Mathematical modeling of hydrogen evolution by \({{{H}}}^{+}\) and \({{{H}}}_{2}{{O}}\) reduction at a rotating disk electrode: theoretical and numerical aspects

This paper discusses mathematical model of hydrogen evolution via \({H}^{+}\) $H^{+}$ and \({H}_{2}O\) $H_{2}O$ reduction at a rotating disc electrode. Rotating disc electrodes are the preferred technology for analysing electrochemical processes in electrically powered cells and another rotating machinery, such as combustion engines, air compressors, gearboxes, and generators. The theory of nonlinear convection–diffusion equations provides the foundation for the model. In the present study, the Akbari-Ganji approach is utilised to solve, concurrently, the mass transport equations of  \({H}^{+}\) $H^{+}$ and \({OH}^{-}\) ${\mathit{OH}}^{-}$   in the electrolyte and on the electrode surface under steady-state circumstances. A general and simple analytical expression is obtained for the reactants' hydrogen and hydroxide ion concentrations. Additionally, numerical solutions using non-standard finite difference methods are presented, and compared with the analytical solution. The exact solution for the limiting case results is presented and examined with the general results. Furthermore, the graphs and tables that compare the theoretical and numerical solutions demonstrated the accuracy and dependability of our paradigm.