Natural convection, conduction and radiation dimensional analysis

A previously presented novel method of dimensional analysis is used to derive the minimum number of dimensionless groups for problems of combined, and interactive, conduction, convection and radiation. The novelty of the method lies in using unspecified parameters to re-scale the governing equations. These are then defined from the governing equations which results in; generalised governing equations, the definition of the relevant re-scaled variables and the derivation of the equation constants. As a result, most of the dimensionals groups then arise from the specification of the boundary conditions. In this paper, a range of different boundaries are considered which gives rise to a derivation of the scaling groups for complex heat transfer problems in a way that systematically minimises the number of groups. Further, it is often advantageous to combine two or more dimensionless groups and therefore the rules governing theses combinations are also derived and presented.