Three-dimensional Buoyancy-driven Flow in a Vertical Channel with Heated Ribs
A numerical study of three-dimensional buoyancy-driven flow in a vertical channel of varying rectangular cross-section is presented. The right vertical wall of the channel is isothermal while heated rectangular ribs are mounted periodically on the left vertical wall. The dimensionless governing equations with appropriate boundary conditions are solved using a time-accurate spectral element method. Flow and heat transfer characteristics are presented for values of Grashof number, Gr, in the range 1 &Mac178; Gr &Mac178; 105, Prandtl number, Pr=0.71, and dimensionless channel reference temperature Q*b @ 0.2 and Q*b @ 0.0. At Gr @ 104 three-dimensional variations appear in both temperature and velocity fields while at Gr* @ 105 both fields experience self-sustained oscillations. The effect of channel reference temperature on the flow and heat transfer is discussed. Two-dimensional simulations are also performed and compared with 3-D predictions at the channel mid-plane. Although for small values of Gr three-dimensional effects are confined very near the end walls, strong 3-D effects are observed in the entire channel at high Gr. Maximum values of field variables computed by the 2-D and 3-D models are compared and deviations are discussed.