The Influence of Geometry on the Thermal Performance of Microchannels in Laminar Flow with Viscous Dissipation

Abstract

Micro heat exchangers (MHXs) may achieve very high heat transfer coefficients thanks to their small dimensions and high Area-to-Volume ratio even in laminar flow. The main drawback of these devices is the high frictional losses – especially for liquid flows – that make viscous dissipation no longer negligible. In order to enhance heat transfer, modification of the channels’ cross-section is a viable strategy. In the present work the fully developed steady laminar flow of a Newtonian liquid through a microchannel subject to H1 boundary conditions in the presence of viscous dissipation is investigated. Entropy generation numbers and FG1a performance evaluation criterion are employed to assess the influence of smoothing the corners of an initially rectangular cross-section, with an aspect ratio ranging from 1 to 0.03 under four different types of geometrical constraints. The governing equations and the results are expressed in non-dimensional form, the intensity of viscous dissipation being exemplified by the Brinkman number, which is demonstrated to increase its maximum allowable value when corners are smoothed. The results are reported as a function of the non-dimensional radius of curvature Rc and aspect ratio and show that smoothing the corners almost invariably brings about a benefit for a fixed heated perimeter.