Laminar convective heat transfer across fractal boundaries
Dipartimento di Ingegneria Chimica Materiali Ambiente Università di Roma "La Sapienza" via Eudossiana 18, 00184 Roma, Italy, EU
Corresponding author: email@example.com
Accepted: 23 March 2010
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 Lévêque problem to investigate the role of fractal boundaries. We show that the thickness δ of the thermal boundary layer scales with the thermal Peclet number as , n being the exponent characterizing the local behaviour of the laminar velocity field at the no-slip fractal wall. Correspondingly, the normalized thermal flux Φ is controlled by the boundary fractal dimension Df and the velocity exponent n according with the scaling law . Numerical results are presented for two different structures having different fractal dimensions: the Koch microchannel of fractal dimension Df = 3/2 and the Koch snowflake microchannel of fractal dimension Df = ln(4)/ln(3).
PACS: 47.15.Cb – Laminar boundary layers / 47.15.Rq – Laminar flow in cavities, channels, ducts, and conduits / 47.53.+n – Fractals in fluid dynamics
© EPLA, 2010