# Interdisciplinary Applied Mathematics

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FIGURE 6.17. The magnitude of velocity slip distribution along the periphery of a circular cylinder at Kn = 0.015. Triangles, Re = 1; 0 degrees corresponds to the rear stagnation point. Circles, Re = 10; 0 degrees corresponds to the front stagnation point.

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FIGURE 6.18. Distribution of tangential stresses along the upper and lower surfaces of circular cylinder at Re = 10 and Kn = 0 (triangles, no-slip case), Kn = 0.015 (circles), Kn = 0.015 and slip coefficient b =10 (squares). Solid and blank symbols show upper and lower surfaces, respectively. Shear stresses are zero at about 0 = 147°, where the flow separates.

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FIGURE 6.19. Distribution of viscous normal stresses along the cylinder periphery at Re = 10 and Kn = 0 (triangles, no-slip case), Kn = 0.015 (circles), and Kn = 0.015 and slip coefficient b = 10 (squares).

6.18 for    the    case of Re = 10.    From this    plot    it    is    evident    that    separation

occurs at an angle approximately 147° from the front stagnation point.

A simulation corresponding to the high-order slip boundary condition is also included (squares). The high-order expansion coefficient b is taken to be a constant (b = 10.0) for convenience. For the range of Knudsen number (0 < Kn < 0.015) investigated, no difference in the separation angle is observed between the slip and no-slip flow cases. For comparison of shear stress variations, we also plot in Figure 6.18 the shear stresses corresponding to the no-slip case. As expected, a reduction in skin friction is obtained especially in the front part of the cylinder where the flow accelerates.

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