Heat transfer and friction factor correlations for slip gaseous fluid flow in confined porous medium with pore-scale LBM modelling

Abstract

The gaseous fluid flow and heat transfer with the consideration of rarefaction effects are important at micro/nano-scales. The formulation of accurate predictive models is beneficial to optimize the heat transfer and friction across the porous domain, in micro- and nano-devices. In this work, the lattice Boltzmann method (LBM) with multiple-relaxation-time (MRT), which offers a natural and robust way to simulate the slip gaseous fluid flow and heat transfer, was applied to the confined porous medium at a pore-scale level. An efficient boundary scheme was utilized at the walls of porous media to consider the velocity slip and temperature jump effect. A two-dimensional porous domain composed of different types of micro obstacles (circle, ellipse and diamond) was established for the pore-scale simulations. Nusselt number (Nu) and friction factor (Cf) were obtained and analyzed across the obstacles with varying Knudsen number (0.0 ≤ Kn ≤ 0.1), Reynolds number (1 ≤ Re ≤ 10) and porosity (0.4 ≤ ε ≤ 0.8). With increasing Re number, Nu number shows an increasing trend for all obstacles, however, for increasing Kn number, Nu number decreases accordingly. Whereas, the friction factor Cf shows a decreasing trend for both increasing Kn and Re numbers. Based on the obtained results, the new predictive correlations for Nusselt number and friction factor were proposed, which will be valuable to understand the slip gaseous flow characteristic in confined porous space.