Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures

Two-dimensional laminar natural convection in air contained in a long horizontal rectangular enclosure with isothermal walls at different temperatures has been investigated using numerical techniques. The time-dependent governing differential equations were solved using a method based on that of Crank and Nicholson. Steady-state solutions were obtained for height to width ratios of 1, 2.5, 10, and 20, and for values of the Grashof number, GrL′, covering the range 4 × 103 to 1.4 × 105. The bounds on the Grashof number for H/L = 20 is 8 × 103 ≤ GrL′ ≤ 4 × 104. The results were correlated with a three-dimensional power law which, yielded H/L=1Nu¯L′=0.0547(GrL′)0.3972.5≤H/L≤20Nu¯L′=0.155(GrL′)0.315(H/L)−0.265 The results compare favorably with available experimental results.