Branch-chain criticality and thermal explosion of Oldroyd 6-constant fluid for a generalized Couette reactive flow

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.