| Issue |
EPL
Volume 90, Number 1, June 2010
|
|
|---|---|---|
| Article Number | 14002 | |
| Number of page(s) | 6 | |
| Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/90/14002 | |
| Published online | 29 April 2010 | |
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: alessandra.adrover@uniroma1.it
Received:
1
December
2009
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
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