The fundamental dimensionless groups for air-to-air energy wheels that transfer both sensible heat and water vapor are derived from the governing non-linear and coupled heat and moisture transfer equations. These dimensionless groups for heat and moisture transfer are found to be functions of the operating temperature and humidity of the energy wheel. Unlike heat exchangers that transfer only sensible heat, the effectiveness of energy wheels is a function of the operating temperature and humidity as has been observed by several energy wheel manufacturers and researchers. The physical meaning of the dimensionless groups and the importance of the operating condition factor (H*) are explained. The dimensionless groups are used in Part II to develop effectiveness correlations for energy wheels.