Using computational simulations, we examine heat transfer enhancement in laminar flows through asymmetric wavy channels with sinusoidal walls. Specifically, we probe the influence of the amplitude and period of the wall waviness as well as the driving pressure on the enhancement of heat transfer for both steady and unsteady flows. Our simulations reveal that for the steady flow occurring at lower flow rates, the heat transfer enhancement is defined by the amplitude of the wall waviness. When the flow rate is increased and the flow transitions to unsteady, the heat transfer enhancement exhibits a stronger dependence on the pressure drop than the amplitude. We find that the increase in heat transfer achieved in the unsteady regime is significantly higher than that in the steady regime. Furthermore, we use a thermal-hydraulic performance factor to investigate if this enhancement outweighs the increased frictional losses the geometry induces. Our data indicates that wavy walled channels with small wave amplitudes outperform straight channels at Reynolds numbers as low as 300 and exhibit greater than 50% improvement at Re approximate to 600. These results are important for designing compact heat exchangers capable of high performance in the laminar regime. (C) 2016 Published by Elsevier Ltd.