This present work investigates the heat transport and fluid flow characteristics of forced convection flow in a wavy channel with sinusoidal shape linearly increasing amplitude using a finite element approach. The streamline and isotherms fields are inspected with varying Reynolds number (Re = 5–200), slope of amplitude (A = 0.04), and power law index (n = 0.2–0.8). The study reveals that the average Nusselt number ( \( \overline{Nu} \) ) are independent with varying amplitude of the wavy channel at a smaller Reynolds number and a higher power law index. A tertiary recirculation zone is observed that leads to an increment of heat transfer, which is depicted in terms of enhancement ratio (ER). At a higher Reynolds number (Re = 200) and lower power law index (n = 0.2), the ER observed a maximum, and after that it decreases with a higher n value. Therefore, the amount of performance factor (PF) observed a maximum at a smaller value of Reynolds number (Re = 5) at n = 0.2, then it gradually decreases with increasing power law index. These findings emphasize the importance of wave and fluid flow parameters in optimizing the heat transfer performance.