Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Abstract

Gas flow and heat transfer in confined geometries at micro-and nanoscales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. Nonequilibrium effects increase with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier–Stokes–Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5≤Π≤2.5), tangential momentum accommodation coefficients, and Knudsen numbers (0.05≤Kn≤12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and the applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained.

Numerical Study of Gas Flow in Super Nanoporous Materials Using the Direct Simulation Monte-Carlo Method

“…All the solid walls were assumed to be fully diffuse, and heat transfer to the solid porous structure was ignored [ 51 , 52 ]. Detail of the present DSMC model [ 3 , 53 ] and the validity of the results are explained thoroughly in our previous works [ 3 , 12 , 13 , 14 , 19 , 54 ].…”

“…The accuracy of the present DSMC model is also assessed in our previous works by comparing the numerical predictions obtained from the model with experimental and theoretical data [ 3 , 12 , 13 , 14 , 19 , 54 ].…”

“…The enhancement of the molecular mean free path due to increasing the wall heat flux is more pronounced at high Knudsen numbers. An increase in the bulk gas temperature, resulting from increasing the wall heat flux, also leads to a decrease in the effective gas viscosity [ 13 , 14 ]. An increase in the molecular mean free path, while the geometry of the porous structure is unchanged, leads to an increase in the Knudsen number, enhancing the non-equilibrium effects such as gas slippage and temperature jump at the solid walls.…”

“…At standard pressure and temperature conditions, gas flow in microporous and mesoporous materials differs considerably from those in macroporous material with pore sizes larger than about [ 6 , 7 , 8 , 9 , 10 ]. Internal pore spacing in microporous and mesoporous materials is comparable to the mean free path of gas molecules [ 11 ], enhancing nonequilibrium effects due to the reduction in the rate of intermolecular collisions and collisions between the gas molecules and solid walls [ 12 , 13 , 14 ]. The Knudsen number (Kn) is a dimensionless quantity that indicates deviation from the equilibrium condition and reads as the ratio of the molecular mean free path to a characteristic length scale (i.e., ).…”

Fluid flow and heat transfer in microchannel heat sinks: Modelling review and recent progress

“…Their results verified the ability of DSMC to solve microporous media, and concluded that this method could effectively simulate micro-porous media with porosity of 40%. Ebrahimi et al [94] used the DSMC method to predict the flow and heat transfer characteristics of pressure-driven nitrogen in divergent microchannels, and analyzed the Knudsen number from slip to free molecular rarefaction regimes, as well as studied the effects of microchannel divergence angle, inlet and outlet pressure ratio and sparsity on the thermal field and flow field. Their results found that the effect of the heat flux gradient on the direction of net heat flux increases with the increase of divergence angle.…”