Forced convection of air through networks of square rods or cylinders embedded in microchannels

Forced convection of air at near-standard conditions through periodical networks of micrometer square rods or cylinders is investigated. The Navier–Stokes equations subjected to first-order velocity-slip condition, and energy equations for the fluid and solid phases are numerically solved for two-dimensional structures. The flow is created by imposing pressure gradients, and heat is volumetrically generated inside the solid rods. Assuming periodicity in the direction transverse to the pressure gradient, the computational domain consists in long open channels, partially filled with solid rods placed regularly. The various structures considered are then modeled as porous media. For the permeability calculations, both volume averaging technique and multiple scale expansion technique are employed, and the results are favorably compared. The slip effect on permeability is highlighted for Knudsen number of about 0.05. On the other hand, the use of a periodic approach in the flow direction for heat transfer calculations is demonstrated not to be based on realistic assumptions. In addition, the importance of axial heat diffusion in channels of width close to one micrometer is emphasized. The reason is found in the low Péclet numbers typically encountered when the incompressible approximation is invoked. Based on numerical solutions at the microscopic scale, a new macroscopic modeling is suggested. Comparisons between numerical solutions and analytical predictions for various networks of rods are discussed. A very good agreement is shown.