An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 104to 9·76 × 105. A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 102 to 105 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 104. Comparisons between the present experimental and numerical results under similar conditions show good agreement.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112076002012

An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders

Laminar and turbulent natural convection in an enclosed cavity

Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k-ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non-uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra-values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra-values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k-ϵ model with logarithmic wall functions, which gives significant overpredictions.

R. K. MacGregor

Papers

Free Convection Through Vertical Plane Layers—Moderate and High Prandtl Number Fluids