Effects of Pressure Gradient on Fluid Flow and Energy Distribution in a Bending Square Channel

Abstract

A precise knowledge on fluid flow and energy distribution in a bending channel is important for the thermal management of various engineering problems. The literature currently lacks a comprehensive understanding on how fluid characteristics and heat transfer in a bending channel are affected by pressure gradients, as well as when and how fluids transit into a turbulent state under continuous pressure gradient. The present study aims to explore the bifurcation structure of the steady solutions, linear stability and velocity distribution of the solutions and the transitional behavior from stead-state to other flow states (i.e., periodic or chaotic) for an extensive domain of the Dean number 0 < Dn ≤ 5000. The geometry of the problem is that the outer and bottom walls are heated while the inner and top are at room temperature. A proper grid analysis and validation are performed as well. The study successfully analyzed four branches of steady solutions where stability exists only in the first branch up to Dn = 2593.3709 and 2- to 7-vortex solutions are observed in the secondary flow. The flow transitions in the unsteady solutions are analyzed exquisitely by performing time-advancement of the solutions followed by inquisition of the phase space of time-dependent solutions. Results show that, if Dn > 2593.3709, the steady-state flow becomes periodic followed by a chaotic solution and 2- to 5-vortex solutions are observed for the unsteady flow. It is noticed that, if Dn > 0, the value of the Nusselt number (Nu) was initially higher on the cooling wall compared to the heated wall and at Dn = 102.67, Nu is found to be equal on both sidewalls and then it started increasing rapidly on the heated walls. The present study figured out how centrifugal force impacts fluid flow for larger pressure gradient, which assists fluid mixing and consequently enhances heat transfer in the fluid.