Laminar convective heat transfer across fractal boundaries

We focus on the characterization of heat-transfer processes in microchannels with fractal boundaries (and translational symmetry in the longitudinal direction) in the presence of a laminar axial velocity field. This corresponds to the generalization of the classical Leveque problem to investigate the role of fractal boundaries. We show that the thickness delta of the thermal boundary layer scales with the thermal Peclet number as delta similar to Pe(eff)(-1/(n+2)), n being the exponent characterizing the local behaviour of the laminar velocity field at the no-slip fractal wall. Correspondingly, the normalized thermal flux F is controlled by the boundary fractal dimension D(f) and the velocity exponent n according with the scaling law Phi similar to Pe(eff)(Df/(n+2)). Numerical results are presented for two different structures having different fractal dimensions: the Koch microchannel of fractal dimension D(f) = 3/2 and the Koch snowflake microchannel of fractal dimension D(f) = ln(4)/ln(3). Copyright (C) EPLA, 2010