CHEMICAL ENGINEERING

MOMENTUM, HEAT AND MASS TRANSFER 305

both heat and mass transfer are taking place between the gas stream and the liquid film.
The film heat transfer coefficient is found to be 100 W/m^2 K. Using a pipe friction chart
and assuming the tubes to behave as smooth surfaces, calculate:

(a) the film mass transfer coefficient, and

(b) the gas velocity at the interface between the laminar sub-layer and the turbulent zone

of the gas. Specific heat of airD 1 .0 kJ/kg K. Viscosity of airD 0 .02 mN s/m^2.

Diffusivity of carbon disulphide vapour in airD 1. 1 ð 10 ^5 m^2 /s. Thermal conduc-

tivity of airD 0 .024 W/m K.

Solution

The Taylor – Prandtl modification of the Reynolds analogy for heat transfer and mass
transfer is discussed in Section 12.8.3 and the relevant equations are:

For heat transfer: R/u^2 Dh/Cpus 1 C ̨Pr 1 D# (equation 12.119)

or: h/CpusD#/ 1 C ̨Pr 1  (i)

For mass transfer: R/u^2 DhD/us 1 C ̨Sc 1 D# (equation 12.120)

or: hD/usD#/ 1 C ̨Sc 1  (ii)

Taking the molecular mass of air as 29 kg/kmol and atmospheric temperature as 293 K,
the density,D 29 / 22. 4  273 / 293 D 1 .206 kg/m^3.

∴ ReDdu/D 50 ð 10 ^3 ð 38 ð 1. 206 / 0. 02 ð 10 ^3 D 114 , 570

and from Fig. 3.7:#DR/u^2 D 0 .0021.

From Table 1.3, the Prandtl number,PrDCp/k

D 1. 0 ð 103 ð 0. 02 ð 10 ^3 / 0. 024 D 0. 833

From Table 1.3, the Schmidt number,ScD/D

D 0. 02 ð 10 ^3 / 1. 206 ð 1. 1 ð 10 ^5 

D 1. 508

Substituting in equation (i):

 100 / 1. 0 ð 103 ð 1. 206 ð 38 D 0. 0021 / 1 C ̨ 0. 833  1 

∴ 0. 00218 D 0. 0021 / 1  0. 167 ̨and ̨D 0. 22

Substituting in equation (ii):

hD/ 38 D 0. 0021 / 1 C 0. 22  1. 508  1 D 0 .00189 andhDD 0 .072 m/s

The gas velocity at the interface of the laminar sub-layer and the turbulent zone,ub
may also be estimated from:

ub/uD 2. 32 Re^0.^125 (equation 12.60)

or: ubD 38 ð 2. 32  114 , 570 ^0.^125 D 20 .6m/s