Abstract
Generalized expressions for both the local and the overall mass-transfer from a sphere and a circular cylinder in steady, oscillating, and pulsating flows are derived by using solutions to velocities around the bodies. The integrals included in these expressions being evaluated numerically, the local mass-transfer distribution profiles around the bodies and the overall mass-transfer expressions are given for these cases.
Comparison between local mass-transfer distributions around the bodies in steady and pulsating flows shows that pulsating flow accelerates the mass transfer particularly on the rear side of the body, where the mass transfer under steady flow is small because of the dead-water region. The approximate expressions of overall mass-transfer under pulsating flow are Sh=2+[(0.654)1.85+(0.648z1/3)1.85]1/1.85Sc1/3Re1/2p for a sphere and Sh=[(0.615)1.74+(0.728z1/3)1.74]1/1.74Sc1/3Re1/2p for a circular cylinder, where Sh=2rokf/D, z=(aω/U∞)3/2(a/ro)1/2, Sc=ν/D and Rep=2roU∞ν (a: amplitude, D: diffusivity, kf: mass-transfer coefficient, ro: radius, U∞: free stream velocity, v: kinematic viscosity, ω: angular frequency). These expressions coincide with ones under steady flow, i.e.,
Sh=2+0.654Sc1/3Re1/2p (sphere), Sh=0.615Sc1/3Re1/2p (circular cylinder) and ones under oscillating flow, i.e., Sh=2+0.917Sc1/3(roaω/ν)1/2(a/ro)1/6 (sphere), Sh=1.03Sc1/3(roaω/ν)1/2(a/ro)1/6 (circular cylinder), according as z→0 and z→∞, respectively. These results are compared with analytical and experimental ones reported previously, and shown to be rather satisfactory.
