Abstract

This work investigates the transition scenario and heat transfer characteristics in a channel with a block tandem, as the flow evolves from a laminar to a transitional regime, by two-dimensional direct numerical simulations (DNS) of the time dependent, incompressible continuity, Navier-Stokes and energy equations. This investigation uses an extended computational domain with 10 blocks to determine the existence of a fully developed flow and self-similar temperature profiles, and a reduced computational domain to investigate the heat transfer enhancement for laminar and transitional flow regimes. The flow characteristics show a transition scenario characterized by two Hopf bifurcations - at two critical Reynolds numbers Rec1 and Rec2- as the flow evolves from a laminar to a periodic flow, and then to a quasi-periodic flow, respectively. The first flow bifurcation occurs at a critical Reynolds number Rec1 that is significantly lower than the critical value for a plane Poiseuille flow; whereas, the second Hopf flow bifurcation occurs at a critical Reynolds number Rec2 > Rec1. For a laminar regime, the global time-average Nusselt number remains almost constant; for a periodic flow, the global time-average Nusselt number increases by a factor of two with respect to the laminar Nusselt number and it increases even more when the flow becomes quasi-periodic. The rate of increase of the global time-average Nusselt number is higher for a quasi-periodic than a periodic flow regime, which is due to a stronger vortex dynamics and better flow mixing in quasi-periodic flow regimes. This investigation demonstrates that significant heat transfer enhancements can be obtained at supercritical transitional flow Reynolds numbers with a minimum of dissipation due to viscous stresses. This enhancement is obtained without the necessity of operating this channel to high volumetric flow rates associated to turbulent flow regimes, which demand high pumping powers. In this channel, the transitional flow regime is more efficient than a laminar flow regime as a method of cooling electronics between both Hopf bifurcations and for transitional Reynolds numbers higher than Rec2.