Conclusions The foregoing general analytical solutions to the linearized cooler-condenser problems have been shown to be useful for designing condensers and analyzing their performance. Equations for calculating vapor-gas mixture and coolant properties as a function of condenser length were given. From these, equations for predicting local heat transfer, core stream and surface condensation rates, and overall thermal loads were developed. Three vapor-noncondensable gas mixtures, typical of those which might be encountered in condenser design problems, were analyzed, and results verify the general applicability of the solutions. The Lewis number has been shown to be a n important criterion of the relative rates of sensible heat and mass transfer in the process. Nomenclature A = condenser area, ft2 a = constant, a t m b = constant, atm/OF C = total rate of condensation, lb mol/hr C, = heat capacity of mixture, Btu/lb mol-”F c, = heat capacity of coolant, Utu/lb-”F F = rate of fog formation, lb mol/hr G = mixture flow rate, lb mol/hr h, = gas-phase heat transfer coefficient, Btu/hr-ft2-”F ho’ = combined heat transfer coefficient, Btu/hr-ftZ-OF i = latent heat of vaporization, Btu/lb mol ,i = factor 12, = mass transfer coefficient, lb mol/hr-ft2-atm L = condenser length, ft Jf = molecular weight, Ib/lb mol N = gas flow rate, lb mol/hr P = pressure, a t m Q = thermal load, Btu/hr p = heat transfer rate, Btu/hr-ft2
T
=
B
= vapor flow rate, lb mol/hr
w
=
temperature, OF coolant flow rate, lb/hr
e ~- hckermann correction factor 1 - e-c
Le Pr Re Sc
= = = =
Lewis number Prandtl number Reynoldsnumber Schmidt number
SUBSCRIPTS B.11 = logarithmic mean g
s
=
= t = w =
vapor interface total coolant
literature Cited Ackermami, G., Ver Deutsch Ing. Forschungsh., 382, 1 (1937). Amundson, N. R .,“hlatheniatical hlethods in Chemical Engineering,” pp 111-127, Prentice-Hall, Englewood Cliffs, N.J., 1966. Colburn, A. P., Drew, T. R., Trans. Amer. Inst. Chem. Engrs., 33, 197 (1937). Colburn, A. P., Edison, A. G., I n d . Eng. Chem., 33, 437 (1941). Colburn, A. P., Hougen, 0. A., ibzd., 26, 1178 (1934). Coughanowr, D. I
