Heat Transfer Characteristics and Enhancement in Symmetric Wavy Channels in a Frequency-Doubling Transition Scenario

We investigate the heat transfer enhancement due to flow mixing enhancement in a frequency-doubling transition scenario in symmetric wavy channels by direct numerical simulations of the mass, momentum and energy equations. The governing equations are solved for laminar and transitional flow regimes by the spectral element method, using a periodic computational domain, and with a high aspect ratio of r = a/(2L) = 0.375, where L is the periodic length, and a, the wavy wall amplitude. The frequency-doubling transition scenario is characterized by one flow bifurcation that develops to a critical Reynolds numbers Re_c, leading to a periodic flow. Further increases in the Reynolds number leads to successive periodic flows where the fundamental frequency ω₁, increases continuously. This scenario is different to the Ruelle-Takens-Newhouse transition scenario obtained for a symmetric wavy channel with an aspect ratio of 0.125, where periodic and quasi periodic flow regimes develop as the Reynolds number increases. Heat Transfer simulations are carried out assuming a constant heat flux on one wall and an adiabatic condition on the other wall. Numerical results demonstrate that the time-average mean Nusselt number increases significantly as the flow passes from a laminar to a periodic flow regime. As the flow becomes periodic and for increasing Reynolds numbers, the Nusselt number increases with respect to the laminar flow Nusselt number, up to a factor of 4, depending on the Reynolds number, which represents a significant heat transfer enhancement due to a better flow mixing. This increase is accompanied by a reasonable increase in both the friction factor and the pumping power. The obtained qualitative and quantitative features are compared to other channel geometries, such as grooved and asymmetric wavy channels, which also develop different transition scenarios.