Reactive operability limits in stress-driven viscoelastic channel flow: Thermal runaway, cooperative erosion and the cold-state admissibility ceiling

Reactive polymer-processing operations may lose their safe operating window through thermal runaway or loss of homogeneous constitutive admissibility. Objective: We quantify this coupled operability limit in stress-driven viscoelastic channel flow of a polymeric liquid with an exothermic reaction. Methodology: For a Gordon–Schowalter (Johnson–Segalman) fluid with temperature-thinning viscosity, we formulate a two-source boundary-value problem — wall-concentrated viscous dissipation and a centre-concentrated Frank–Kamenetskii reactive source — governed by the dissipation group 𝛿 , the elasticity 𝐸 , the Damköhler load 𝐷 ⁢ 𝑎 and the Arrhenius non-ideality ɛ , and we solve it by two-parameter continuation validated against closed-form anchors and an independent finite-difference solver. Results. Reaction erodes the operability boundary strongly and almost linearly, by about a quarter per unit Damköhler, the magnitude being set by a closed-form 24:1 reactive-to-viscous potency ratio. At any positive dissipative load the cool branch always terminates at a thermal fold: the constitutive bound acts only as the exact cold-state admissibility ceiling 𝐸 0 ⁡ ( 𝐷 ⁢ 𝑎 ) , equal to unity for 𝐷 ⁢ 𝑎 ≤ 2 . 7 6 4 1 9 6 . At zero viscous load the boundary collapses at the planar Frank–Kamenetskii value 𝐷 ⁢ 𝑎 𝑐 ≈ 3 . 5 1 , nearly independently of elasticity. At a representative reactive-extrusion point ( 𝐸 = 0 . 2 5 , 𝐷 ⁢ 𝑎 = 0 . 5 ), reaction lowers the computed dissipation allowance by 12%, equivalent to about a 6% reduction in admissible pressure forcing when the other groups are fixed.