Numerical simulation of the optimal spacing for a radial finned tube cooled by a rectangular jet. I – Average thermal results

• Slot jet of air on a finned cylinder is a compound technique to enhance heat transfer.
• Numerical simulations are done with two-equation turbulent models (RNG k–ɛ and SST k–ω).
• Radial fins have a rectangular profile with a fixed total volume as constrain.
• Maximum heat transfer is at the minimum slot to cylinder distance.
• Maximum heat transfer is at the maximum fin spacing to fin height ratio.

The present work investigates the average heat transfer on a finned cylinder cooled by a rectangular jet of height H. The diameter of the external cylinder, without fins, is D and the cylinder to slot ratio D/H is equal to 1. Numerical simulations are carried on with two turbulent models, RNG k–ɛ and SST k–ω. The jet flow can be characterized by the Reynolds number, defined with the diameter of the external cylinder without fins, D, or with the hydraulic diameter of the rectangular slot, Dhydr ≈ 2H. Two turbulent flows are investigated at ReD = 7100, or ReDhydr = 13,200, and at ReD = 19,700, or ReDhydr = 36,700. The main goal of the paper is to evaluate the optimal spacing, s, between the fins, and the optimal slot-to-cylinder distance, S/H, which maximize the average heat transfer on the finned cylinder. The optimization process is performed for a pitch of 3 mm and at a given value of the fin volume. The numerical simulations show that an optimal configuration is obtained when the ratio s/l of the spacing, s, to fin height, l, is maximum, and the cylinder is set at the slot-to-cylinder distance, S/H = 3.