Three-dimensional simulation of slip-flow and heat transfer in a microchannel using the lattice Boltzmann method

Abstract

In micro-and nano-flows, since the molecular mean free path is comparable to the system's characteristic length, the effect of rarefaction should be considered. In this category of flows, the continuum assumption is no longer valid; therefore, heat transfer, velocity profile and pressure drop markedly and depart from those which are common to macro-flows. Rarefaction may occur in various applications, such as in zero gravity flights and vacuum devices. This phenomenon can occur at the wall surfaces when the Mach number is sufficiently small, which is the case of interest in this study. In these conditions, at the solid-fluid interfaces, the fluid has a slip velocity and a temperature jump is also present. Three-dimensional, thermally developing incompressible laminar flows in a square microchannel with constant temperature walls are studied numerically using the lattice Boltzmann method. The effect of rarefaction on the velocity and temperature distributions and on the Nusselt number is analysed. The LBM predictions are compared with those obtained using the Navier-Stokes equations with the slip condition for the same configuration. The results indicate that an increase of the slip velocity yields an increasing Nusselt number, whereas an increase of the temperature jump has the opposite effect on the Nusselt number values; therefore, the combined result of these two competing effects may yield an increase or decrease on the Nusselt number.

Lattice Boltzmann modeling and simulation of velocity and concentration slip effects on the catalytic reaction rate of strongly nonequimolar reactions in microflows

“…The diffusive boundary condition is the only boundary condition that intrinsically has the potential to estimate slip velocity when the Knudsen number is relatively high. The validity of the diffusive boundary condition for a wide range of Knudsen numbers (up to 2.0) has been studied in several past works, using the first and second velocity derivatives at the solid wall [14,22,24,25]. These studies have mostly focused on the development of models with the capacity to predict slip velocities for a particular range of Knudsen numbers with a well-resolved grid.…”

“…Therefore, the results show that the slip velocity model with diffusive boundary condition can be utilized for very narrow and finely discretized pores and channels leading to more efficient and inexpensive simulations. For higher Knudsen numbers (Kn > 0.2), the Knudsen layer should be taken into account in the slip velocity model by incorporating the second derivative of velocity at the solid wall as discussed in [24][25][26]65]. Finally, the results discussed in this section are generally independent of the relaxation time.…”

“…Therein, correlations are employed involving first and second-order velocity gradients at the wall to impose a slip velocity at the solid boundary. The Maxwell model is generally consistent with the gas kinetic theory, hence it has been extensively developed for different applications and different slip flow regimes [22][23][24][25][26]. Lastly, there have been attempts to include more grids, i.e.…”

Thermal performance investigation of a mini natural circulation loop for solar PV panel or electronic cooling simulated by lattice Boltzmann method

“…The double distribution function approach has been applied successfully to diverse thermal fluid dynamics problems, e.g. natural circulation in cavities or heat transfer in a microchannel [19]. The two-way coupling between the hydraulic field and the thermal field was achieved by considering a forcing term F i proportional to the local temperature representing the buoyancy force (Boussinesq hypothesis).…”

Thermal Lattice Boltzmann Model for Nonisothermal Gas Flow in a Two-Dimensional Microchannel

“…In this model, the governing equations of mass and momentum conservation are satisfied at each lattice nodes. e thermal lattice Boltzmann method is used to simulate two-and three-dimensional microchannel flows by using velocity slip and temperature jump boundary conditions [24,25] and has been studied in several papers [8][9][10][11][27][28][29][30]. In this paper, the TLBM and FDM are used to simulate micro-Poiseuille flow, in the slip regime, which is usually encountered in the MEMS devices [31].…”