Numerical calculations of laminar and turbulent natural convection in water in rectangular channels heated and cooled isothermally on the opposing vertical walls

Abstract

Natural convection was computed by finite-difference methods using a laminar model for 2 (wide) × 1 and 1 × 1 enclosures for Ra from 10 6 to 10 9 and Pr = 5.12 and 9.17, and a k- ϵ turbulent model for a square enclosure for Ra from 10 10 to 10 11 and Pr = 6.7. The average Nusselt numbers agree well with the correlating equation of Churchill for experimental and computed values. The computed velocity profile along the heated wall is in reasonable agreement with prior experimental values except for the thin boundary layer along the lower part of the wall where a finer grid size than was computationally feasible appears to be necessary. A detailed sensitivity test for constants of the k- ϵ model was also carried out. The velocity profile at the middle height and the average Nusselt number was in even better agreement with the experimental results when the turbulent Prandtl number was increased to four and the constant c 1 was decreased by 10%. A more refined turbulent model and finer grid divisions appear to be desirable, particularly for larger Ra.