Permeability effect on heat transfer and flow dynamics past two tandem 45°-inclined square cylinders

In this study, two-dimensional transitional flow and convective heat transfer past two tandem porous square cylinders inclined at 45° are numerically investigated using the lattice Boltzmann method (LBM) at a Reynolds number ( R e ) of 150 and a Prandtl number ( P r ) of 0.71 across a wide range of Darcy numbers ( 1 0 − 5 ≤ D a ≤ 1 0 − 2 ) and spacing ratios ( 1.5 ≤ L / D ≤ 10 ). The results show that permeability and spacing ratio primarily govern wake transition, categorizing the flow into four distinct regimes: Overshoot (OS), Overshoot–Primary (OP), Primary–Secondary (PS), and Primary–Twolayer–Secondary (PTS). High permeability ( D a = 1 0 − 2 ) induces strong internal fluid penetration that completely suppresses vortex shedding, forming a steady laminar wake (OS regime). At lower permeabilities ( D a ≤ 1 0 − 3 ), transitions across OP, PS, and PTS regimes are quantitatively bounded by specific hydrodynamic thresholds, including the lowest mean drag on the downstream cylinder, flow asymmetry, and maximum fluctuating lift. Crucially, this study identifies that at small to moderate spacings ( L / D ≤ 5 ), convective heat transfer on the downstream cylinder is enhanced, achieving a maximum increase of up to 18% in the average Nusselt number compared to the upstream cylinder. Meanwhile, the upstream cylinder exhibits identical hydrodynamic and thermal characteristics as an isolated single porous cylinder at sufficiently large L / D .