Reactive electro-conductive non-Newtonian (gel) duct flows arise in a variety of industrial applications including hybrid propulsion, smart rheological manufacturing systems, complex geothermal systems and chemical process engineering. Motivated by these technological applications, a mathematical model is developed to simulate the steady, laminar exothermic reactive electro-magneto-hydrodynamic combustible non-Newtonian natural convective transport in a vertical duct. Static uniform axial electrical field and transverse magnetic field are imposed. The Frank-Kamenetskii thermal explosion theory is utilized and also the Carreau fluid model, the latter due to its ability to simulate shear-thinning, Newtonian and shear-thickening behaviour. The duct contains a homogenous, isotropic porous medium and to accomodate Forchheimer inertial drag effects, a non-Darcian model is deployed. The duct walls are permeable enabling suction and injection effects to be studied. Viscous and Joule heating (Ohmic dissipation) are also featured in the model. Following a scaling transformation, the dimensionless emerging non-linear ordinary differential boundary value problem is solved with a robust numerical method (Mathematica shooting algorithm). Validation with an Adomian decomposition method (ADM) is included. Velocity, temperature, duct wall skin friction and Nusselt number are computed for the influence of all key parameters and depicted in graphs and tables. An increment in Frank-Kamenetskii parameter boosts temperatures and accelerates the duct flow. Elevation in power-law rheological index and Weissenberg number produces significant damping in the flow and also temperature reduction across the duct. Increasing Darcy number and Forchheimer number suppress temperature magnitudes in proximity to the duct walls but induce a slight heating effect in the core zone. Greater values of Grashof number accelerate the duct flow and boost temperatures. Higher magnitudes of Hartmann number suppress temperatures near the duct walls but elevate them in the core region of the duct. Larger Brinkman number strongly acentuates temperatures as does electrical field (Joule) dissipation. Detailed physical interpretations are provided and some pathways for future investigations are briefly outlined.

KEYWORDS: EMHD gel propellants; F-K thermal explosion theory; heat transfer; Darcy-Brinkman-Forchheimer porous medium; Joule heating; Carreau non-Newtonian fluid; Numerical; rocket ducts.