CHEMICAL ENGINEERING

306 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 12.13

Obtain the Taylor – Prandtl modification of the Reynolds’ analogy between momentum
and heat transfer and give the corresponding analogy for mass transfer. For a particular
system a mass transfer coefficient of 8. 71 ð 10 ^6 m/s and a heat transfer coefficient of
2730 W/m^2 K were measured for similar flow conditions. Calculate the ratio of the velocity
in the fluid where the laminar sub-layer terminates, to the stream velocity. Molecular
diffusivityD 1. 5 ð 10 ^9 m^2 /s. ViscosityD1mNs/m^2. DensityD1000 kg/m^3 .Thermal
conductivityD 0 .48 W/m K. Specific heat capacityD 4 .0kJ/kgK.

Solution

The Taylor – Prandtl modification to heat and mass transfer is discussed in Section 12.8.3
resulting in the modified Lewis relation:

hDDh/Cp[1C ̨Pr 1 ]/[1C ̨Sc 1 ] (equation 12.121)

In this case: PrDCp/kD 4 ð 103 ð 1 ð 10 ^3 / 0. 48 D 8. 33

and: ScD/DD 1 ð 10 ^3 / 1000 ð 1. 5 ð 10 ^9 D 667

Substituting:

 8. 71 ð 10 ^6 D[2730/ 4000 ð 1000 ][1C ̨ 8. 33  1 ]/[1C ̨ 667  1 ]

0. 01276 D 1 C 7. 33 ̨/ 1 C 666 ̨and ̨D 0. 844

PROBLEM 12.14

Heat and mass transfer are taking place simultaneously to a surface under conditions
where the Reynolds analogy between momentum, heat and mass transfer may be applied.
The mass transfer is of a single component at a high concentration in a binary mixture,
the other component of which undergoes no net transfer. Using the Reynolds analogy,
obtain a relation between the coefficients for heat transfer and for mass transfer.

Solution

The solution to this problem is presented in Sections 12.8.1 and 12.8.2 and the relation
between the coefficients for heat transfer and mass transfer is:

hDCBw/CTCphD (equation 12.112)

PROBLEM 12.15

Derive the Taylor – Prandtl modification of the Reynolds analogy between momentum and
heat transfer.
In a shell and tube type condenser, water flows through the tubes which are 10 m long
and 40 mm diameter. The pressure drop across the tubes is 5.6kN/m^2 and the effects of
entry and exit losses may be neglected. The tube walls are smooth and flow may be taken