The Role of the Viscous Dissipation in Heated Microchannels

Many experimental works appeared in the last decade in the open literature dealing with forced convection through microchannels. The earliest experimental results on single-phase flows in microchannels evidenced that for channels having a hydraulic diameter less than $1mm$ the conventional continuum models can no longer be considered as able to accurately predict pressure drop and convective heat transfer coefficients. This conclusion seemed to be valid for both gas and liquid flows. Sometimes the authors justified this conclusion by invoking new micro-effects, e.g., electrostatic interaction between the fluid and the walls or scaling effects (axial heat conduction, viscous forces, conjugate heat transfer, wall roughness, and so on). In this paper the role of the viscous dissipation in liquids flowing through heated microchannels will be analyzed by using the conventional theory. We will present a correlation between the Brinkman number and the Nusselt number for silicon ⟨100⟩ and ⟨110⟩ microchannels. It will be demonstrated that the fluid is of importance in establishing the exact limit of significance of the viscous dissipation in microchannels; a criterion to analyze the significance of the viscous effects will be presented. The role of the cross-section aspect ratio on the viscous dissipation will be highlighted. The main goal of this work is to demonstrate that the problem of heat transfer enhancement in microdevices cannot be solved by indefinitely reducing the microchannel dimensions because the viscous dissipation effects shall offset the gains of high heat transfer coefficients associated with a reduction in the channel size.