Thermal performance optimization of microchannels with smoothed corners assuming laminar flow and non-negligible viscous heating

Micro heat exchangers are characterized by high area-to-volume ratios, which allow very high values of the heat transfer coefficients even in laminar, forced convection. Higher friction losses, however, must be accounted for - especially for liquid flows - due to the small hydraulic diameter of the channels, making viscous dissipation no longer negligible, as is customary for larger-sized ducts. In the present work, the heat transfer performance of a micro heat exchanger is enhanced through a geometrical optimization of the channel section geometry. A fully developed, steady, laminar flow of a Newtonian liquid through a microchannel, with a rectangular cross section with rounded corners, is considered. The H1 thermal boundary condition is applied to the heated walls of the microchannel. Entropy Generation Numbers are evaluated when FG1b Performance Evaluation Criterion (PEC) is studied, in order to assess the influence of smoothing the corners of the starting cross section. Aspect ratio ranging between 0.03 and 1 are investigated and four different geometrical constraints applied when varying the smoothing radius. Both literature data and correlations numerically obtained by the authors are used in order to estimate the required Poiseuille number and Nusselt number as a function of channel geometry. The governing equations deriving from macroscopic energy and entropy balances are expressed in a non-dimensional form, as are the results presented. The magnitude of viscous heating is quantified by the Brinkman number, which also depends on the channel geometry. The resulting trends of PEC objective function and Entropy Generation Numbers are presented as a function of the non-dimensional corner smoothing radius for different values of both the channel aspect ratio and the imposed Brinkman number, showing that smoothing corners brings benefits in terms of both the entropy generation and the PEC objective function, when the heated perimeter is fixed and viscous dissipation is not negligible.