Homotopy and adomian semi-numerical solutions for oscillatory flow of partially ionized dielectric hydrogen gas in a rotating MHD energy generator duct

Abstract

Hydrogen-based MHD power generators offer significant advantages over conventional designs. The optimization of these energy devices benefits from both laboratory scale testing and computational simulation. Motivated by this, in the current work, a mathematical model is developed for MHD pumping of partially ionized hydrogen in a rotating duct with oscillatory, Maxwell displacement and magnetic induction effects under an inclined static magnetic field. Perfectly electrically conducting duct walls are assumed. The non-dimensional conservation equations are solved using the power-series based Homotopy Analysis Method (HAM) with an appropriate embedding parameter. Detailed graphical visualization of the impact of emerging parameters on the non-dimensional primary and secondary velocity components (u,v) and magnetic induction components (bx,by) across the duct is presented. Average squared residual errors for all key variables εu,εv,εbx,εby with associated CPU times at various orders of the HAM iteration are also included. Validation with an Adomian Decomposition Method (ADM) is also conducted, and excellent agreement is obtained (tabulated). The computations have shown that with increasing inverse Ekman number strong damping is observed in the primary flow whereas the secondary flow is accelerated, in particular in the core region of the duct. With elevation in Maxwell displacement effect (for the case of a 45° inclined magnetic field i.e. θ=π/4 ) there is a strong decrease in primary magnetic induction at the lower wall of the duct and elevation in magnitudes at the upper duct wall; however, in the core region no tangible modification is computed. The opposite trend is observed for the secondary magnetic induction. With increasing magnetic Prandtl number (i.e. ratio of magnetic Reynolds number to ordinary Reynolds number) in the presence of strong Maxwell displacement current, strong magnetic field and high inverse Ekman number, the primary velocity is accelerated in both the left and right half space of the duct with a dip in magnitude at the centreline. However, the secondary velocity exhibits a much lower enhancement in both zones with only weak acceleration near the duct walls. Both velocity components achieve symmetrical distributions about the duct centreline. A significant depletion in primary magnetic induction is computed near the lower duct wall with enhancement near the upper duct wall; the contrary behaviour is exhibited by the secondary induced magnetic field. Applications of the study arise in hybrid rotating hydrogen based MHD energy generators and furthermore the computations provide a good basis for generalization to 3-dimensional flows with commercial multi-physical fluid dynamic codes e.g. ADINA-F, COMSOL, ANSYS FLUENT-Maxwell wherein further phenomena may be explored including Alfven wave effects and dielectric losses.