Potential flow of a second‐order fluid over a tri‐axial ellipsoid

Abstract

The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

Perturbation of a Temperature Field by an Inhomogeneity

“…Suppose that, after the inhomogeneity is introduced, the temperatures in regions 1 and 2 are T (1) and T (2) , respectively. Then, T (1) = T ∞ + T * , where T * is the perturbation of the external field due to the introduction of the inhomogeneity.…”

“…Let the space external to the body be referred to as region 1 while the space occupied by the body is region 2 (see Figure 1). In what follows, the corresponding subscripts 1 and 2 on material constants as well as superscripts (1) and (2) on field quantities shall refer to these two regions.…”

Characterization of azimuthal and radial velocity fields induced by rotors in flows with a low Reynolds number

“…Moreover, for axisymmetric rotations, simple symmetry arguments suggest that such a radial flow can not occur. In addition, theoretical works [10][11][12] on non-axisymmmetric rotations appear to be restricted to ellipsoidal bodies and prove to be quite challenging from a mathematical point of view. The work of Camassa et al [10], for instance, treats the problem of an ellipsoid sweeping out a double cone in Stokes flow.…”