The enhancement characteristics of heat transfer, through a transition scenario of flow bifurcations, in asymmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element method. The heat transfer characteristics, flow bifurcation and transition scenarios are determined by increasing the Reynolds numbers for three geometrical aspect ratios r = 0.25, 0.375, and 0.5, and Prandtl numbers 1.0 and 9.4. The transition scenarios to transitional flow regimes depend on the aspect ratio. For the aspect ratios r = 0.25 and 0.5, the transition scenario is characterized by one Hopf flow bifurcation. For the aspect ratio r = 0.375, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a periodic flow. and a second Hopf flow bifurcation from a periodic to quasi-periodic flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies omega(1), and omega(2), respectively. For all the aspect ratios and Prandtl numbers, the time-average mean Nusselt number and heat transfer enhancement increases with the Reynolds number as the flow evolves from a laminar to a transitional regime. For both Prandtl numbers, the highest increase in the Nusselt number occurs for the aspect ratio r = 0.5: whereas, the lowest increases happen to r = 0.25. The increase of the Nusselt number occurs at the expense of a higher pumping power, which, for both Prandtl numbers, grows as the aspect ratio increases from r = 0.25 to r = 0.5 for reaching a specific Nusselt number. This enhancement is obtained without the necessity of high volumetric flow rates associated with turbulent flow regimes, which demand much higher pumping powers. Significant heat transfer enhancements are obtained when the asymmetric wavy channel is operated in the appropriate transitional Reynolds number range. (C) 2009 Elsevier Ltd. All rights reserved.