Enhancing the efficiency of industrial water electrolysis for hydrogen production is vital for the energy transition. In Alkaline Water Electrolysis (AWE), hydrogen is produced at the cathode, and the bubbles are formed when the local hydrogen concentration exceeds the solubility limit. It is important to understand the exact local conditions that result in the nucleation of bubbles in this multi-phase and reactive system. With modeling, it is possible to gain insight into the relation between various local properties, but the model needs to include all relevant physics and chemistry. Thus, this work focuses on the multi-species electrochemical transport phenomena with reaction occurring on the electrode-electrolyte interface. The electrochemical transport phenomena and the bubble nucleation are meso-scale phenomena occurring at the electrode-electrolyte interface. Lattice Boltzmann Method (LBM) is well suited for modeling meso- scale behavior but it is computationally memory expensive. Consequently, a hybrid approach combining Finite Difference Method (FDM) and LBM has been developed to simulate transport phenomena in the migration-diffusion problem with heterogeneous reaction kinetics. The Debye-Hückel theory is used as a benchmark to validate the developed model. Subsequently, the model is employed to simulate the transport phenomena occurring in the hydrogen half-cell of AWE, with a specific focus on the Hydrogen Evolution Reaction (HER) governed by the Butler-Volmer kinetics equation. The model captures the dynamic evolution of physical parameters such as electric potential, concentration of species, and fluxes within the system particularly in the Electric-Double layer (EDL). The effect of electrode potential on the distribution of species involved in the reaction are studied by performing simulations for different electrode potential. The influence of secondary fluxes on the species distribution is studied by implementing a spatially varying boundary condition to the reacting site. Finally, the formulated methodology is extended to solve a multi-phase system with species transportation occurring around a catalyst particle.