This paper reports the optimal geometry of an array of fins that minimizes the thermal resistance between the substrate and the flow forced through the fins. The flow regime is laminar. Two fin types are considered: round pin fins, and staggered parallel-plate fins. The optimization of each array proceeds in two steps: The optimal fin thickness is selected in the first step, and the optimal thickness of the fluid channel is selected in the second. The pin-fin array is modeled as a Darcy-flow porous medium. The flow past each plate fin is in the boundary layer regime. The optimal design of each array is described in terms of dimensionless groups. It is shown that the minimum thermal resistance of plate-fin arrays is approximately half of the minimum thermal resistance of heat sinks with continuous fins and fully developed laminar flow in the channels.
This is an experimental numerical and theoretical study of the heat transfer on a pin-finned plate exposed to an impinging air stream. The pin fins are aligned with the air approach velocity. The base plate and the fin cross section are square. It is demonstrated experimentally that the thermal conductance between the plate and the air stream can be maximized by selecting the fin-to-fin spacing S. Next, a simplified numerical model is used to generate a large number of optimal spacing and maximum heat transfer data for various configurations, which differ with respect to fin length (H), fin thickness (D), base plate size (L), fluid type (Pr), and air velocity (ReL). Finally, the behavior of the optimal spacing data is explained and correlated theoretically based on the intersection of asymptotes method. The recommended correlations for optimal spacing, Sopt/L ≅ 0.81 Pr−0.25 ReL−0.32, and maximum thermal conductance, (q/ΔT)max/kaH ≅ 1.57 Pr0.45 ReL0.69 (L/D)0.31, cover the range D/L = 0.06 − 0.14, H/L = 0.28−0.56, Pr = 0.72−7, ReD = 10−700, and ReL = 90−6000.
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