Entropy generation and thermal criticality analysis of Casson fluid exothermic double reaction in a convective cooling channel

The need to minimise energy losses and improve thermal efficiency has driven research on thermal irreversibility in non-Newtonian fluids. Excessive heat generation must be controlled to avoid runaway and failure. This study investigates entropy generation and thermal criticality in Casson fluid subjected to a double-step exothermic reaction in a convectively cooled channel. A mathematical model for coupled momentum, and energy transport is solved using a weighted residual Galerkin method. Results show that increasing the Casson parameter strengthens molecular cohesion, enhances heat transport and increases entropy near the walls. The criticality parameter reduces with stronger reaction rates, while convective cooling delays runaway. A 25 to 30 percent rise in Casson parameter gives about twelve percent increase in entropy production, showing sensitivity to rheological variations. The study offers useful insight for design and optimisation of thermal systems using Casson-type fluids, including chemical reactors, polymer processing and biofluid transport where heat regulation is important. These findings highlight the strong relationship between viscosity variation, heat dissipation and thermal irreversibility, offering guidance for improving efficiency and preventing instability in industrial processes. The model and results can support safer system design, reduce operational risks, guide material selection and improve energy management strategies effectively in practice.