Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions

Abstract

A solution to a benchmark problem for a three-dimensional mixed-convection flow in a horizontal rectangular channel heated from below and cooled from above (Poiseuille-Rayleigh-Bénard flow) is proposed. This flow is a steady thermoconvective longitudinal roll flow in a large-aspect-ratio channel at moderate Reynolds and Rayleigh numbers (Re = 50, Ra = 5,000) and Prandtl number Pr = 0.7. The model is based on the Navier-Stokes equations with Boussinesq approximation. We propose reference solutions resulting from computations on large grids, Richardson extrapolation (RE), and cubic spline interpolations. The solutions obtained with one finite-difference, one finite-volume, and two finite-element codes are in good agreement, and reference values for the flow and thermal fields and for the heat and momentum fluxes are given with four to five significant digits.