Transient convective heat transfer in a porous circular cylinder

We employ a one-domain immersed boundary method to solve the Darcy–Brinkman–Forchheimer equations and examine the combined effects of permeability, fluid properties, and flow inertia on convective cooling around a porous circular cylinder in uniform flow. A mode diagram identifies four distinct wake modes: impermeable steady, impermeable shedding, permeable shedding, and fully permeable steady. As the Darcy number (Da) increases, throughflow intensifies, the thermal boundary layer becomes thinner, wake recirculation diminishes, and vortex shedding is suppressed, leading to a near doubling of the time-averaged Nusselt number (Nu) and a faster thermal response. An increase in the Prandtl number (Pr) steepens surface temperature gradients and improves heat removal without affecting the wake structure. The Reynolds number (Re) impacts heat transfer by thinning the boundary layer and modulating wake dynamics—remaining limited at low Re, enhanced by vortex shedding at moderate Re, and maximized at high Re due to strong inertial effects and throughflow. Peak local heat transfer occurs just downstream of the front stagnation point, where external acceleration intersects with internal throughflow. An empirical correlation, Nu¯*=2.21Da0.137 Re0.566 Pr0.392, quantifies the dominant influences of inertia and thermal diffusivity, along with the secondary effect of permeability. These results inform the design of porous-media heat exchangers and thermal management systems, emphasizing the effectiveness of high permeability in combination with moderate to high Re and Pr for rapid and efficient forced convection cooling.