Tham khảo tài liệu 'the mems handbook introduction & fundamentals (2nd ed) - m. gad el hak part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 9-6 MEMS Introduction and Fundamentals 1 ----N-S No-slip BC ----------LB N-S Beskok slip ----AB Beskok slip o Beskok Karniadakis 1999 0 0 1 2 0 1 2 u U1 FIGURE Comparison of velocity profiles at various streamwise locations of the microchannel Knin Knout and Pin Pout N-S Navier-Stokes LB Lattice-Boltzmann AB Augmented Burnett. In Equations and a is the accommodation coefficient. a 1 for a noncatalytic wall. Agarwal 2005 has recently obtained an exact analytical solution for velocity along the channel as follows u iJl V 2y 2 MKnHa2 ỈI dx B0U Ha Ha 2sinh I 2 I 2a KHacosh I 2 I . cosh Hay 1 1 a2K2Ha2 sinh Ha 2aKHacosh Ha The solution given by Equation is valid for both first-order Maxwell-Smoluchowki 1879 and second-order Beskok 1999 slip boundary conditions. In Equation K is the local Knudsen number Kn x and Kn is the Knudsen number at the outlet. The solution as written has been obtained with first-order boundary condition however if K is replaced by K 1 bK it becomes valid for second-order boundary condition . In the absence of magnetic field the solution given by Equation is the same as given in Beskok and Karniadakis 1999 . We now compute the analytical solution give by equation for M Mach number at outlet Knout Knudsen number at outlet Knin Knudsen number at inlet and Pin Pout inlet pres-sure outlet pressure . Figure shows the velocity profiles at three streamwise locations x and computed using the LBGK method and their comparison with profiles computed using the Navier-Stokes N-S equations with and without slip augmented Burnett AB equations with slip and 2006 by Taylor Francis Group LLC Lattice Boltzmann Simulations of Slip Flow in Microchannels 9-7 Comparison of mass flow rates along the microchannel. Comparison of pressure distributions along the centerline of the microchannel. Comparison of streamwise velocity distributions along .
