Shape uncertainty analysis of laminar forced convection in a round microchannel with viscous dissipation

TL;DR

This paper investigates how shape uncertainties in microchannels affect laminar forced convection, using numerical simulations with random wall roughness profiles to analyze flow and heat transfer characteristics.

Contribution

It introduces a numerical method to assess the sensitivity of flow and heat transfer to shape uncertainties in microchannels with wall roughness.

Findings

Shape uncertainty significantly impacts flow and heat transfer.

Fanning friction factor varies with wall roughness.

Nusselt number is sensitive to shape modifications.

Abstract

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.