Thermal management of rocket nozzles using MHD copper-ionic liquid nanofluid in Jeffery-Hamel flow

This paper investigates the Jeffrey-Hamel (J–H) magnetohydrodynamic flow of a partially ionized power-law nanofluid (PL-NF) for regenerative cooling of rocket engine nozzles subjected to extreme heat flux to address critical thermal management problems. The PL-NF is prepared by dispersing copper nanoparticles (thermal conductivity ) in ionic liquid EMIMBF 4 , which remains stable up to . This combination was chosen due to its excellent thermophysical properties and non-Newtonian rheological response consistent with verified experimental measurements and established property correlations. The fundamental equations include the Navier–Stokes system, Ohm's law for current density, and Fourier's law for thermal conductivity, fully accounting for Hall currents, ion slip, and Darcy–Forchheimer resistance in porous media. Solutions are calculated using the BVP4c solver in MATLAB, providing a residual error tolerance of less than . The analysis focuses on the roles of key dimensionless groups: Reynolds number , inertial parameter , Eckert number , porosity parameter , and nanoparticle volume fraction . Results show that the superior thermal conductivity of the IL nanofluid exceeds that of conventional coolants, enabling nozzle operation at gas temperatures up to . Magnetohydrodynamic (MHD) forces further improve flow control and suppress skin friction. Detailed profiles of velocity, temperature, skin friction coefficient and Nusselt number show that viscous heating and flow acceleration in the convergent section create steep temperature gradients near the divergent walls, while vortex structures degrade the cooling uniformity. Higher porosity reduces the volumetric velocity and pulse thickness, converting kinetic energy into heat and increasing local temperatures. Response surface methodology (RSM) combined with ANOVA , adjusted identifies the nanoparticle volume fraction as the dominant factor in heat transfer efficiency. Overall, the IL nanofluid, when used with MHD control, significantly reduces wall temperature and friction losses in high-thrust engines such as the Falcon 9 Merlin and Saturn V F-1, confirming its effectiveness for advanced rocket nozzle thermal protection. • Copper nanoparticles, known for their exceptional thermal conductivity, are dispersed in an ionic liquid EMIMBF 4 , which remains stable at high temperatures, providing efficient heat removal from rocket engine nozzles exposed to high combustion temperatures. • The integration of MHD, Hall currents, and ion sliding mechanisms improves flow control, reduces surface friction, and provides specific thermal management benefits. • In this paper, the J–H flow model is extended by incorporating a Darcy–Forchheimer porous medium formulation, which facilitates a detailed study of fluid flow and heat transfer in converging-diverging nozzle channels. • BVP4c and RSM with ANOVA ( , adj. ) optimize , , ; most impacts temperature. • Used in high-performance engines such as the Falcon 9 Merlin or Saturn V F-1, partially ionized IL nanofluid significantly reduces nozzle wall temperatures under high heat fluxes , improving thermal protection and system durability.