A numerical study of unsteady heat and fluid flow through a rotating curved channel with variable curvature

Abstract

A numerical study on unsteady fluid flow and heat transfer through a rotating curved square channel with variable curvatures (0.1 ≤ 8 ≤ 0.5) is presented numerically by using a spectral method. The bottom wall of the duct is heated while cooling from the ceiling. A rotation of the channel about the center of curvature is imposed in the positive and negative direction for the Taylor number −500 ≤ Tr ≤ 2000, and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. At first, steady solutions are obtained by using Newton-Raphson iteration method with path continuation technique. As a result, two branches of steady solutions with two- to six-vortex solutions are obtained. Then, in order to study the non-linear behavior of the unsteady solution, time evolution calculation as well as their phase spaces are obtained, and it is found that for positive rotation Coriolis force enforces the curvature effect that results in to turn the chaotic flow into steady-state flow through periodic or multi-periodic flows. For negative rotation, however, it is found that Coriolis force exhibits an opposite effect to that of the curvature so that the unsteady flow undergoes through various flow instabilities. The present study elucidates the role of secondary vortices on convective heat transfer and it is found that convective heat transfer is significantly enhanced by the secondary flow.