When implementing the Buckingham PI theorem, it is common to use basis dimensions such as [MASS, LENGTH, TIME], where each is a base SI unit (kilogram, meter, second).
I am attempting a dimensional analysis of a heat transfer system which is represented by basis dimensions [MASS, LENGTH, TIME, TEMPERATURE]. However, I have no need to directly access [TIME], and eliminating it would be beneficial; I have a small number of physical dimensions.
Is it valid to utilize the basis dimensions [POWER, LENGTH, TEMPERATURE] for my analysis, where [POWER] in (watts) can be expressed as LENGTH^2 * MASS * TIME^-3 in the [MASS, LENGTH, TIME, TEMPERATURE] system? My concern is that [POWER] can be expressed in part by [LENGTH], which is also a dimension in my [POWER, LENGTH, TEMPERATURE] system; will this double-dipping on the units interfere with the results?