Page 85 - Modelling in Transport Phenomena A Conceptual Approach

66 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

4.1 REFEmNCE TEMPERATURE AND
CONCENTRATION

The evaluation of the dimensionless numbers that appear in the correlation re-
quires the physical properties of the fluid to be known or estimated. The physical
properties, such as density and viscosity, depend on temperature and/or concen-
tration. Temperature and concentration, on the other hand, vary as a function of
position. Two commonly used reference temperatures and concentrations are the
bulk temperature or concentration and the film temperature or concentration.

4.1.1 Bulk Temperature and Concentration

For flow inside pipes, the bulk temperature or concentration at a particular location
in the pipe is the average temperature or concentration if the fluid were thoroughly
mixed, sometimes called the mixing-cup temperature or concentration. The bulk
temperature and the bulk concentration are denoted by Tb and Cb, respectively,
and are defined by

(4.1-1)

and

(4.1-2)

where v, is the component of velocity in the direction of mean %ow.
For the case of flow past bodies immersed in an infinite fluid, the bulk temper-
ature and bulk concentration become the free stream temperature and free stream
concentration, respectively, i.e.,

Ta = T, For flow over submerged objects
cb = cm (4.1-3)

4.1.2 Film Temperature and Concentration

The film temperature, Tf, and the film concentration, cf, are defined as the arith-
metic average of the bulk and surface values, i.e.,

(4.1-4)