Thermal Boundary Condition of First Type in Fourier Pseudospectral Method

The purpose of this paper is to extend a novel numerical methodology, combining thermal immersed boundary and Fourier pseudospectral methods called IMERSPEC. This methodology has been developed for incompressible fluid flow problems modeled using Navier-Stokes, mass and energy equations. The numerical algorithm consists of Fourier pseudospectral method (FPSM), where Dirichlet boundary condition is modeled using an immersed boundary method (multi-direct forcing method). The new method combines the advantages of high accuracy and low computational cost provided by FPSM to the possibility of managing complex and non periodical geometries given by immersed boundary method. In the present work this new methodology is applied to the problem of heat transfer for natural convection in the annulus between horizontal concentric cylinders and conducted to validate the capability and efficiency of present method. Results for this application are presented and good agreement with available data in the literature have been achieved.