Environmental Engineering Reference
In-Depth Information
Nu
RePr
Sh
ReSc
St
=
St
=
Pe
=
RePr
Pe
=
ReSc
(dimensionless numbers are: Nu
=
Nusselt; Pr
=
Prandlt; St
=
Stanton; Re
=
Reynolds;
Pe
=
Peclet; Sh
=
Sherwood; Sc
=
Schmidt).
Example
In forced convection around a sphere of diameter D , the correlation for the heat transfer
coefficient associated with heat transfer between the bulk fluid and the sphere surface is:
Re 1/2 Pr 1/3
Nu
=
2
+
.
For the same physical situation, the mass transfer correlation would be:
Re 1/2 Sc 1/3
Sh
=
2
+
.
There are two important points to mention at this time.
1 The characteristic length that is used must be given with the correlation. It can be a
linear length, a radius, a diameter, etc. So, be certain.
2 The dimensions associated with the mass transfer coefficient can vary depending on the
flux equation used to define k . So, again, be certain, since the dimensions can change
the functional form of the correlation and you want to make sure that the k you calculate
is the one that you need.
B.2
Methodology for selecting the proper correlation for a mass
transfer coefficient
1 What is the exact nature of the fluid flow? As an example, take a hollow tube (pipe) as
the solid surface. Is the flow inside or outside the tube? Is the tube horizontal or vertical?
Is there just one tube or are there several? If there are several, what is the pattern of their
arrangement? You can also have fluid-fluid interactions (gas-liquid, for example).
2 For dilute binary mixtures, use the fluid properties of the concentrated component. This
is reasonable since the concentration of the dilute component will have a negligible
effect on the physical properties of the fluid. For concentrated solution, you will need
to use averaging rules for that property.
3 Calculate the Reynolds number ( Re ). This value will indicate if the flow is laminar or
turbulent. Be careful; the transition value of Re depends on the flow configuration.
4 Determine the type of coefficient desired. Do you want a local value (at a point on the
solid surface) or an average value over a length?
You can now check various correlations to find the one that matches your needs. Most
heat transfer or mass transfer texts contain additional correlations.
Search WWH ::




Custom Search