General Correlations for Laminar Flow Friction Loss and Heat Transfer in Plain Rectangular Plate-Fin Cores

New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: $(fRe)$$∼(L/dhRe)1/2$⁠, and Nu $∼(L/dhRe)1/2Pr1/3ϕ(α)$⁠, where f, Re, and Nu are all based on the hydraulic diameter d_h of the interfin flow channel. Generalized correlations for both $(fRe)$ and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0 < α ≤ 1.