Convection dimensional analysis

A modification of the method of inspectional analysis is presented for convective heat transfer applications. Inspectional analysis is used to derive the appropriate non-dimensional groups by non-dimensionalising the governing equations. In the past, this was always achieved by the introduction of boundary conditions into the governing equations and, consequently, it was never clear whether the groups were derived from the equations or the boundary conditions. In the new method presented here, the governing equations are used to derive the minimum number of groups without reference to boundary conditions and to define the non-dimensional dependant and independent variables. These variables are then used to define boundary and initial conditions which in turn generate boundary condition specific groups. The sum of the two groups give the total number of non-dimensional groups. By this means, the method is put on a clearer and more rational footing. Examples are presented for free and forced flows, for a wide range of boundary conditions. These show, for the first time, both the scaling of common convective problems and mathematical proof of the derivation of sets of well-known dimensional groups.