The particular results obtained for the laminar boundary layer over a
flat plate at zero incidence may be written

(1) |

and

(2) |

These results, in this generalised form, are found to apply to a very wide range of heat and mass transfer situations, for forced convection transfer to or from surfaces curved or flat, parallel or inclined, to turbulent or laminar flows, where

The following examples are given for heat transfer but would apply equally well to mass transfer

- 1.
- For laminar flow through long smooth tubes, having diameter
*d*as the characteristic dimension,*h*far from the entrance, is found semi-empirically to be given by:

- 2.
- For turbulent flow through long smooth tubes, having diameter
*d*as the characteristic dimension,*h*far from the entrance, is found empirically to be given by:

- 3.
- For flow through packed beds of spheres, diameter
*d*, by experiment

- 4.
- For turbulent flow over a flat plate

Dividing equation (1) by *Re*_{x}*Pr*

and

ie

the Chilton-Colburn j-factor for heat transfer which is a function of

- a dimensionless heat transfer coefficient, a function only of

Dividing equation (2) by *Re*_{x}*Sc*

and

ie

the Chilton-Colburn j-factor for mass transfer which is a function of

- a dimensionless mass transfer coefficient, a function only of

The exact solution for the boundary layer over flat plates gave

and

Thus for the laminar boundary layer over a flat plate

This is the complete form of the Chilton-Colburn analogy, relating all
three forms of transport in one expression. The equation is exact for
laminar boundary layers over flat plates and is satisfactory for systems
of other geometries provided no form drag is present. For systems with
form drag it has been found that

ie

This equation, relating convective heat and mass transfer, is valid for gases and liquids within the ranges, 0.6 <

David Balmer Last modified: Wed Dec 2 16:19:47 GMT