The present study is concerned with the flow behavior of the rarefied gas over a rectangular square cylinder. Attention has been focused on the transition regime between the continuous flow (at low Knudsen number) and the molecular flow (at high Knudsen number). The direct simulation Monte Carlo method (DSMC) is employed for predicting the distributions of density, velocity, and temperature for the external cross-flow. Meanwhile the pressure, skin friction, and net heat transfer coefficients on the surfaces of the cylinder are also evaluated. The length (l) and width (h) of the cross-section of the cylinder are both fixed at 0.06 m. The Mach number (Ma) ranges from 0.85 to 8, and the Knudsen number (Kn) is in the range 0.01⩽Kn⩽1.0. Results for various parameter combinations are presented. For some special cases, the numerical predictions are compared with existing information, and close agreement has been found. [S0098-2202(00)01404-8]

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