Pseudo-Spectral and Variational Iteration Simulation of Exothermically-Reacting Rivlin-Ericksen Viscoelastic Flow and Heat Transfer in a Rocket Propulsion Duct

A pseudo-spectral numerical method is employed to study the steady, laminar, incompressible flow and heat transfer in a cylindrical conduit, as a simple model of non-Newtonian reactive gel propellant flow in a hybrid rocket chamber. Convective cooling is included The exothermic reaction is modeled using Arrhenius kinetics and a third grade non-Newtonian Rivlin-Ericksen ("differential" fluid) model employed to simulate viscoelastic effects. The dimensionless momentum and energy conservation equations are solved under appropriate boundary conditions. The effects of viscoelastic parameter (γ), activation energy parameter (ε), Frank-Kamenetskii parameter (λ), Biot number (Bi), and viscous heating parameter (m) on velocity and temperature evolution in the regime are studied in detail. Excellent correlation between the present pseudo-spectral simulations, Maple quadrature, and a variational iteration method (VIM) is achieved. The study has important applications in hybrid aerospace propulsion systems utilizing reactive gels and further confirms the excellent stability and adaptability of pseudo-spectral and variational iteration techniques in nonlinear aerospace fluid mechanics simulations.