Curvature induced instability characteristics of laminar flow and heat transfer through a bent square channel

Investigation of laminar flow characteristics through a bent square channel (BSC) is an attractive phenomenon to researchers because of its wide use in the engineering field. However, a detail investigation on curvature induced instability characteristics and energy distribution through the BSC over a mass range of the pressure gradient are rarely available. The current paper, therefore, provides an overview of the flow instability and convective heat transfer (CHT) through a BSC with constant curvature (delta = 0.5) covering a wide domain of the Dean number (0 < Dn <= 5000). A temperature difference is applied across the walls for the Grashof number, Gr = 100, where the outer-lower sidewalls (OLSW) are heated while the inner-top sidewalls (ITSW) in room temperature. At first, steady solutions are inspected by path continuation technique and consequently a structure of four branches is obtained comprising with 2- to 4-vortex solution. Linear stability analysis shows that the flow is stable for 0 < Dn <= 4410.14. In the unstable region, time -dependent solutions are particularly obtained and flow transition is meticulously determined by analyzing phase plot (PP) and power spectrum (PS) analysis of the solutions. A diagram of the unsteady solution (US) with respect to various curvatures (0.001 <= delta <= 0.5) is displayed and it is found that the flow is imposed by the centrifugal-buoyancy instability. The CHT is calculated analyzing temperature gradients and it is reported that CHT is enhanced as Dn is increased. A diagram of the vortex-structure in Dean vs. curvature plane is explored which shows that the channel curvature dominates the secondary vortices and proportionally increases the overall CHT in the fluid. Finally, the current numerical investigations are compared with experimental out-comes and a good match is noticed.