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A theoretical investigation of double exothermic reaction–diffusion of couple stress fluid and thermal ignition branched chain with optical radiation and exponential Reynold's viscosity is examined in a channel. With isothermal temperature and low ambient heat exchange, the fluid flow is influenced by the upper motion of the wall and the applied pressure. The Arrhenius generalized reaction model is considered for the non-Newtonian species diffusion without material consumption in the presence of pre-exponential factor. The nonlinear dimensionless, viscous exothermic reactive couple stress fluid model is solved by an implicit semi finite difference technique to determine parametric sensitivities. The outcomes of the numerical computation are demonstrated in graphs and tables. It is revealed from the investigation that the thin radiation and couple stress material reduces temperature distribution which resulted into an improved fluid viscosity. Thermal explosion can be avoided by careful monitoring of heat generating terms. [ABSTRACT FROM AUTHOR]