Laminar Forced Convection in a Porous Circular Microduct with Wall Roughness Effects

The study presented in this paper is devoted to the laminar forced convection heat transfer in a porous microduct with a circular cross section. At small cross-section scales, the effects of roughness at the duct walls may be important for the evaluation of the heat transfer rate. The analysis aims to provide the Nusselt number as a quantity dependent on the boundary shape uncertainty by averaging over statistical samples of microducts having different roughness distributions generated randomly. Each statistical sample refers to a prescribed ratio between the maximum size of the wall roughness and the microduct nominal radius, and to a prescribed number of nodes employed to draw the boundary shape. Boundary conditions of either uniform wall temperature (T condition) or wall heating (H1 or H2 conditions) are considered. The results show that both the roughness and the number of nodes defining the microduct cross-sectional shape tend to inhibit the heat transfer: a sufficiently high value of the roughness amplitude may halve the Nusselt number relative to the smooth case. The Nusselt number obtained for the H2 condition decreases faster with the roughness amplitude compared with the Nusselt number obtained for the T and H1 conditions.