Thermal and solutal Marangoni convection in three-layered viscous flows: Insights for liquid metal battery optimization

• The study numerically investigates thermal and solutal Marangoni convection in three-layered viscous flows, directly relevant to the optimization of liquid metal batteries for renewable energy storage. • The homotopy perturbation method is employed to solve the coupled nonlinear transport equations, yielding insights into the fundamental physics of heat and mass transfer in complex battery geometries. • Velocity profiles exhibit a pronounced core region of maximum flow speed, which decays toward the channel walls, informing electrode–electrolyte contact stability in liquid metal batteries. • The findings support the development of thermal management systems for grid-scale batteries, potentially improving energy density, durability, and charge–discharge efficiency.