Oblate spheroids transfer

The mechanism of mass transfer to the external flow is essentially the same as for spheres in Chapter 5. Figure 6.8 shows numerically computed streamlines and concentration contours with Sc = 0.7 for axisymmetric flow past an oblate spheroid (E = 0.2) and a prolate spheroid (E = 5) at Re = 100. Local Sherwood numbers are shown for these conditions in Figs. 6.9 and 6.10. Figure 6.9 shows that the minimum transfer rate occurs aft of separation as for a sphere. Transfer rates are highest at the edge of the oblate ellipsoid and at the front stagnation point of the prolate ellipsoid. 

No data are available for heat and mass transfer to or from disks or spheroids in free fall. When there is no secondary motion the correlations given above should apply to oblate spheroids and disks. For larger Re where secondary motion occurs, the equations given below for particles of arbitrary shape in free fall are recommended. 

Sehlin, R. C., Forced-Convection Heat and Mass Transfer at Large Peclet Numbers From Axisymmetric Body in Laminar Flow Prolate and Oblate Spheroids, M.S. Thesis (Chem. Eng.), Carnegie Inst. Thechn., Pittsburgh, 1969. 

A. Strong, G. Schneider, and M. M. Yovanovich, Thermal Constriction Resistance of a Disc with Arbitrary Heat Flux—Finite Difference Solution in Oblate Spheroidal Coordinates, AIAA-74-690, AIAA/ASME1974 Thermophysics and Heat Transfer Conference, Boston, MA, July 15-17,1974. 

The problem of mass transfer from a moving Newtonian fluid to a swarm of prolate and/or oblate stationary spheroidal adsorbing particles under creeping flow conditions is solved using a spheroidal-in-cell model. The flow field through the swarm was obtained by using the spheroid-in-cell model proposed by Dassios et al. [5]. An adsorption - 1st order reaction - desorption scheme is used as boundary condition upon the surface of the spheroid in order to describe the interaction between the diluted mass in the bulk phase and the solid surface. The convective diffusion equation is solved analytically for the case of high Peclet numbers where the adsorption rate is also obtained analytically. For the case of low Pe a non-... 

Problem 9-17. Heat Transfer From an Ellipsoid of Revolution at Pe S> 1. In a classic paper, Payne and Pell. J. Fluid Meek 7, 529(1960)] presented a general solution scheme for axisymmetric creeping-flow problems. Among the specific examples that they considered was the uniform, axisymmetric flow past prolate and oblate ellipsoids of revolution (spheroids). This solution was obtained with prolate and oblate ellipsoidal coordinate systems, respectively. 

External transient conduction from an isothermal convex body into a surrounding space has been solved numerically (Yovanovich et al. [149]) for several axisymmetric bodies circular disks, oblate and prolate spheroids, and cuboids such as square disks, cubes, and tall square cuboids (Fig. 3.10). The sphere has a complete analytical solution [11] that is applicable for all dimensionless times Fovr = all A. The dimensionless instantaneous heat transfer rate is QVa = Q AI(kAQn), where k is the thermal conductivity of the surrounding space, A is the total area of the convex body, and 0O = T0 - T, is the temperature excess of the body relative to the initial temperature of the surrounding space. The analytical solution for the sphere is given by... 

V r, V, z r, V- 6 Tl. V, z Tl, V, z T1,0, V 0 0 0,1 0, oo OQ 1,0 1, OO 1,2 1,2,3 12 ID constant volume condition cylindrical coordinates spherical coordinates elliptical cylinder coordinates bicylinder coordinates oblate and spheroidal coordinates zero thickness limit based on centroid temperature zeroeth order, first order value on the surface and at infinity infinite thickness limit first eigenvalue value at zero Biot number limit first eigenvalue value at infinite Biot number limit solids 1 and 2 surfaces 1 and 2 cuboid side dimensions net radiative transfer one-dimensional conduction... 

Solutions for the transfer coefficients around axisymmetric bodies of revolution (oblate and prolate spheroids and bubbles with spherical cups shapes) in potential flow were also reported (LI8) and related to experiment (Cl a). 

Fe(CN)6] (S = 1/2) and [Mn(CN)e] (S = 1), which are prominent building blocks of magnetic materials (Prussian-blue-type magnets) [49]. Interestingly, from the shift anisotropies, the spin distribution in different directions of the crystal lattice could be distinguished as well (oblate and prolate spheroids at C and N, respectively), indicating that the induction of spin at the C atoms involves polarization of electrons in s-type orbitals parallel to the M-CN axis, while direct spin transfer to the N atoms involves p-type orbitals perpendicular to that axis (see Fig. 25). 

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