Numerical study of three‐dimensional incompressible thermal flows in complex geometries

Abstract

In part I of this study, a three‐dimensional finite difference iterative solver capable of handling the coupled Navier‐Stokes and energy equations for incompressible viscous flows was described and validated with two‐ and three‐dimensional benchmarks. Part II describes the results of the computational study of two distinct complex geometries: 1) two‐dimensional and three‐dimensional natural convection in cavity whose surface is cooled while two internal blocks are heated; 2) two‐dimensional and three‐dimensional natural convection in the region defined by two interconnected cavities of different sizes which are differentially heated. All computations have been performed for a Prandtl number of 1.0, and different values of the Rayleigh number ranging between 103 and 106 depending on the problem. In the first problem, three‐dimensional effects in the top region of the cavity trap fluid in vortices near the top of the heated blocks adversely affecting heat transfer in the region while enhancing it in the region between the two heated blocks. In the second problem, the sudden expansion of fluid as it leaves the top cavity and enters the bottom one generates three‐dimensional wakes in the bottom cavity that enhance the convective heat transfer across the system walls near them. These studies tend to suggest that three‐dimensional effects play a very important role in the enhancement of convective heat transfer in complex geometries, especially at higher Rayleigh numbers.