A homogenization approach for buoyancy-induced flows over micro-textured vertical surfaces
نویسندگان
چکیده
Asymptotic homogenization is employed to formulate upscaled effective boundary conditions at a smooth virtual surface for natural-convection flow over periodically roughened vertical wall, bypass the expensive numerical resolution of and temperature fields near within wall corrugations. Microscale problems are found by expanding near-wall variables in terms small parameter $\epsilon$ , ratio between microscopic macroscopic length scales. The expressions velocity provided up second-order accuracy . case transverse square ribs considered as representative example. classical Navier-slip condition streamwise spanwise components modified second order gradient normal stress time derivative shear stress. slip additionally corrected buoyancy term first temperature-gradient order. appears only transpiration condition. A Robin-like found, where with representing thermal slip. levels applicability range mimic behaviour investigated under laminar conditions, comparison results full feature-resolving simulations. formal validity limit approximation sought single criterion ( $C$ ), which combines effects Grashof number ribs’ density. introduced model further tested on different rib geometries.
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ژورنال
عنوان ژورنال: Journal of Fluid Mechanics
سال: 2022
ISSN: ['0022-1120', '1469-7645']
DOI: https://doi.org/10.1017/jfm.2022.320