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This research considers the third-grade liquid flow and criticality branched-chain of a thermal reaction in a Couette generalized medium with a nonlinear viscosity model. A dimensionless transformation of the system momentum and heat equations are carried out. Compared with the diffusion coefficient, the flow is stimulated by initiation reaction rate, reaction branch-chain order, non-Newtonian term, thermal Grashof number, and pressure gradient. The reactive fluid is fully exothermic with consumption of the material, and the heat exchange in the system is greater than the exchange of heat with the ambient. A semianalytical collocation weighted residual scheme is employed for the branch-chain slice bifurcation, dimensionless energy, and momentum solutions. The results show that exponential decreases in the thermal fluid viscosity can help in controlling the boundless heat produced by the Frank-Kamenetskii term and initiation reaction rate. Therefore, the results will help in stimulating positive combustion processes.

On Criticality for a Generalized Couette Flow of a Branch-Chain Thermal Reactive Third-Grade Fluid with Reynold’s Viscosity Model