Dimensionless groups: Buckingham n theorem In heat transfer by forced flow of fluid over a tube surface. the parameters which are physically important in determining the fuid$-$side heat$-$transfer coefficient $($a conductance h$)$ are the characteristic diameter of the pipe D$.$ the fluid velocity u$.$ and viscosity i $($in poise$)$ density p$.$ specific heat at constant pressure C$,($in calories per mole per degroe$).$ and the thermal conductivity of the fluid ki$,($in calories per second per centimeter per degree$).$ The Buckingham r theorem states that the functional relationship between q quantities whose units can be given in terms of $p$ fundamental units can be written as a function of $q-p$ dimensionless groups. The fundamental units in heat transfer are mass $m,$ length $l,$ time $t,$ and temperature $T.$

$($a$)$ Express $h,D,u,,,C_p,$ and $k$ in terms of such units, i$.$e$.,$ variable $=m^a{l}^b{t}^c{T}^d.$

$($b$)$ Four dimensionless groups are commonly formed from these variables: $),Re$