Heat transfer enhancement via Görtler flow with spatial numerical simulation

Purpose The centrifugal instability mechanism of boundary layers over concave surfaces is responsible for the development of quasi-periodic, counter-rotating vortices aligned in a streamwise direction known as Gortler vortices. By distorting the boundary layer structure in both the spanwise and the wall-normal directions, Gortler vortices may modify heat transfer rates. The purpose of this study is to conduct spatial numerical simulation experiments based on a vorticity–velocity formulation of the incompressible Navier–Stokes system of equations to quantify the role of the transition in the heat transfer process. Design/methodology/approach Experiments are conducted using an in-house, parallel, message-passing code. Compact finite difference approximations and a spectral method are used to approximate spatial derivatives. A fourth-order Runge–Kutta method is adopted for time integration. The Poisson equation is solved using a geometric multigrid method. Findings Results show that the numerical method can capture the physics of transitional flows over concave geometries. They also show that the heat transfer rates in the late stages of the transition may be greater than those for either laminar or turbulent ones. Originality/value The numerical method can be considered as a robust alternative to investigate heat transfer properties in transitional boundary layer flows over concave surfaces.