NSh or N N~ = 2 + 0.4 N~2 r~ ( Ns, or Npr) 0.42 (4) 450 < N R~ < 10,000, N s , or Npr < 250 NSh or NN= = 2 + 0.27 N R ,~.~~ ( N s c or N p r ) ' I 3 450 < N R~ < 10,000, 250 < Nsc (5) NSh = 2 + 0.175 N R~~,~~ NSC',~' (6) Table 1 shows the average absolute deviation and the standard deviation between experimental transfer coefficients and coefficients calculated from the equations.Hammerton and Gamer (9) obtained data for carbon dioxide bubbles in glycerine. Two of these data points could be expected to represent rigid sphere mass transfer. (3) shows an average absolute deviation of 27% for these data which represent a Schmidt number of 1.78 x lo7.
Extrapolation of Equation
SUMMARYSmoothed heat and mass transfer data for rigid spheres have been plotted to investigate the exponents of the Reynolds and Schmidt numbers for Equation (1). The results indicate that the exponent for the Schmidt number increases with the Reynolds number and that the exponent for the Reynolds number indicates an eddy contribution from the wake at Reynolds numbers greater than 450. NOTATION C p = specific heat, B.t.u./lb.m "F. Dp = diameter of rigid sphere, ft. D = diffusivity, sq.ft./sec. h = heat transfer coefficient, B.t.u./sec./sq.ft. "F. k = thermal conductivity, B.t.u./sec./sq.ft. "F./ft. k, = mass transfer coefficient, ft./sec. NNu = h D,/k, Nusselt number N p r = C, p/k, Prandtl number NRe = Dp V / V , Reynolds number N~~ = v / D , Schmidt number N S h = k, D p / D , Sherwood number V = slip velocity, ft./sec. p = viscosity, lb.m/ft./sec. v = kinematic viscosity, sq.ft./sec.