Compatibility and mutual interaction among the dimensionless groups present in the Navier-Stokes and energy differential equations

A method is proposed for obtaining a compatibility relationship among the Prandtl, Reynolds, Grashof and Eckert numbers, present in the transport differential equations for heat and momentum. This method enables one to calculate consistent multipliers for all terms in the aforesaid equations without reference to any physical system. The analysis reveals that natural convection and viscous dissipation cannot simultaneously affect solutions to transport equations with an equal and high intensity.