We have three length scales: 
, 
and 
are also problem
parameters. Thus any solution, heta transfer or fluid mechanics (i.e. Nu, 
, 
, 
, 
,
) are all function of the above dimensionless parameters. for example
In the above problem we considered only one velocity scale 
and one time scale
.In order problem multiple velocity and time scale may appear.
Example 1. two velocity scales or one velocity scale and one angle of attack.
Example 2: two time scales.