Viscous dissipation effects on slip flow heat transfer in rhombic microchannels

Abstract

This study aimed to numerically investigate the viscous dissipation effect on forced convection in rhombic microchannels for gases in a slip flow regime. The numerical analysis was carried out by assuming a 2D steady-state flow. The solution of governing equations was obtained by adopting the finite element method and assuming that the fluid is Newtonian, with constant thermophysical properties, and in a fully developed laminar flow regime. The solution of the momentum equation is obtained by considering a first-order boundary condition, while the solution of the energy balance equation is obtained by assuming a constant wall heat flux (H2 boundary condition) and taking into account the wall temperature jump. The validation of the numerical model was carried out using the data available in the scientific literature. The numerical outcomes obtained for several values of the acute angle of the rhombus, the Knudsen number (i.e., rarefaction effects), and the Brinkman number (i.e., viscous dissipation effects) reveal that viscous forces play an opposite role with respect to rarefaction and significantly affect the convective heat transfer coefficient, especially for low Knudsen numbers and for high values of the acute angle. In particular, it was observed that Nu is significantly affected by the Brinkman number for acute angles higher than 50°.

Keywords

• Micro flow
• Rarefaction effects
• Viscous dissipation
• Noncircular cross-sections