  The shape of a microchannel is usually affected by a significant uncertainty
due to the small size of the cross-section, comparable with the typical
wall-roughness length scale. Such an uncertainty is present at any scale, but
it is definitely amplified and, hence, significantly important when the
hydraulic diameter becomes smaller than some tenth micrometers. The focus of
this paper is on the numerical analysis of the sensitivity to shape random
modification, within a prefixed maximum extent, of the main flow and heat
transfer characteristics of fully-developed forced convection. The numerical
solutions are carried out by employing a finite-element solver repeated over a
statistical sample of randomly generated perimetral profiles that simulate the
wall roughness. The study includes the evaluation of the Fanning friction
factor and of the Nusselt number for the T, H1 and H2 thermal boundary
conditions.
