Improving thermal performance while minimizing pressure differences and irreversibility characteristics remains a persistent challenge in thermo-mechanical systems. This study investigates a corrugated channel with different profiles (triangular, square, and elliptical) for steady, laminar, incompressible, and mixed convective flow through a backward-facing step. The impact of corrugated wall geometrical characteristics, such as height, width, and angle, on hydrothermal performance is explored. Additionally, the study investigates the influence of inline and staggered arrangements for various channel configurations. The finite element method is employed for numerical investigation of thermohydraulic and irreversibility characteristics. Results, presented through streamlines, contours, and line plots, reveal a significant modulation of reattachment length based on corrugate architecture. Notably, the local Nusselt number is highest at the initial interaction with the corrugated channel, regardless of the channel configuration. Hydrothermal measurements highlight elliptical configurations as optimal, exhibiting a 60% improvement in thermal performance compared to a non-corrugated channel. Moreover, increasing corrugate height results in higher Nusselt numbers, pressure drops, and irreversibility. Reduced corrugate width leads to a higher Nusselt number due to the formation of a secondary recirculation zone. An elliptical corrugate with a 0° angle inclination yields the highest Nusselt number by facilitating a stronger recirculation zone. Thus, optimal corrugated wall configuration involves higher height, lower width, and no angle inclination, emphasizing the significant impact of these parameters on hydrothermal performance and their importance as design characteristics.