Circular cylinder freely rotating

Freely rotating cylinder. Now let us consider a circular cylinder freely floating in an arbitrary linear shear Stokes flow (Re —i 0). The velocity distribution for such a flow remote from the cylinder is still given by relations (2.7.8). 

In view of the no-slip condition on the surface of the circular cylinder freely floating in a shear flow, this cylinder rotates at the constant angular velocity equal to the rotation flow velocity at infinity. This means that the following boundary conditions for the fluid velocity components must be satisfied on the cylinder surface ... 

Freely rotating cylinder. Now let us consider convective mass transfer to the surface of a circular cylinder freely suspended in an arbitrary linear shear Stokes flow (Re -> 0). In view of the no-slip condition, the cylinder rotates at a constant angular velocity equal to the angular velocity of the flow at infinity. The fluid velocity distribution is described by formulas (2.7.11). The streamline pattern qualitatively differs from that for the case of a fixed cylinder. For 0 0, there are no stagnation points on the surface of the cylinder and there exist two qualitatively different types of flow. For 0 < Ifigl < 1, there are both closed and open streamlines in the flow, the region filled with closed streamlines is adjacent to the surface of the cylinder, and streamlines far from the cylinder are open (Figure 2.11). For Ifl l > 1, all streamlines are open. 

Figure 9-18. Streamlines for a freely rotating circular cylinder in simple, linear shear flow (9-306). Contours 0 to 0.75 in increments of 1/16.

Problem 9-5. Heat Transfer From a Freely Rotating Circular Cylinder in Shear Flow... 

Figure 2.11. Linear shear flow past a freely rotating circular cylinder in the 7Z -plane (the limit streamlines P = Ps are marked bold) (a) simple shear flow ( STg = 1) (b) general case of plane shear flow (0 < n < 1)...

An experimental verification [405] of the fact that the leading term of the asymptotic expansion of the mean Sherwood number for Pe 1 is independent of the Peclet number for a freely rotating circular cylinder in a simple shear flow ( ff = 1) showed good qualitative and quantitative agreement with the theoretical results [132]. The measured mean Sherwood number was 2.65, which is close to the corresponding asymptotic value (4.11.4). 

When all the rotations are possible in the solid state the symmetry increases to hexagonal. This form corresponds to the close packing of spheres or cylinders and the molecule is in a rotational crystalline state, characterized by rigorous order in the arrangement of the center (axes) of the molecules and by disordered azimuthal rotations [118]. If the chain molecules are azimuthally chaotic (they rotate freely around their axes), their average cross sections are circular and, for this reason, they choose hexagonal packing. The ease of rotation of molecules in the crystal depends merely on the molecular shape, as in molecules of an almost spherical shape like methane and ethane derivatives with small substituents, or molecules of a shape close to that of a cylinder (e.g., paraffin-like molecules). 

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