Three-dimensional roughness effect on microchannel heat transfer and pressure drop Giulio Croce * , Paola D’agaro, Carlo Nonino DiEM, Universita ` degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italy Received 7 August 2006 Available online 6 August 2007 Abstract Surface roughness may have a significant impact on microchannel performances, since at such a small scale it is nearly impossible to obtain an actual smooth surface. The numerical approach allows a detailed description of the surface imperfections; thus, we can easily separate roughness from other microscale effects. In this paper, roughness is modelled as a set of three-dimensional conical peaks dis- tributed on the ideal smooth surfaces of a plane microchannel. Different peak heights and different peak arrangements are considered at various Reynolds numbers. Periodicity conditions in both transverse and streamwise directions allow the reduction of the domain to a small volume containing one or two peaks. The performances of parallel plate rough channels are compared with standard corre- lation. Results show a remarkable effect of roughness on pressure drop, and a weaker one on the Nusselt number. The performances are dependent on the geometrical details of the roughness elements. The impact of the uncertainty in the definition and measurement of the hydraulic diameter is also discussed. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Microchannel; Roughness; Periodic boundary conditions; Laminar flow; Pressure drop; Heat transfer 1. Introduction The interest in heat transfer and pressure drop in micro- channels has been constantly growing over the past decade, as shown by the extended reviews reported in Refs. [1,2]. However, although a large pool of experimental data is available, we do not yet have a complete comprehension of all the aspects of the microscale flow behaviour. This is partially due to the fact that raw experimental data may even be somehow misleading, in the sense that the glo- bal performance parameters are strongly influenced by a number of competing effects and different uncertainties, whose relative importance is very difficult to estimate. Fur- thermore, July et al. [3] showed that the experimental uncertainty, dominated by the error in diameter measure- ments, may induce up to a 10% difference in the evaluation of the Poiseuille number for smooth fused silica tubes and up to 20% for stainless steel tubes. Thus, experimental data are only useful to prove deviations from standard theory above such magnitudes. In addition to the error in diame- ter measurements, these discrepancies can be ascribed to a variety of causes, including compressibility effects in gases, viscous dissipation, variation of thermophysical properties with temperature, entrance and exit losses, conjugate heat transfer and surface roughness. This yields some scattering of experimental data. In fact, whereas most literature refer- ences report heat fluxes higher or equal to those predicted by the corresponding macroscale correlations (see, as an example, [4]), one can even find some quotations of the opposite effect [5]. The computational approach can, thus, be useful to understand the basic physics of the problem, since one can easily select or neglect any of the relevant effects (such as viscous dissipation or surface roughness), and analyse every single facet of the problem. Here, we will focus on the estimation of the roughness effect. At the microscale level it is nearly impossible to 0017-9310/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.06.021 * Corresponding author. Tel.: +39 0432 558018; fax: +39 0432 558027. E-mail address: giulio.croce@uniud.it (G. Croce). www.elsevier.com/locate/ijhmt Available online at www.sciencedirect.com International Journal of Heat and Mass Transfer 50 (2007) 5249–5259