The present analysis deals with the heat transfer characteristics and entropy generation investigation for a non-Newtonian fluid flowing in a wavy passage having three different corrugation profiles, namely, sinusoidal, trapezoidal, and triangular, having the exact dimensions, amplitude, and wavelength. The discretization of governing equations has been carried out using the finite volume method, and for pressure–velocity coupling SIMPLE algorithm is adopted. Power law model is adopted for modeling the non-Newtonian behavior in the study. The present investigation is reported for the index of power law ranging from 0.4 to 1.6 and Reynolds number varying from 25 to 125. The variation of an average Nusselt number, dimensionless drop in pressure, performance factor, thermal entropy generation, viscous entropy generation, and Bejan number are observed for different values of Reynolds number and power law index. The study helped us in concluding that the value of the average Nusselt number is the highest for a trapezoidal-shaped corrugated channel; on the other hand, drop in pressure is also the highest for a trapezoidal channel. However, if conclusions are to be made based on the performance factor, then at high Reynolds number flow, the sinusoidal-shaped corrugated channel is preferred for shear-thinning fluids, and the triangular-shaped corrugated channel is preferred for shear-thickening fluids, whereas the triangular-shaped corrugated channel is preferred for both the shear-thickening and shear-thinning fluids for a low Reynolds number flow. Entropy generation analysis shows that both the thermal and viscous entropy generations are maximum for a trapezoidal channel followed by the sinusoidal channel and the least entropy generations occur in the case of the triangular channel.