Interdisciplinary Applied Mathematics

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The results we present in the next few figures are for a microchannel with aspect ratio (L/h = 20) and inlet to exit pressure ratio П. The Knudsen number at the channel outlet is 0.20. The discretization with the p,Flow program involves ten elements in the flow direction and two elements in the cross-flow direction, employing sixth-order polynomial expansions per direction in each element. Convergence is verified by increasing the order of the polynomial expansions while keeping the number of spectral elements fixed.    In    addition,    we monitor    the    residuals of    the    global    conservation    of

mass and momentum. The results presented in these runs conserve mass and momentum with 0.01% error. The DSMC results are performed for the case П = 2.28 with 24,000 cells, of which 600 cells are in the flow direction and 40 across the channel; a total of 480,000 molecules are simulated. The results are sampled (time-averaged) for 1.0 x 105 time steps. Convergence is also verified by monitoring mass balance; maximum errors are less than 1%.

Diffuse reflection (av = 1.0) is assumed for the interaction of gas molecules with the channel walls. The value of the accommodation coefficient av is an important factor, since the slip amount is significantly affected by small variations in av due to the factor (2 — av)/av. For example, av = 0.9 (compared to unity) results in a 22% increase in the slip amount. The DSMC simulations are performed for a nominal value of av = 1.0. To investigate the effective value of av in the simulation we record the values of the tangential momentum of impinging (т;) and reflected (тг) gas molecules at every time step. Based on these values and the tangential momentum of gas corresponding to that    of    the    wall    tw,    we    compute    av    =    (т; — тг)/(т;    — tw ).

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