Coupled heat and mass transfer in reactive parallel‐plate flow: A perturbative G raetz model with modal symmetry and A rrhenius kinetics

We analyze coupled heat and mass transport of a reactive species in Newtonian plane Couette–Poiseuille flow between parallel plates, with a reactive lower wall and a non‐catalytic absorbing upper wall. The model includes viscous dissipation, heat of reaction, and Arrhenius temperature dependence in the homogeneous first‐order reaction rate. In the small‐Brinkman‐number regime Br ≪ 1 with weakly exo‐/endothermic kinetics ( Q = Br q , q = O(1)), the system admits a perturbative semi‐analytical solution. The leading order recovers the isothermal reactive Graetz problem, while the first correction in Br involves two Sturm–Liouville bases: a mass base and a thermal base sharing the parabolic velocity weight. We prove a modal‐symmetry selection rule showing that only odd‐numbered modes contribute when the velocity profile and source terms are symmetric under . The fully developed dissipation‐induced temperature field is obtained in closed form as a quartic polynomial. Validation against a fully coupled implicit finite‐difference solver confirms practical agreement in the small‐ regime, with modal validation errors of order 10⁻⁴ and coupled‐field errors below 5% for . The thermal‐reactive coupling modestly accelerates axial species conversion. Quantitatively, the effective axial decay rate increases approximately linearly with ; in the validated small‐ range, the local sensitivity is , shortening the 90%‐conversion length by about 1.4% at . The analysis is directly relevant to the design of reactive coating systems and catalytic microchannel reactors operating in the small‐Brinkman regime.