Theorem

The first step to solve the fluid and heat transfer problem is to find out how many parameters are involved. Let n variables having a general relation as

If the variables may be described with m number of fundamental dimensional units e.g. length, l, time, t, temperature, K, and mass, m, then these variables can be grouped into m-n dimensionless terms

Example :

Fundamental quantity L U k h

length l 1 -3 -1 1 2 1 0 0

mass m 0 1 1 0 0 1 1 0

time t 0 0 -1 -1 -2 -3 -3 0

degree K 0 0 0 0 -1 -1 -1 1

There are 4 fundamental dimensions, m=4 and 8 variables n=8, there will be terms

for

solving the set of algebraic equations yeilds , , and which gives

Nusselt number Similarly

then

example Laminar Boundary layer (small Ec)