Plate-fin heat sink forced convective heat transfer augmentation with a fractal insert

The interaction of fractal grid-induced turbulence on plate-fin heat sink is numerically investigated at flow Reynolds number of Re_Dh = 7.3 × 10⁴. Three fractal grids of different number of fractal iterations N, namely: The rectangular fractal grid of N = 2 (RFG₂), square fractal grid of N = 3 (SFG₃), and square fractal grid of N = 4 (SFG₄)are employed to perturb the windward fluid flow. For each case, the effects of eight fractal grid first iterative bar thicknesses t₀ at five different inter-fin distances δ are investigated. Results show that Nusselt number Nu and pressure drop ΔP increase with t₀ for all cases. 57%, 51% and 43% of forced convective heat transfer augmentations are observed using SFG₃, RFG₂ and SFG₄, respectively, than that of the control plate-fin heat sink. The thermal and fluid flow perturbation promoted by SFG₃ outperforms the rest with Nu = 7.07 × 10³ at δ = 10 and 25 mm, but at a cost of higher ΔP. RFG₂'s maximum Nu is 6.82 × 10³ where wider δ of δ = 50 mm is preferred, and SFG₄ is 6.42 × 10³ at δ=10 mm. Interestingly, SFG₄ enjoys a lower ΔP, which is highly energy sustainable. The strength of SFG₃-induced turbulence intensity is able to infiltrate deeper into the fins at a higher flow rate, which may facilitate the continuous restructuring of inter-fin flow boundary layers, thus promoting thermal dissipation. In short, plate-fin heat sink forced convection is strongly dependent on the interaction between the insert configuration and the induced flow structures within fins, of which, the effects of t₀ and δ are highly correlated.