study visually examines thermo‐dynamical phenomena such as thermal runaway due to the exothermic reaction and investigates how velocity and temperature respond to variations in system parameters. The numerical findings indicate that the interplay between porous medium, viscosity variation, and thermal effects significantly influences the flow and thermal behavior, providing valuable insights for optimizing and controlling such fluid systems in practical applications.