Enhanced laminar-flow heat transfer at fiber-flocked surfaces

Abstract

High-conductivity carbon fibers have been “flocked”, or perpendicularly attached onto surfaces, thus enabling heat transfer enhancement for such fiber-flocked surfaces. Here, an analysis is performed for fully developed laminar flow and heat transfer in plane and cylindrical ducts with fiber-covered walls. The fiber volumetric packing density is sparse such that single-cylinder correlations are applied for the drag and heat transfer between the fibers and the fluid; this gives rise to body-type terms in the momentum and energy equations for the fiber region near the wall. These equations are solved by singular perturbation theory, and matched to the core flow without fibers. The result of this analysis is in terms of friction factor and Nusselt number multipliers, which are constant for all laminar Reynolds numbers, but which vary strongly with the length of the fibers relative to the duct half-width or radius. For large fiber conductivities and relative lengths, the results indicate a greater heat transfer enhancement than hitherto possible.