An investigation of natural convection in a three dimensional square wavy channel

Natural convection in a three dimensional wavy channel, which is composed of numerous two dimensional cross sections, is investigated numerically. The method of elliptic partial differential equations grid generation is adopted to construct a distribution of grids on each cross section. The distributions of the whole cross sections are piled up in sequence from the inlet to outlet to form a three dimensional channel. In order to solve a low speed compressible flow problem, the compressibility and viscosity of the working fluid are taken into consideration, and the non-reflecting boundaries at the inlet and outlet of the channel are held. The Bossinesq assumption is then no longer necessary. As well, the methods of the Roe scheme, preconditioning and dual time stepping matching the implicit LUSGS algorithm (Implicit Lower Upper symmetric Gauss–Seidel algorithm) are simultaneously used to solve governing equations. Effects of the Rayleigh number and the ratio of the amplitude to wave length on heat transfer rates of the channel are examined. Results of both this study and existing studies have good agreements.